Buoyancy-Driven Two Phase Flow and Boiling Heat Transfer...

Buoyancy-Driven Two Phase Flow and Boiling Heat Transfer in Narrow Vertical Channels

A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL

OF THE UNIVERSITY OF MINNESOTA BY

Karl John Larson Geisler

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Dr. Avram Bar-Cohen, Ph.D., Adviser

February 2007

© Karl John Larson Geisler 2007 SOME RIGHTS RESERVED This work is licensed under the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0

License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ or send a

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i

ACKNOWLEDGEMENTS

First and foremost, I cannot begin to thank my advisor, Dr. Avram Bar-Cohen, for the

many years of support and guidance. I have been very fortunate to have had the

opportunity to work so closely with an advisor that has so much to offer and is willing to

share it so freely.

I would like to thank the members of my Ph.D. examining committee: Professors

Terrence W. Simon, Richard W. Goldstein, and Gregory T. Cibuzar. Your diligent review

and critique of my research is much appreciated.

The work on which this thesis is based would not have been possible without the

excellent support staff and facilities available in the Mechanical Engineering Department.

I would like to thank Bob Hain and all who have worked on the MEnet staff over the

years for providing computing infrastructure and support that enhanced every aspect of

this research. The experimental apparatuses used in this research owe their physical

realization to the expert supervision and advice of Mel Chapin in the ME student shop. I

also owe a great deal to Bob Nelson, Peter Zimmermann, Professor James Ramsey and

Barb Pucel for making special facility arrangements for me during the most critical phase

of the experimental effort. Kevin Roberts provided much advice and assistance related to

fabricating silicon parts in the Microtechnology Laboratory.

Many thanks go to Loctite Corporation and Saint-Gobain Performance Plastics for their

generous donation of product samples. I would also like to thank 3M for supplying

Fluorinert™ liquid and technical support. The numerical components of the research

ii

would not have been possible without the generous academic support of Fluent Inc. and

ANSYS Inc.

To my graduate school colleagues—including, but not limited to Alex Gladkov, Steve

Olson, Gary Solbrekken, Madhu Iyengar, Sridhar Narasimhan, Mehmet Arik, Suzana

Prstic, Fadi Ben-Achour, Kyoung-Joon Kim, Jivtesh Garg, K.C. Coxe, Kazuaki Yazawa,

Rich Kaszeta, Abhay Watwe, and Vadim Gektin—thank you for making our time

together interesting, educational, challenging, fun, and, most of all, memorable.

I must thank my parents Jake and Carol, my sister (Dr. Lisa) and all of the members of

my extended families for all of the love and support they have given me throughout my

entire academic career. My successes are a reflection of your faith in my potential.

Finally, to my wife Amy, there is no limit to my appreciation for your support and

sacrifice over this long and arduous decade. True love indeed.

iii

DEDICATION

This dissertation is dedicated to my son Samuel. Follow your passion.

iv

ABSTRACT

In order to accommodate anticipated 500–1000 kW/m2 heat fluxes of microelectronic

devices with passive immersion cooling, significant enhancement of the pool boiling

critical heat flux (CHF) limit of candidate dielectric liquids is required. However,

emerging 3-D packaging technologies may present the greatest near-term thermal

management challenges. In response, the present study seeks to elucidate the effects of

confinement on buoyancy-driven two phase flow and boiling heat transfer to assist in the

systematic exploitation of device geometry and extended surfaces for enhanced liquid

cooling of 2- and 3-D microelectronic devices.

Microelectronics-scale parallel plate channel boiling experiments were conducted for

20 mm long silicon and aluminum heaters. Channel spacing was varied to provide

channel aspect ratios as high as 67, for symmetrically and asymmetrically heated

channels. Deteriorated CHF performance is observed with decreasing channel spacing.

This behavior is accurately predicted by extending a correlation available in the literature.

Silicon heater channels show significant low-flux enhancement at Bond numbers less

than 1, and an enhancement mechanism based on vapor and nucleation site interaction

effects is proposed.

A methodology for the optimization of immersion cooled 3-D stacked dice is developed,

and an equation relating optimum spacing to die length, thickness, and fluid properties is

derived. Optimum geometries are found to be able to dissipate hundreds of megawatts per

cubic meter. Parametric effects are explored, and modifications to the governing

v

volumetric heat dissipation optimization equation to address localized device hot spots

and other unique phenomena are also addressed.

Finally, a numerical methodology is developed to efficiently explore parametric effects

on longitudinal, rectangular plate fin heat sink boiling performance—including, perhaps

for the first time, the explicit dependence of fin spacing on boiling heat transfer and CHF.

Silicon heat sink performance is observed to continually improve down to the smallest fin

spacing investigated, to nearly five times the CHF limit of the unfinned surface. The

higher temperature superheats of the polished silicon surfaces and confinement-driven

low flux enhancement yield greatly increased heat dissipation. Device heat fluxes of

1000 kW/m2 may be dissipated by employing higher conductivity heat sink materials or

more complex geometries.

vi

CONTENTS

Acknowledgements .............................................................................................................. i

Dedication .......................................................................................................................... iii

Abstract .............................................................................................................................. iv

Contents.............................................................................................................................. vi

List of Tables.....................................................................................................................xii

List of Figures ................................................................................................................... xv

Nomenclature .................................................................................................................. xxv

Chapter 1: Introduction ................................................................................................... 1

1.1 Electronic Cooling Requirements ............................................................................ 1

1.2 Immersion Cooling of Electronics ........................................................................... 4

1.3 Boiling Heat Transfer............................................................................................... 6

1.3.1 Single Phase Natural Convection and the Onset of Nucleate Boiling ............ 7

1.3.2 Fully Developed Nucleate Boiling.................................................................. 8

1.3.3 Critical Heat Flux............................................................................................ 9

1.3.4 Application to Electronics Cooling............................................................... 11

1.4 Boiling Heat Sinks ................................................................................................. 13

1.5 Focus of the Current Research ............................................................................... 16

1.6 Organization of the Dissertation ............................................................................ 17

1.6.1 Measurement Units ....................................................................................... 19

Chapter 2: Natural Convection Boiling in Vertical Channels .................................... 21

2.1 Literature Review Summary .................................................................................. 22

vii

2.2 Monde et al. (1982)................................................................................................ 25

2.3 Bar-Cohen and Schweitzer (1985b) ....................................................................... 27

2.4 Fujita et al. (1987, 1988)........................................................................................ 34

2.5 Guo and Zhu (1997) ............................................................................................... 38

2.6 Xia et al. (1996) ..................................................................................................... 39

2.7 Bonjour and Lallemand (1997, 1998) .................................................................... 41

2.8 Chien and Chen (2000) .......................................................................................... 43

Chapter 3: Experimental Design ................................................................................... 46

3.1 Experimental Module............................................................................................. 47

3.2 Silicon Heaters ....................................................................................................... 49

3.3 Aluminum Heater Assemblies ............................................................................... 54

3.4 Experimental System ............................................................................................. 56

3.5 Experimental Measurements.................................................................................. 61

3.6 Uncertainty Estimates ............................................................................................ 64

3.6.1 Zeroth Order Temperature Measurement Uncertainties.............................. 64

3.6.2 Zeroth Order Heater Power Measurement Uncertainties ............................ 66

3.6.3 First Order Bias Errors: Parasitic Heat Losses and Thermocouple

Placement..................................................................................................... 68

3.6.3.1 Silicon Heater First Order Bias Errors............................................. 69

3.6.3.2 Aluminum Heater First Order Bias Errors....................................... 75

3.6.4 Complete First Order Uncertainty Estimates............................................... 80

Chapter 4: Pool Boiling Characterization .................................................................... 83

4.1 Basic Saturated Pool Boiling Experiments ............................................................ 83

4.2 Effect of Surface Roughness.................................................................................. 89

4.3 Critical Heat Flux................................................................................................... 95

4.4 Saturated Pool Boiling Data Summary .................................................................. 97

4.5 Subcooled Pool Boiling ......................................................................................... 99

viii

Chapter 5: Channel Boiling.......................................................................................... 102

5.1 Silicon Channel Experiments............................................................................... 103

5.1.1 Polished Silicon Channels ......................................................................... 103

5.1.2 Scratched Silicon Channels ....................................................................... 107

5.1.3 Subcooled Silicon Channels ...................................................................... 108

5.2 Aluminum Channel Experiments......................................................................... 110

5.3 Effect of Confinement on CHF ........................................................................... 111

5.4 Low Flux Enhancement ....................................................................................... 114

5.4.1 Convective Enhancement .......................................................................... 119

5.4.2 Thin Film Evaporation and Transient Conduction .................................... 124

5.4.3 Vapor and Nucleation Site Interactions ..................................................... 125

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies .................................... 128

6.1 Single Phase Natural Convection Cooling of 3-D Stacked Dies ......................... 129

6.1.1 The Heat Transfer Coefficient ................................................................... 129

6.1.2 Natural Convection Correlations ............................................................... 131

6.1.3 Composite Equations for Vertical Channels.............................................. 134

6.1.4 Maximizing Heat Transfer......................................................................... 137

6.1.5 Optimizing Channel Spacing ..................................................................... 138

6.1.6 Sample Calculations for Die Stacks Immersed in FC-72 ......................... 142

6.2 Two Phase Passive Immersion Cooling of 3-D Stacked Dies ............................. 146

6.2.1 Maximum Volumetric Heat Dissipation at CHF ....................................... 146

6.2.2 Optimum Die Spacing ............................................................................... 148

6.2.3 Effect of System Pressure .......................................................................... 151

6.2.4 Sub-CHF Volumetric Heat Transfer Coefficients ..................................... 152

6.3 Die Stack Notes and Observations....................................................................... 155

ix

Chapter 7: Design and Optimization of Boiling Heat Sinks ..................................... 157

7.1 Fin Conduction Analysis Methodology ............................................................... 159

7.2 Aluminum Boiling Heat Sink Parametric Study.................................................. 164

7.2.1 Basic Aluminum Boiling Heat Sink Results ............................................. 165

7.2.2 Optimum Aluminum Boiling Heat Sinks .................................................. 168

7.2.3 Effect of Fin Height ................................................................................... 172

7.2.4 Effect of Fin Thermal Conductivity........................................................... 173

7.3 Silicon Boiling Heat Sink Parametric Study........................................................ 180

7.3.1 Optimum Silicon Boiling Heat Sinks ........................................................ 182

7.3.2 Fin Height and Fin Efficiency ................................................................... 186

7.3.3 Effect of Fin Thermal Conductivity........................................................... 189

7.4 Boiling Heat Sink Notes and Observations.......................................................... 192

Chapter 8: Summary and Recommendations ............................................................ 195

8.1 Contributions........................................................................................................ 195

8.1.1 Experimental Contributions....................................................................... 195

8.1.2 Theoretical Contributions .......................................................................... 197

8.2 Recommendations for Future Work..................................................................... 200

Appendix A: Fluid Properties and Boiling Correlation Parameters........................ 202

Appendix B: Review of Boiling Heat Sink Literature ............................................... 205

B.1 Klein and Westwater (1971) ................................................................................ 205

B.2 Abuaf et al. (1985) ............................................................................................... 207

B.3 Park and Bergles (1986)....................................................................................... 207

B.4 Kumagai et al. (1987) .......................................................................................... 209

B.5 Anderson and Mudawar (1988, 1989), Mudawar and Anderson (1990, 1993) ... 210

B.6 McGillis et al. (1991)........................................................................................... 211

B.7 Dulnev et al. (1996) ............................................................................................. 212

B.8 Guglielmini et al. (1996, 2002), Misale et al. (1999) .......................................... 212

x

B.9 Fantozzi et al. (2000) ........................................................................................... 213

B.10 Rainey and You (2000), Rainey et al. (2003) ...................................................... 215

B.11 Yeh (1997) ........................................................................................................... 216

Appendix C: Experimental Apparatus Photographs and Schematics ..................... 218

Appendix D: Thermal Anemometry in Two Phase Flows......................................... 238

D.1 Basic Principles.................................................................................................... 239

D.2 Comparison with Other Techniques..................................................................... 245

D.2.1 Resistivity Probes....................................................................................... 245

D.2.2 Optical Probes ............................................................................................ 245

D.2.3 Laser Doppler Anemometry....................................................................... 246

D.3 Sources of Measurement Error............................................................................. 248

D.3.1 System Disturbance Effects and System-Sensor Interactions.................... 248

D.3.2 Calibration Errors....................................................................................... 250

D.3.3 Observational Errors .................................................................................. 250

D.4 Uncertainty Analysis............................................................................................ 253

D.4.1 Zeroth Order Bias and Precision Errors ..................................................... 254

D.4.2 First Order Precision Errors ....................................................................... 254

D.4.3 First Order Bias Corrections ...................................................................... 257

D.4.3.1 Propagation of Errors in Void Fraction Equation ......................... 257

D.4.3.2 Void Velocity Distribution Effect................................................. 258

D.4.3.3 Liquid and/or Vapor Film Left on Probe ...................................... 258

D.4.3.4 Bubble Deformation and Deflection............................................. 259

D.4.4 Total First Order Uncertainty Estimates .................................................... 260

D.5 Summary and Concluding Remarks .................................................................... 261

xi

Appendix E: Data Acquisition Software ..................................................................... 262

E.1 Data Acquisition Program Listing ....................................................................... 264

Appendix F: CFD Simulation of Two Phase Channel Flow...................................... 276

F.1 Simulation Parameters ......................................................................................... 277

F.1.1 Bubble Correlations .................................................................................... 278

F.1.2 Bubble Parameter Estimates ....................................................................... 280

F.2 CFD Modeling Process ........................................................................................ 285

F.2.1 Model Geometry and Computational Grid ................................................. 286

F.2.2 Initial Single Phase Simulation................................................................... 290

F.2.3 Transient VOF Simulation.......................................................................... 294

F.3 VOF Simulation Results and Discussion ............................................................. 299

F.4 Next Steps ............................................................................................................ 314

F.5 File and Command Listings ................................................................................. 316

F.5.1 GAMBIT Journal File................................................................................. 316

F.5.2 Steady-State Simulation FLUENT Options................................................ 318

F.5.3 VOF Simulation FLUENT Options ............................................................ 319

Appendix G: Boiling Fin Analysis Batch File............................................................. 322

G.1 Aluminum Fin Batch File..................................................................................... 326

G.2 Silicon Fin Batch Modifications .......................................................................... 322

G.3 Average Boiling Fin Heat Transfer Coefficient................................................... 334

Appendix H: Experimental Silicon Heat Sink Design ............................................... 343

Appendix I: Boiling Curve Data Tables...................................................................... 351

Bibliography .................................................................................................................. 356

xii

LIST OF TABLES

Table 1.1: 2005 ITRS Technology Requirements for Single Chip Packages

(SIA, 2005).......................................................................................................................... 3

Table 1.2: Saturated Boiling Predictions at CHF for Various Fluorinert™ Liquids ........ 11

Table 1.3: Summary of Experimental Boiling Heat Sink Studies..................................... 15

Table 2.1: Summary of representative studies of natural convection boiling in vertical

channels............................................................................................................................. 24

Table 2.2: Comparison of property groupings used in the Monde et al. (1982)

correlation for CHF in vertical rectangular channels, Eq. (2.1), for various fluids at

saturated conditions........................................................................................................... 26

Table 2.3: Saturated fluid properties and Bond number results for methanol and

HFC4310 ........................................................................................................................... 45

Table 3.1: Experimental Measurements............................................................................ 61

Table 3.2: Keithley 2000 DMM 1-year DC voltage measurement accuracy when

operated in a 23°C ± 5°C environment (Keithley, 1999).................................................. 64

Table 3.3: Solid objects included in the silicon heater Icepak model ............................... 70

Table 3.4: Material properties used in the Icepak analyses............................................... 71

Table 3.5: Solid objects included in the aluminum heater Icepak model ......................... 76

Table 3.6: Summary of temperature measurement uncertainty contributions .................. 81

xiii

Table 4.1: Experimental run and correlating parameter summary.................................... 98

Table 4.2: Saturated boiling curve polynomial curve fit coefficients of Eq. (4.3)............ 98

Table 4.3: Pool boiling critical heat flux data summary ................................................... 98

Table 4.4: Subcooled boiling curve polynomial curve fit coefficients of Eq. (4.3)

for polished silicon heaters.............................................................................................. 100

Table 4.5: Effects of liquid subcooling and system pressure on CHF for various

Fluorinert liquids, relative to saturated, 101 kPa (1 atm) conditions........................... 101

Table 5.1: Relationship between channel spacing and Bond number values for select

fluids, based on saturation properties at atmospheric pressure ....................................... 117

Table 6.1: Summary of C coefficient values for various cases ....................................... 133

Table 6.2: Results of example calculations for single phase natural convection

cooling of 3-D die stacks immersed in saturated FC-72 at atmospheric pressure .......... 142

Table 7.1: Polynomial coefficients of Eq. (7.3) .............................................................. 166

Table 7.2: Select optimum EDM aluminum heat sink configurations

(20 × 20 mm base)........................................................................................................... 169

Table 7.3: Optimization results for various 20 mm wide heat sinks............................... 176

Table 7.4: Results of the thermal conductivity parametric analysis, with δ = 0.3 mm,

L = 20 mm, and ∆T = 22.4°C .......................................................................................... 190

Table A.1: Saturation properties and property groupings at atmospheric pressure ........ 203

Table A.2: FC-72 saturation properties as a function of pressure (3M, 1990) ............... 204

Table D.1: Relative comparison of various two-phase flow measurement techniques .. 247

Table D.2: Variation of void fraction with fluctuation threshold. Bold values

correspond to the critical fluctuation thresholds identified by Resch et al. (1974) ........ 254

xiv

Table F.1: Boiling parameter predictions for saturated FC-72 at atmospheric pressure

(101 kPa) based on Eqs. (F.1)–(F.8) ............................................................................... 282

Table F.2: Summary and comparison of simulation results............................................ 309

Table G.1: Temperature (°C) dependent boiling heat transfer coefficients (W/m2) for

silicon channels, based on the data of Fig. 5.1 ................................................................ 334

Table G.2: Single fin analysis results for 0.4 mm thick fins with a base temperature

12°C above saturation, based on EDM aluminum surface boiling heat transfer

coefficients ...................................................................................................................... 335

Table G.3: Single fin analysis results for 0.3 mm thick fins with a base temperature

22°C above saturation, based on 0.3 mm polished silicon channel heat transfer

coefficients ...................................................................................................................... 339

Table I.1: Boiling curve data of Fig. 5.1 for symmetric 20 × 30 mm polished silicon

heater channels ................................................................................................................ 351

Table I.2: Boiling curve data of Fig. 5.2 for asymmetric 20 × 30 mm polished silicon

heater channels ................................................................................................................ 352


heater channels ................................................................................................................ 352

Table I.4: Boiling curve data of Fig. 5.4 for asymmetric 20 × 20 mm scratched silicon

heater channels ................................................................................................................ 353

Table I.5: 30°C subcooled boiling curve data of Fig. 5.6 for asymmetric polished

silicon heater channels .................................................................................................... 353

Table I.6: Boiling curve data of Fig. 5.7 for asymmetric aluminum heater channels..... 354

Table I.7: Channel CHF data of Fig. 5.8......................................................................... 355

xv

LIST OF FIGURES

Figure 1.1: Variation of achievable surface heat flux with available temperature

difference for various heat transfer modes and fluids (Kraus and Bar-Cohen, 1983) ........ 4

Figure 1.2: The boiling curve for heat flux-controlled boiling ........................................... 7

Figure 1.3: Confined boiling configuration: a vertical array of parallel rectangular

plates.................................................................................................................................. 16

Figure 2.1: Effect of channel aspect ratio on CHF—Monde et al. (1982) correlation,

Eq. (2.1), normalized by wide channel limit (L/δ→0) ...................................................... 27

Figure 2.2: Comparison of forced convection correction factors: Schweitzer (1983)

data and Eq. (2.16) ............................................................................................................ 32

Figure 2.3: Comparison of two phase heat transfer coefficient correlation, Eq. (2.17),

with the experimental data of Bar-Cohen and Schweitzer (1985b) for symmetrically-

heated 240 mm high by 66 mm wide channels submerged in saturated water ................. 33

Figure 2.4: Comparison of Schweitzer (1983) and Fujita et al. (1988) experimental data

for boiling of water in asymmetric channels, showing variation of normalized boiling

surface superheat with channel spacing ............................................................................ 37

Figure 2.5: Effect of channel aspect ratio on CHF—Bonjour and Lallemand (1997)

correlation, Eq. (2.21) ....................................................................................................... 42

Figure 3.1: The experimental module ............................................................................... 48

Figure 3.2: Photograph of the finned water cooled heat sink/module wall....................... 48

Figure 3.3: A 20 × 20 mm heater mounted on a polycarbonate module wall ................... 51

xvi

Figure 3.4: Silicon heater for moveable shaft assembly, 20 × 30 mm.............................. 51

Figure 3.5: Experimental apparatus photograph including heater support shaft and

positioning screw assembly............................................................................................... 52

Figure 3.6: View from underside of experimental module, 2 mm heater spacing............ 53

Figure 3.7: Aluminum heater assembly parts: a) boiling surface (EDM finish) with

foil thermocouple, and b) shaft with cartridge heater ....................................................... 54

Figure 3.8: Polished aluminum heater assembly in polycarbonate wall ........................... 55

Figure 3.9: Pictorial representation of overall experimental system................................. 56

Figure 3.10: Photograph of the thermocouple terminal block .......................................... 57

Figure 3.11: Output signal from a constant temperature hot film anemometer, with

each peak representing a bubble passage event ................................................................ 60

Figure 3.12: Example of real-time data acquisition graph of temperature

measurements .................................................................................................................... 62

Figure 3.13: Example of real-time data acquisition graph of heater electrical

parameters ......................................................................................................................... 63

Figure 3.14: Isometric view of silicon heater Icepak model ............................................. 69

Figure 3.15: Top view of silicon heater assembly model ................................................. 71

Figure 3.16: Sample temperature and velocity results for silicon heater Icepak model

(Pheater = 45 W, hb = 8000 W/m2) ...................................................................................... 73

Figure 3.17: Results of parasitic heat loss analysis for silicon heaters ............................. 74

Figure 3.18: Isometric view of silicon heater Icepak model ............................................. 75

Figure 3.19: Top view of aluminum heater assembly model............................................ 76

Figure 3.20: Sample temperature and velocity results for aluminum heater Icepak

model (Pheater = 60 W, hb = 5578 W/m2) ........................................................................... 78

Figure 3.21: Results of aluminum heater assembly parasitic heat loss analysis ............... 79

Figure 4.1: Pool boiling curve for polished silicon heater in saturated FC-72 ................. 84

Figure 4.2: Comparison of pool boiling curves for silicon heaters in saturated FC-72 .... 85

Figure 4.3: Transient pool boiling data for aluminum heater in saturated FC-72............. 88

Figure 4.4: Pool boiling curve for rough aluminum EDM surface ................................... 88

xvii

Figure 4.5: Magnified photographs of aluminum heater surface formed by wire EDM .. 91

Figure 4.6: Magnified photographs of aluminum surface after sanding with 600 grit

sandpaper........................................................................................................................... 92

Figure 4.7: Magnified photographs of scratched silicon heater surface ........................... 93

Figure 4.8: Unconfined pool boiling curves for various silicon and aluminum surface,

comparison of surface roughness effect and Cooper (1984) correlation, Eq. (4.1) .......... 94

Figure 4.9: Variation of effusivity term of Eq. (4.2) with heater thickness for silicon

and aluminum.................................................................................................................... 96

Figure 4.10: Polished silicon heater pool boiling curves for 19 and 32°C subcooled

liquid.................................................................................................................................. 99

Figure 4.11: Subcooling enhancement of CHF for polished silicon heaters, compared

to subcooling factor from Arik and Bar-Cohen (2003) CHF correlation, Eq. (4.4)........ 101

Figure 5.1: Boiling curves for symmetric 20 × 30 mm polished silicon heater

channels........................................................................................................................... 104

Figure 5.2: Boiling curves for asymmetric 20 × 30 mm polished silicon heater

channels........................................................................................................................... 104

Figure 5.3: Boiling curves for asymmetric 20 × 20 mm polished silicon heater

channels........................................................................................................................... 106

Figure 5.4: Boiling curves for asymmetric 20 × 20 mm scratched silicon heater

channels........................................................................................................................... 107

Figure 5.5: Enhancement ratios for asymmetric 20 × 20 mm scratched and polished

silicon heater channels .................................................................................................... 108

Figure 5.6: 30°C subcooled boiling curves for asymmetric polished silicon heater

channels........................................................................................................................... 109

Figure 5.7: Boiling curves for asymmetric aluminum heater channels........................... 110

Figure 5.8: Dependence of CHF data on aspect ratio and comparison with correlation

of Bonjour and Lallemand (1997), Eq. (5.1)................................................................... 112

xviii

Figure 5.9: Dependence of symmetric channel CHF data on aspect ratio and

comparison with correlation of Bonjour and Lallemand (1997), Eq. (5.1)..................... 113

Figure 5.10: Enhancement ratios for symmetric polished silicon heater channels at

various heat fluxes (kW/m2)............................................................................................ 115

Figure 5.11: Enhancement ratios for asymmetric polished silicon heater channels at

various heat fluxes (kW/m2)............................................................................................ 115

Figure 5.12: Bond number comparison of confinement-driven enhancement from

asymmetrically heated channels...................................................................................... 116

Figure 5.13: Comparison of FC-72 symmetric and asymmetric channel boiling

curves from Figs. 5.1 and 5.2 based on reduced heat flux .............................................. 119

Figure 5.14: Confinement contribution to experimental heat transfer coefficients for

asymmetric polished silicon heater channels compared to Bar-Cohen and Schweitzer

(1985b) thermosyphon boiling model, Eq. (2.17)........................................................... 120

Figure 5.15: Enhancement ratios for symmetric polished silicon heater channels

compared to Bar-Cohen and Schweitzer (1985b) model at various heat fluxes

(kW/m2)........................................................................................................................... 122

Figure 6.1: Isothermal Nusselt number correlations, symmetric heating,

CT,ip = 0.705..................................................................................................................... 135

Figure 6.2: Isothermal Nusselt number correlations, asymmetric heating,

CT,ip = 0.705..................................................................................................................... 135

Figure 6.3: Isoflux Nusselt number correlations, based on maximum temperature

(z = L), symmetric heating, Cq”,ip = 0.60 ......................................................................... 136

Figure 6.4: Isoflux Nusselt number correlations, based on maximum temperature

(z = L), asymmetric heating, Cq”,ip = 0.60 ....................................................................... 136

Figure 6.5: Optimum spacing as a function of plate thickness: isothermal plates,

symmetric heating, CT,ip = 0.705 ..................................................................................... 140


asymmetric heating, CT,ip = 0.705 ................................................................................... 140

xix

Figure 6.7: Optimum spacing as a function of plate thickness: isoflux plates,

maximum temperature (z = L), symmetric heating, Cq”,ip = 0.60.................................... 141

Figure 6.8: Optimum spacing as a function of plate thickness: isoflux plates,

maximum temperature (z = L), asymmetric heating, Cq”,ip = 0.60.................................. 141

Figure 6.9: Heat transfer coefficient and heat flux variations for isothermal die

stacks, immersed in saturated FC-72 at atmospheric pressure, 20 mm in length (L)

with spacings (δ) of 5, 0.5, 0.4, and 0.2 mm................................................................... 143

Figure 6.10: Single phase natural convection heat transfer coefficients for isothermal

die stacks, 20 mm in length, in saturated FC-72 at atmospheric pressure ...................... 144

Figure 6.11: Single phase natural convection heat transfer coefficients for isothermal

die stacks, 20 mm in length, in saturated FC-72 at atmospheric pressure, with

∆T = 10°C........................................................................................................................ 145

Figure 6.12: Volumetric heat dissipation at CHF for stacked silicon dies immersed in

saturated FC-72: L = 20 mm, P = 101 kPa (1 atm) ......................................................... 148

Figure 6.13: Optimum channel spacing calculated using Eq. (6.30) for saturated

FC-72 at 101 kPa (1 atm), ψ = 0.002412 ........................................................................ 149

Figure 6.14: Loci of maxima of volumetric heat dissipation for stacked silicon dies

immersed in saturated FC-72 at 101 kPa (1 atm)............................................................ 150

Figure 6.15: Volumetric heat dissipation variation with die thickness for stacked

silicon dies immersed in saturated FC-72 at 101 kPa (1 atm) at optimum channel

spacings, δopt, calculated using Eq. (6.30)....................................................................... 150

Figure 6.16: Die stack volumetric heat dissipation as a function of superheat, based

on the symmetric channel boiling data of Fig. 5.1, with t = 0.1 mm .............................. 153

Figure 6.17: Die stack volumetric heat transfer coefficient as a function of die

superheat, based on the symmetric channel boiling data of Fig. 5.1, assuming

t = 0.1 mm ....................................................................................................................... 154

Figure 6.18: Die stack volumetric heat transfer coefficient as a function of die

superheat, based on the symmetric channel boiling data of Fig. 5.1............................... 154

xx

Figure 7.1: Longitudinal rectangular plate fin heat sink geometry with nomenclature .. 158

Figure 7.2: Experimental boiling heat sink data with results of the FEA-based model.. 162

Figure 7.3: Boiling heat dissipation per unit fin length, L, for 20 mm high aluminum

fins with EDM surface, in saturated FC-72 at 101 kPa (1 atm) ...................................... 166

Figure 7.4: Maximum heat sink heat dissipation for various aluminum fin thicknesses

and numbers fins, L = W = 20 mm, EDM aluminum in saturated FC-72 at 101 kPa

(1 atm) ............................................................................................................................. 167

Figure 7.5: Loci of maxima of aluminum heat sink performance curves, EDM

aluminum in saturated FC-72 at 101 kPa (1 atm) ........................................................... 168

Figure 7.6: Fin spacings for optimum geometries of Fig. 7.5, EDM aluminum in

saturated FC-72 at 101 kPa (1 atm)................................................................................. 170

Figure 7.7: Fin thicknesses for optimum geometries of Fig. 7.5, EDM aluminum in

saturated FC-72 at 101 kPa (1 atm)................................................................................. 170

Figure 7.8: Relationship between fin thickness and spacing for optimum geometries

of Fig. 7.5, EDM aluminum in saturated FC-72 at 101 kPa (1 atm)............................... 171

Figure 7.9: Enhancement ratios for optimum aluminum boiling heat sinks with eight

to thirty-two fins, EDM surface in saturated FC-72 at 101 kPa (1 atm) ......................... 171

Figure 7.10: Total heat sink heat dissipation as a function of fin height for select

optimum aluminum heat sinks described in Table 7.2.................................................... 172

Figure 7.11: Effect of thermal conductivity on enhancement ratios for optimized

20 mm wide heat sinks, based on experimental EDM aluminum heat transfer

coefficients ...................................................................................................................... 175

Figure 7.12: Height required to achieve 95% of asymptotic maximum for optimum

fins of Table 7.3 .............................................................................................................. 177

Figure 7.13: Effect of anisotropy on fin heat dissipation for pyrolytic graphite

(2000 W/mK in-plane) fins with low conductivity (5 W/mK) direction oriented

parallel to the fin thickness.............................................................................................. 179

Figure 7.14: Temperature-dependent silicon thermal conductivity (Incropera and

De Witt, 1996)................................................................................................................. 180

xxi

Figure 7 15: Symmetric silicon channel heat transfer coefficients for various

spacings, based on the experimental channel boiling curves of Fig. 5.1 ........................ 182

Figure 7.16: Fin thickness trends for polished silicon heat sinks with 0.3 mm fin

spacing and 20 mm sink length ....................................................................................... 183

Figure 7.17: Maximum base heat flux (kW/m2) for 20 mm long optimum silicon heat

sinks and individual contributions from each fin and exposed inter-fin base area (W).. 184

Figure 7.18: Comparison of optimum 20 mm long silicon and aluminum heat sinks .... 185

Figure 7.19: Silicon boiling heat sink performance as a function of fin height, δ = 0.3

mm, t = 0.29 mm, and L = 20 mm................................................................................... 186

Figure 7.20: Single fin heat dissipation for 0.29 mm thick aluminum and silicon fins,

with base temperatures at the superheat corresponding to 45 kW/m2 for each surface .. 188

Figure 7.21: Comparison of aluminum and silicon fin efficiencies for 0.29 mm thick

fins, with base temperatures at the superheat corresponding to 45 kW/m2 for each....... 188

Figure 7.22: Effect of thermal conductivity on enhancement ratios and height required

to achieve 95% of asymptotic maximum, for 20 mm long heat sinks and experimental

polished silicon heat transfer coefficients ....................................................................... 191

Figure 7.23: Product of density, specific heat, and thermal conductivity for various

candidate heat sink materials (Incropera and De Witt, 1996) ......................................... 193

Figure C.1: Front view of aluminum experimental module............................................ 219

Figure C.2: Top view of aluminum experimental module .............................................. 220

Figure C.3: Bottom view of aluminum experimental module ........................................ 221

Figure C.4: Side view of aluminum experimental module ............................................. 222

Figure C.5: Polycarbonate window, 0.25” thick ............................................................. 223

Figure C.6: Shaft-supporting polycarbonate wall, 0.25” thick ....................................... 224

Figure C.7: Polycarbonate shaft support, 2.5” deep........................................................ 225

Figure C.8: Silicon heater substrate and modified module wall, 0.25” thick

polycarbonate .................................................................................................................. 226

Figure C.9: Aluminum module leg standoff blocks........................................................ 227

Figure C.10: Aluminum module legs, 12” long (not to scale) ........................................ 228

xxii

Figure C.11: Aluminum module feet, 12” long .............................................................. 229

Figure C.12: Aluminum fixture for 20 × 20 mm silicon heater electrode sputtering

process............................................................................................................................. 230

Figure C.13: Aluminum fixture for 20 × 30 mm silicon heater electrode sputtering

process............................................................................................................................. 231

Figure C.14: Photograph of aluminum fixture for 20 × 30 mm silicon heater

electrode sputtering process ............................................................................................ 232

Figure C.15: Photograph of backside of module assembly including module legs ........ 233

Figure C.16: Photograph of backside of module with 20 × 30 mm silicon heater

installed ........................................................................................................................... 234

Figure C.17: Photographs of module interior through bottom window: a.) unpowered

heaters, large channel spacing, δ ≈ 5 mm; b.) single unconfined heater, powered ......... 235

Figure C.18: Experimental boiling heat sink drawing .................................................... 236

Figure C.19: Experimental boiling heat sink photographs.............................................. 236

Figure C.20: Experimental boiling heat sink apparatus .................................................. 237

Figure D.1: Typical response of cylindrical probe signal due to passing bubble

(Bruun and Farrar, 1988)................................................................................................. 240

Figure D.2: Typical anemometer signal in bubbly two-phase flow (Hsu et al., 1963)... 242

Figure D.3: Illustration of fluctuation threshold for an air/water two-phase flow

(Resch et al., 1974) ......................................................................................................... 251

Figure D.4: Fluctuation threshold determination (Resch et al., 1974)............................ 252

Figure D.5: Identification of critical fluctuation threshold, lcr2 (Resch et al., 1974) ...... 253

Figure F.1: Ratio of difference between channel and unconfined heat fluxes to

unconfined heat flux at a given wall superheat, Eq. (F.9), for the asymmetric

channel data of Fig. 5.2 ................................................................................................... 281

Figure F.2: Bubble growth rate predicted by Mikic and Rohsenow (1969) correlation . 285

Figure F.3: CFD model geometry ................................................................................... 287

xxiii

Figure F.4: GAMBIT screen-shot of model geometry showing vertices, edges, and

faces................................................................................................................................. 288

Figure F.5: GAMBIT screen-shot showing mesh details in vicinity of vapor inlet........ 289

Figure F.6: Scaled solution residuals for initial steady-state single phase solution........ 293

Figure F.7: Temperature results for initial steady-state single phase solution................ 293

Figure F.8: Velocity results for initial steady-state single phase solution ...................... 294

Figure F.9: Nucleation site mass flux profiles ................................................................ 297

Figure F.10: Scaled solution residuals for the first 5 bubble generation cycles of the

5 mm channel simulation ................................................................................................ 300

Figure F.11: Phase contour plots at 4 ms time steps from the beginning of the VOF

simulation through the first seven bubble generations, δ = 5 mm .................................. 301

Figure F.12: Inlet and outlet mass flow rates as a function of time, δ = 5 mm............... 302

Figure F.13: Contour plots of 5 mm channel liquid phase volume fraction at various

simulation times .............................................................................................................. 303

Figure F.14: Heater top and bottom heat flux as a function of time, δ = 5 mm.............. 304

Figure F.15: Time-averaged inlet and outlet mass flow rates, δ = 5 mm........................ 305

Figure F.16: Time-averaged heater top and bottom heat fluxes, δ = 5 mm.................... 306

Figure F.17: Temperature contour plot at end of 5 mm channel VOF simulation.......... 307

Figure F.18: Surface heat flux profiles for 5 mm channel single phase natural

convection solution and VOF simulation results at t = 1.34 s ........................................ 307

Figure F.19: Velocity contour plot at end of VOF simulation, δ = 5 mm ...................... 308

Figure F.20: Comparison of temperature results from single phase numerical

simulations ...................................................................................................................... 310

Figure F.21: Contour plots of narrow channel liquid phase volume fraction at various

simulation times .............................................................................................................. 312

Figure F.22: Surface heat flux profiles from narrow channel simulation results............ 313

Figure F.23: Comparison of temperature results from two phase numerical

simulations ...................................................................................................................... 313

xxiv

Figure G.1: Contour plot of fin temperatures resulting from the ANSYS™ batch file

shown in Section G.1 with input parameters corresponding to the experimental

boiling heat sink discussed in Section 7.1 and a base temperature 14°C above

saturation ......................................................................................................................... 325

Figure G.2: Variation of single fin heat dissipation with thermal conductivity for

asymptotically-high, 0.4 mm thick fins, with a 12°C base superheat, assuming EDM

aluminum boiling heat transfer coefficients.................................................................... 336

Figure G.3: Effective fin height to achieve 95% of maximum, for fins of Table G.2 .... 336

Figure G.4: Surface temperature profiles for the fins of Table G.2 ................................ 337

Figure G.5: Surface temperature profiles of Fig. G.4 graphed vs. normalized distance

along fin height................................................................................................................ 338

Figure G.6: Variation of maximum single fin heat dissipation with thermal

conductivity for asymptotically-high, 0.3 mm thick fins, with a 22°C base superheat,

assuming 0.3 mm polished silicon channel heat transfer coefficients ............................ 339

Figure G.7: Effective fin height required to achieve 50% of maximum, for the fins

of Table G.3..................................................................................................................... 340

Figure G.8: Surface temperature profiles for the fins of Table G.3 ................................ 341


along fin height................................................................................................................ 341

Figure H.1: Illustration of proposed silicon heat sink design ......................................... 344

Figure H.2: Model geometry for finite element analysis of single silicon heat sink fin. 345

Figure H.3: Electrical results: a.) voltage distribution b.) current density ...................... 346

Figure H.4: Electrical results: Joule heating distribution................................................ 347

Figure H.5: Temperature results, quarter symmetry model of heat sink......................... 348

Figure H.6: Photograph of dies after attempted fusing ................................................... 350

xxv

NOMENCLATURE

As discussed in Section 1.6.1, the International System of Units (SI) as defined by ASME

Guide SI-1, ASME Orientation and Guide for Use of SI (Metric) Units Ninth Edition

(ASME, 1982) and IEEE/ASTM SI 10™-2002, American National Standard for Use of

the International System of Units (SI): The Modern Metric System (ASTM, 2002) is used

throughout this dissertation.

A area (m2)

Bi Biot number, hL/k

Bl Boiling number, Eq. (5.4)

Bo Bond number, Eq. (5.3)

C Nusselt number correlation constant, Eq. (6.6)

Cfr Fanning friction factor

Csf fluid/surface constant in Rohsenow (1952) correlation, Eq. (1.4)

cp specific heat (J/kgK)

D diameter (m)

El Elenbaas number, Eq. (6.8)

El’ Modified Elenbaas number, Eq. (6.10)

Fr Froude number, u/(g·Y)1/2

g gravitational acceleration (m/s2)

G mass flux (kg/m2s)

Gr Grashof number, Eq. (6.4)

xxvi

h heat transfer coefficient (W/m2K)

hfg latent heat of evaporation (J/kgK)

H fin height or channel depth (m), Figs. 1.3 and 7.1

I current (A)

k thermal conductivity (W/mK)

L channel, fin, or heater length (m), Figs. 1.3 and 7.1

M molecular weight (g/mol)

N number of fins or plates

Nu Nusselt number, Eq. (6.2)

P pressure (Pa)

power (W)

Pr reduced system pressure, P/Pcrit

Pr Prandtl number, Eq. (6.3)

R electrical resistance (Ω)

Re Reynolds number, Eq. (2.12)

S slip ratio, Eq. (2.7)

q’ heat flow per unit length (W/m)

q" heat flux (W/m2)

Q heat flow (W)

r radius (m)

Ra Rayleigh number, Eq. (6.5)

Rp RMS surface roughness in Eq. (4.1) (µm)

t fin, plate, or heater thickness (m), Figs. 1.3 and 7.1

T temperature (ºC)

u velocity (m/s)

V volume (m3)

voltage (V)

W array or heat sink width (m), Figs. 1.3 and 7.1

x mass quality

Y depth of flow in hydraulic jump

xxvii

z coordinate in channel length/flow direction (m)

Greek Symbols

α void fraction

thermal diffusivity, k/ρcp (m2/s)

β volumetric thermal expansion coefficient (1/K)

δ channel or fin spacing (m), Figs. 1.3 and 7.1

φ forced convection correction factor of Eq. (2.2)

γ nucleate boiling suppression factor of Eq. (2.2)

µ dynamic viscosity (Pa·s)

ν specific volume (m3/kg)

ψ fluid density and reduced pressure grouping of Eq. (6.29)

ρ mass density (kg/m3)

σ surface tension (N/m)

τ time (s)

Subscripts

b boiling, bubble, heat sink base

c convective

CHF critical heat flux

crit critical

f liquid state

fd fully developed

fg difference between liquid and gas phases

g gas/vapor state

h heater

i indexing variable

ip isolated plate

j indexing variable

xxviii

L channel exit

opt optimum

q” isoflux

sat saturation

sub subcooling

T total

T isothermal

TP two phase

w wall or heater

1

CHAPTER

ONE

INTRODUCTION

Driven by the need for thermal management solutions that can satisfy the evermore

demanding needs of the microelectronics industry, the research presented in this

dissertation is aimed at the ultimate goal of successful design and optimization of

enhanced geometries for boiling heat transfer in high performance electronic systems. As

motivation for the thesis, the following introductory sections contain detailed discussions

of both anticipated future thermal management needs as well as past studies of

performance-enhancing boiling structures.

1.1 ELECTRONIC COOLING REQUIREMENTS

The Semiconductor Industry Association's 2005 edition of The International Technology

Roadmap for Semiconductors (ITRS) represents a consensus of industry, governmental,

and university experts on future technology and research needs of the semiconductor

industry (SIA, 2005). This extensive report assesses anticipated technology requirements

of the following product categories:

Chapter 1: Introduction 2

• Low Cost, Hand Held, and Memory

• Cost/Performance — desktop and laptop personal computers, telecommunications

• High Performance — workstations, servers, supercomputers

• Harsh — “under the hood” and other harsh environment products

Table 1.1 contains a summary of anticipated thermal packaging requirements for the

Cost/Performance, High Performance, and Harsh product categories. The established

timetable is based on the year in which products demanding the specified requirements

are expected to be fully qualified and brought to production. As shown in this table, with

available temperature differences expected to drop and heat fluxes expected to increase,

required thermal resistances of advanced cooling technologies are expected to drop

roughly 50% over the next decade. While anticipated average die heat fluxes range 500–

1000 kW/m2 (50–100 W/cm2), non-uniform chip-level heat generation can lead to hot

spots with heat fluxes six or more times the die average, further exacerbating thermal

management challenges (Yang et al., 2006) (Bar-Cohen et al., 2006).

Table 1.1 presents projected thermal packaging trends for single chip microelectronic

packages. In addition, the 2005 ITRS identifies the thermal management of 3-D stacked

multi-chip packages as a near-term “difficult challenge.” 3-D stacking increases

integrated circuit (IC) density, providing increased capabilities and performance on a

smaller printed circuit board (PCB) footprint area. In addition, 3-D packages

accommodate shorter interconnect distances between devices, improving electrical

performance. However, these advantages come at the expense of decreased physical

access to the die areas for heat removal. A first-order approach for cooling these devices

is to rely on conduction through the various layers up to the top of the package and/or

down to the underlying PCB. Advanced package-level thermal management approaches

for 3-D packages typically propose including some sort of between-die solid material to

improve lateral heat spreading (e.g. Gerlach and Joshi, 2006). More research and

development related to cooling 3-D electronic structures is needed.


Table 1.1: 2005 ITRS Technology Requirements for Single Chip Packages (SIA, 2005)

Cost-Performance 2005 2007 2010 2015 2020

Chip Size (mm)† 12 12 12 12 12

Maximum Ambient Temperature (°C)‡ 45 45 45 45 45Maximum Junction Temperature (°C) 100 95 90 90 90

Available Temperature Difference (°C)* 55 50 45 45 45

Maximum Heat Flux (kW/m2) 650 740 850 980 1120Required Junction-to-Ambient Specific Thermal Resistance × 105 (K·m2/W)* 8.5 6.8 5.3 4.6 4.0

High-Performance 2005 2007 2010 2015 2020

Chip Size (mm)† 24 26 28 27 27

Maximum Ambient Temperature (°C)‡ 55 55 55 55 55Maximum Junction Temperature (°C) 100 95 90 90 90



Harsh 2005 2007 2010 2015 2020

Chip Size (mm)† 10 10 10 10 10Maximum Ambient Temperature (°C) 150 150 200 200 200Maximum Junction Temperature (°C) 175 175 220 220 220



† The ITRS presents chip size in terms of area. The square root of published values are

shown here to indicate linear chip dimensions. ‡ Values shown are the application or product ambient, rather than operational ratings

typically specified by component vendors. * Derived quantity based on ITRS data.


0.1

1

10

100

1000

1 10 100 1000

Available Temperature Difference (K)

Ach

ieva

ble

Surf

ace

Hea

t Flu

x (k

W/m

2 )

Direct air, n

atural convectio

n + radiation

Direct air, f

orced co

nvection

Immersion, natural co

nvection flu

orocarbons

Water, force

d

convection

Imm

ersio

n –

boilin

g flu

oroc

arbo

ns

0.1

1

10

100

1000

1 10 100 1000

Available Temperature Difference (K)

Ach

ieva

ble

Surf

ace

Hea

t Flu

x (k

W/m

2 )

Direct air, n

atural convectio

n + radiation

Direct air, f

orced co

nvection

Immersion, natural co

nvection flu

orocarbons

Water, force

d

convection

Imm

ersio

n –

boilin

g flu

oroc

arbo

ns

Figure 1.1: Variation of achievable surface heat flux with available temperature

difference for various heat transfer modes and fluids (Kraus and Bar-Cohen, 1983).

1.2 IMMERSION COOLING OF ELECTRONICS

Figure 1.1 provides a graphical representation of the variation of required temperature

difference with surface heat flux for a variety heat transfer conditions and cooling fluids.

Relating to the Cost/Performance and High Performance product categories of Table 1.1,

Fig. 1.1 suggests that for a maximum available temperature difference of 40 K, natural

convection and forced convection air cooling are only effective for removing heat fluxes

up to approximately 0.5 kW/m2 and 2.5 kW/m2, respectively. Despite this fact, air

cooling dominated microprocessor thermal management schemes in the 1990s, but only

Chapter 1: Introduction 5 through the aggressive exploitation of high density extended surfaces and various heat

spreading and air handling techniques (Bar-Cohen, 1999).

In the 2000s, liquid cooling of personal computers (PCs) has generally been limited thus

far to the domain of “overclockers” and other enthusiasts (2004’s Apple PowerMac G5

being one notable exception). These systems are most often water-based and limited to

single phase forced convection. In these cases the cooling is indirect, requiring a thermal

interface between the device and liquid cooled cold plate. However, single and two phase

liquid cooled microchannel heat sinks have taken center stage in the scholarly heat

transfer research of the early 2000s—some fabricated directly on the back side of active

silicon devices (e.g. Chang et al., 2005).

Historically, direct liquid cooling, where dielectric liquids are allowed to come into direct

contact with active devices, has only been implemented commercially in high

performance supercomputers, such as the Cray-2 (Danielson et al., 1986) and the CDC

ETA-10 (Vacca et al., 1987) of the 1980s, as well as the prototype SS-1 supercomputer

of the early 1990s (Ing et al., 1993). The Cray X1 supercomputer (project name Cray

SV2) employs direct contact spray evaporative cooling of its multichip modules (Pautsch,

2001). As performance demands continue to increase, with ever-stringent volume,

weight, and power consumption limits, it may soon be necessary to tap further into the

vast resources of liquid cooling, which, as seen in Fig. 1.1, can transfer hundreds of

kilowatts of heat per square meter through temperature differences as low as 10°C.

Direct cooling of electronics with dielectric liquids offers a number of inherent benefits.

Liquid filled enclosures can protect components by retarding moisture and foreign

particle penetration, while the dielectric liquid contained within provides electrical

insulation. Further, the naturally-generated agitation of a boiling liquid can assist in

mixing and effective spreading of heat within an enclosure. This “bubble pumping” can

alleviate the need for active pumping and provide increased system reliability over

pumped gas or liquid systems. As the envelope of the enclosure may have many times

Chapter 1: Introduction 6 more surface area than the heat dissipating component(s), a passive liquid cooled system

may be well suited to a variety of external cooling techniques. In the case of 3-D stacked

die devices, dielectric cooling liquids could passively circulate between dies and around

the interconnects to yield very high volumetric cooling rates. This scheme would not only

provide enhanced temperature uniformity of the silicon layers to reduce stresses induced

by differential expansion, but it would also accommodate Joule heating in high current

density interconnect.

1.3 BOILING HEAT TRANSFER

The definition of the heat transfer coefficient

TA

Qh∆

≡ (1.1)

may be rearranged to explicitly state the relationship between temperature difference and

heat flux shown in Fig. 1.1.

Thq ∆=′′ (1.2)

Thus, the steep slope of the boiling band in Fig. 1.1 indicates heat transfer coefficients

significantly higher than those typically achievable with single phase convective cooling.

Even though boiling heat transfer can provide for the removal of a large range of heat

fluxes over a small temperature range, there are limits to its applicability and

effectiveness which must be considered in the design of passive, immersion cooled

systems. The boiling curve of Fig. 1.2, discussed in detail in the following subsections,

shows the relationship between heat flux and surface superheat typically observed in heat

flux-controlled heat transfer from a surface immersed in an otherwise quiescent pool of

liquid (i.e. pool boiling).


TransitionBoiling

Fully-DevelopedNucleate Boiling

FilmBoiling

CHF

ONB

a

bc

hg

f

ed

Single Phase Natural Convection

Surface Superheat, (Tsurface – Tsat)

Surf

ace

Hea

t Flu

x, q

”

TransitionBoiling


FilmBoiling

CHF

ONB

a

bc

hg

f

ed


TransitionBoiling


FilmBoiling

CHF

ONB

a

bc

hg

f

ed


Surface Superheat, (Tsurface – Tsat)

Surf

ace

Hea

t Flu

x, q

”

Figure 1.2: The boiling curve for heat flux-controlled boiling.

1.3.1 Single Phase Natural Convection and the Onset of Nucleate Boiling

The portion of the curve between points a and b in Fig. 1.2 represents single phase

convection, characterized by the relatively low q” vs. ∆T slope. Point b represents the

onset of nucleate boiling (ONB) where the surface temperature is high enough to begin

bubble nucleation. Once one bubble is generated, it may trigger other nucleation sites,

and many more bubbles immediately follow. When this happens, the surface cools very

quickly, and its temperature drops very rapidly to point c.

Once nucleate boiling has been established, where bubbles are generated at and emanate

from distinct nucleation sites on the surface, boiling may be sustained below point c, until

the boiling heat transfer rate approaches the single phase convection rate, and the last

Chapter 1: Introduction 8 nucleation sites stop generating bubbles. It is the presence of bubble embryos in

nucleation sites that makes this possible. Rough surfaces with nucleation sites that require

little superheat to create a bubble embryo, or those that already contain a minute pocket

of trapped gas that can serve as a bubble embryo, may show little or no difference

between the increasing and decreasing heat flux curves. In general, the required

temperature difference between points b and c required to initiate nucleation is highly

statistical in nature but may be as high as 30°C for highly wetting liquids and highly

polished surfaces (Bar-Cohen and Simon, 1988).

1.3.2 Fully Developed Nucleate Boiling

The portion of the curve between points c and d in Fig. 1.2 represents the nucleate boiling

regime. The steep slope in this region illustrates the high heat transfer coefficients

associated with nucleate boiling. Significant increases in heat flux may be obtained with

very modest increases in temperature. This steep slope is why the nucleate boiling regime

is of prime interest in electronics cooling applications.

Despite its highly non-linear temperature dependence, nucleate boiling is often correlated

as a linear function of superheat via a (temperature-dependent) boiling heat transfer

coefficient

( )satsurfacesurface TTAhQ bb −= (1.3)

Recognizing the heat transfer contribution of bubbles agitating the liquid and drafting hot

liquid away from a boiling surface, Rohsenow (1952) defined a bubble Reynolds number

and bubble Nusselt number and developed a correlation for saturated nucleate pool

boiling that may be expressed in the form

( ) ( ) 11

satw

1

fg

gffgfb Pr

−−

−= r

r

sfs

p TTCh

cghh

σρρ

µ (1.4)

Chapter 1: Introduction 9 with fluid properties evaluated at the saturation temperature. The constant Csf as been

interpreted as reflecting the influence of cavity size distribution on bubble generation for

a given fluid/surface combination (Kraus and Bar-Cohen, 1983), and includes the effect

of contact angle, assumed independent of pressure and not included in the Rohsenow

(1952) correlation due to a lack of data. For the experimental data on which Eq. (1.4) was

based, s was found to range from 0.8 to 2.0 but was centered around a value of 1.7 for

“clean” surfaces. The parameter r may fall between 1/5 and 1/2 but is often taken to equal

a value of 1/3, following the Rohsenow derivation. In practice, all three parameters may

be determined empirically to best fit the data. While the literature contains many studies

evaluating Eq. (1.4) for a wide variety of fluids and surfaces, e.g. (Pioro, 1999) and

(Jabardo, 2004), no unifying or predictive trends for these constants have been identified

as of yet. Note that s and Csf appear only once in Eq. (1.4), and they appear together, with

s as the exponent of Prandtl number and Csf multiplying it. However, while the Prandtl

number may be expected to vary with pressure, Csf is assumed to be independent of

pressure. In the absence of data spanning a range of pressures, a value of s = 1.7 may be

assumed.

1.3.3 Critical Heat Flux

As the nucleate boiling process continues to higher and higher heat fluxes and approaches

point d in Fig. 1.2, an increasing amount of vapor is being generated, and it becomes

difficult for fresh liquid to reach the surface. Point d represents the Critical Heat Flux

(CHF), where the large volume of generated vapor prevents fresh liquid from

replenishing the supply at the surface. As a result, the surface becomes blanketed by a

thin layer of vapor and increases greatly in temperature (points d to e). The region of the

curve that contains points e, f, and g represents the film boiling regime, where the

dominant modes of heat transfer are conduction and radiation across the vapor blanket. If

the surface temperature drops below point g, the vapor blanket becomes unstable, breaks

up, and liquid is allowed to come in contact with the surface to reinitiate the nucleate

boiling process (point h).

Chapter 1: Introduction 10 As the temperature excursion from points d to e in Fig. 1.2 can be on the order of 100°C

or more, electronics cooling applications are most often restricted to the single phase and

nucleate boiling regimes, with CHF as an absolute upper limit. Therefore, in order to take

advantage of the high heat transfer coefficients associated with nucleate boiling, it is

necessary to stay below the CHF limit of a given system to prevent catastrophic failure.

The well known Kutateladze-Zuber CHF relation (Zuber, 1958) was developed for

saturated pool boiling on large, thick, upward-facing horizontal plates.

4/1gffgfgCHF )]([

24ρρσρπ −=′′ ghq (1.5)

The Zuber analytical treatment considered the Taylor instability criterion for coalesced

bubble vapor columns and defined CHF as occurring when the liquid-bubble interface

becomes unstable. More recent research has suggested that, for horizontal heaters, lateral

bubble coalescence creates dry patches on the surface that eventually reach the

Leidenfrost temperature and cause CHF (Arik and Bar-Cohen, 2003). Mudawar et al.

(1997) derived an interfacial lift-off model for CHF on vertical surfaces based on an

analysis of Kelvin-Helmholtz waves. Their resulting equation is identical in form to

Eq. (1.5), despite being based on a different mechanism. Regardless of its derivation,

Eq. (1.5) remains relatively accurate and, in particular, captures the effect of pressure on

CHF. A CHF correlation by Arik and Bar-Cohen (2003), based on Eq. (1.5) but expanded

to include a variety of additional parametric effects as discussed in detail in Chapter 4,

has been shown to have a typical accuracy of ±25%.

As can been seen in the material properties shown in Table A.1 of Appendix A, it is

primarily the difference in heat of vaporization between water and the Fluorinert

liquids that dominates Eq. (1.5) and leads to great differences in CHF predictions. The

Kutateladze-Zuber correlation predicts 1110 kW/m2 (111 W/cm2) for water, while, as

Table 1.2 shows, CHF for the Fluorinert liquids is typically on the order of 100–

200 kW/m2 (10–20 W/cm2). Further, elevated system pressure increases the liquid

saturation temperature and provides a CHF benefit.

Chapter 1: Introduction 11 Table 1.2: Saturated Boiling Predictions at CHF for Various Fluorinert Liquids

101 kPa 203 kPa 304 kPa FC-72 CHF (kW/m2) 137 164 179

Tsat (°C) 56.6 78.8 93.4 ∆Tsat,CHF (ºC) 28.8 23.7 20.7

FC-84 CHF (kW/m2) 162 205 Tsat (°C) 82.5 106 ∆Tsat,CHF (°C) 27.2 14.2

FC-77 CHF (kW/m2) 181 Tsat (°C) 101 ∆Tsat,CHF (°C) 31.1

1.3.4 Application to Electronics Cooling

Despite their wide range of boiling points, the Fluorinert liquids have similar properties

and, hence, boiling performance. Despite the frequently observed bending of the nucleate

boiling curve toward higher temperatures near CHF, Table 1.2 contains approximate

boiling surface temperature predictions at CHF based extrapolating the Rohsenow

correlation, Eq. (1.4) assuming s = 1.7, r = 1/2.6, and Csf = 0.0056. With boiling

superheats around 30°C, FC-72 at 101 kPa (1 atm) is an attractive choice for commercial

applications, as chip temperatures can be maintained below typical maximum allowable

temperature of 90–100°C (Table 1.1). In light of the 500–1000 kW/m2 (50–100 W/cm2)

target electronics cooling heat fluxes shown in Table 1.1, it is clear that significant

enhancement of pool boiling CHF will be required to employ dielectric liquids like FC-

72 in immersion cooled electronic systems.

While active boiling techniques (e.g. flow boiling, jet impingement, spray cooling) can

provide heat transfer rates well in excess of unenhanced pool boiling, passive systems can

provide a variety of additional advantages, such as low noise, zero power consumption,

and potentially increased reliability. Numerous passive enhancement techniques have

Chapter 1: Introduction 12 been shown to increase the already high heat transfer rates of nucleate boiling and CHF,

including the use of microscale surface treatments (Mudawar and Anderson, 1993)

(O'Connor and You, 1995) (Baldwin et al., 2000) (Arik et al., 2007) and liquid mixtures

(Lee and Normington, 1993) (Avedisian and Purdy, 1993) (Arik, 2001). While all these

techniques aim to increase the effective boiling heat transfer coefficient and delay CHF,

Eq. (1.1) suggests that an equally obvious method for passive enhancement is to extend

the heat transfer area, A, by attaching an array of fins, or heat sink, to the heat dissipating

surface.

Complexities inherent to the boiling process (nucleation site characteristics, interfacial

stability, two phase flow, etc.) make the prediction of boiling heat transfer rates and CHF

significantly more complicated and significantly less accurate than comparable single

phase calculations. Therefore, any attempts to augment boiling heat transfer with high

density heat sinks need to consider the impact of the modified geometry on the boiling

heat transfer coefficient. Furthermore, due to ongoing microsystem miniaturization, the

effects of physical confinement in electronic systems may further complicate the heat

transfer processes involved and lead to enhanced or deteriorated performance relative to

unconfined pool boiling. Geisler et al. (2004) explored the use of boiling and passive

immersion cooling in a military electronics application. The entire module was 18 mm

thick, and due to the confined geometry the liquid experienced minimal circulation

resulting in a highly stratified liquid condition. As a result, much of the submerged

condenser surface area was ineffective in removing heat from the liquid, limiting module

performance. On a smaller scale, in the case of immersion cooled 3-D packages,

confinement effects could be expected to be even more severe, potentially leading to

reduced nucleate boiling CHF.

Chapter 1: Introduction 13 1.4 BOILING HEAT SINKS

Several researchers have pursued numerical, analytical, and experimental investigations

of the boiling behavior of single fins (e.g. Haley and Westwater (1966), Lin and Lee

(1996), Unal (1987), Yeh and Liaw (1993)), though systematic studies of arrays of

multiple fins have been somewhat less common. Since the landmark study by Klein and

Westwater (1971) of boiling heat transfer from multiple fins, through the beginning of the

21st century, heat sinks have been shown to provide substantial nucleate boiling

enhancement as well as increases in the effective CHF limit compared to the array base

area. While early boiling fin array studies were driven primarily by nuclear reactor

cooling needs, increases in microelectronics cooling applications since the late 1980s

have fueled interest in extended and enhanced boiling surfaces for dielectric liquids.

Table 1.3 presents a summary of representative experimental studies of boiling heat sinks

in passive, natural convection systems from the past four decades. It should be noted that

throughout this dissertation heat sink orientation will be referred to in terms of the base

area. Thus, a “vertical” heat sink has a vertically-oriented base area from which fins

protrude horizontally, and vice versa. It is clear from the entries of Table 1.3 that a wide

variety of boiling heat sink geometries aimed at microelectronics cooling applications

have been investigated. These boiling heat sink studies are reviewed in depth in

Appendix B.

While typical boiling heat sink performance enhancement of 2 to 3 times that of the

unfinned base with the same surface characteristics is evident in the literature, fin spacing

rationales are typically based on generalized recommendations of previous studies (based

on a limited amount of data) and/or simply related to the expected or average bubble

departure diameter (if discussed at all). Complex, though quite approximate, theoretical

treatments of boiling heat transfer from fin arrays provide limited satisfaction, as they

neglect the effect of fin spacing and fluid confinement on boiling heat transfer rates.

Clearly, the gap must be bridged between these experimental studies which often show

Chapter 1: Introduction 14 significant boiling enhancement on surfaces created by closely spaced plates or fins and

theoretical treatments aimed at exploring optimum boiling heat sink geometries.


Table 1.3: Summary of Experimental Boiling Heat Sink Studies.

Circ. Square Height Spacing P Sub.D (mm) W (mm) V H t , D (mm) Geometry H (mm) δ (mm) (kPa) (°C) NC ONB NB CHF FLM

Klein and Westwater (1971) R113 water Cu N/A1 × 6.35

sq. pins rect. pins

plates29, 19 0–27.4 × ×

Abauf et al . (1985) R113 Cu 51, 76 × 1.6 sq. pins 3.2 1.6 4–101 0 × ×Park and Bergles (1986) R113 Cu 4.34–4.72 × 0.2–0.733 rect. plates 0.64 0.24–0.9 101 0, 16 × × ×Kumagai et al. (1987) R113 Cu 10 × × 0.2–1.5 rect. plates 1–10 0.28–2 × × × × ×Anderson and Mudawar (1988, 1989) Mudawar and Anderson (1990, 1993)

FC-72 FC-87 Cu 12.7 × 3.63–12.7 sq. pins

circ. pins 7.26–40 0.6 101 0, 35 × × ×McGillis et al . (1991) water Cu 12.7 × 0.7, 1.84 sq. pins 0–10.2 0.3–3.58 4, 9 0 × ×Dulnev et al . (1996) R113 Cu 40 5 × 5.5 rh. pins6 20 1.6Guglielmini et al . (1996) Misale et al . (1999) Guglielmini et al . (2002)

HT55 FC-72 Cu 30 × × 0.4, 0.8 sq. pins 3 0.4, 0.8 51–203 0 × × ×

Fantozzi et al . (2000) HCFC141b Al 30 × 2 rect. plates 2, 5, 10 2 101 0 × × ×Rainey and You (2000) Rainey et al . (2003) FC-72 Cu7 10 × × 1 sq. pins 0–8 1 30–150 0–50 × × × ×

Heat Transfer RegimesCross SectionBase Area System

Fluid(s) Mat.StudyFins

Orient.

Notes: 1. fins penetrated into the liquid through an unheated base 2. heater size = 5 × 5 mm 3. also tested solid copper block with and without vertical holes (0.34–0.89 mm in diameter), all structures were nominally 1 mm thick 4. nominal ± 0.2 mm 5. hexagonal base 6. most rhomboid, some triangular, due to base shape 7. explored effects of highly polished, machine roughened, and microporous coated surface finishes


H

L

W

tδ

H

L

W

tδ Figure 1.3: Confined boiling configuration: a vertical array of parallel rectangular plates.

1.5 FOCUS OF THE CURRENT RESEARCH

The focus of this research is the pool boiling behavior of a vertical array of parallel

rectangular plates, as illustrated in Fig. 1.3. The gravity vector is taken to be parallel to

the plate length, L. This basic geometry has been chosen for its representation of 3-D

stacked die components and longitudinal plate fin heat sinks. (In the nomenclature of

Fig. 1.3, a plate fin heat sink would have a base area equal to L × W and a fin protrusion

height H, as shown in Fig. 7.1) Studies of natural convection boiling in vertical, parallel

plate channels available in the literature provide a starting point for an in-depth

experimental, analytical, and numerical investigation of the complex, two phase,

buoyancy-induced flow expected in the inter-plate spaces and resulting heat transfer rates

from the confining surfaces.


The research is focused on determining:

1. the effect of confinement on nucleate boiling heat transfer rates

2. a methodology for identifying spacings at which the growing vapor fraction in the

channel threatens to result in channel dry out (CHF) and heat transfer degradation

3. implications for the thermal management of 3-D chip stacks

4. processes for the design and optimization of boiling heat sinks to effectively

exploit and/or mitigate the effects of geometrical confinement

As the parametric domain of interest is focused on applications in the thermal

management of electronic devices, the dielectric liquid FC-72 is employed in typical

microelectronics-scale experimental parallel plate channels. Experiments are performed

to explore the effect of channel geometry on the boiling process and to quantify the

amount of heat transfer enhancement or degradation observed, compared to unconfined

pool boiling. Theoretical analyses of the experimental configurations are then pursued to

assist in the explanation of observed empirical trends and facilitate the design and

optimization of confined boiling structures.

1.6 ORGANIZATION OF THE DISSERTATION

With the motivational and introductory aspects of the work addressed in earlier sections

of this chapter, Chapter 2 continues the analysis of published studies to explore the

underlying physics and fundamental phenomena encountered in natural convection

boiling heat transfer in narrow vertical channels. Various enhancement models from the

literature are discussed. Thus, Chapter 2 lays the foundation on which experimental and

theoretical investigations, which comprise the core of this dissertation, have been built.

The experimental apparatus and measurement system are detailed in Chapter 3, complete

with detailed estimates of measurement errors and uncertainties. Results of the basic pool


boiling characterization experiments are presented and discussed in Chapter 4. These

experiments provide a baseline of comparison for the channel boiling experiments

described in Chapter 5. Additional effects of surface roughness and liquid subcooling are

included in both chapters. Chapter 5 also contains theoretical analyses of the effects of

confinement on nucleate boiling and CHF, including an exploration of relevant non-

dimensional parameters and potential enhancement mechanisms identified and discussed

in the literature.

In Chapters 6 and 7, data and correlations from the previous chapters are used to design

and optimize various confined immersion cooling structures. Both single and two phase

heat transfer analyses are performed for possible 3-D stacked die package configurations

in Chapter 6. Parallel plate boiling data and correlations are then combined with fin

conduction analyses to explore the heat transfer performance of longitudinal rectangular

plate fin heat sinks in Chapter 7. The results of general parametric studies are discussed,

and geometrical configurations that maximize total heat dissipation are identified.

Chapter 8 contains a summary of the key contributions of the dissertation.

Recommendations for future work are also presented.

Appendices A and B have been introduced earlier in this chapter and include

thermophysical property data for various fluids and a review of the boiling heat sink

literature, respectively. Appendices C, D, and E are related to the experimental system

and are referred to primarily in Chapter 3. Appendix F describes multiphase

computational fluid dynamics (CFD) simulations of buoyancy-driven saturated boiling in

narrow vertical channels developed to investigate potential channel enhancement

mechanisms, as discussed in Chapter 5. Appendix G details the finite element analysis

(FEA) input files employed in the heat sink optimizations of Chapter 7, and Appendix H

describes attempts to fabricate a silicon heat sink. Appendix I presents the channel

boiling curve data of Chapter 5 in tabular form.


1.6.1 Measurement Units

As both fundamental and applied research often utilizes work performed in a variety of

fields for a variety of applications, the importance of a consistent, coherent system of

measurement units is clear. Therefore, the International System of Units (SI) will be used

throughout this dissertation.

Common practice in much of the electronics cooling literature (particularly in the U.S.) is

to specify heat flux in derived units based on the centimeter (i.e. W/cm2). The

Semiconductor Industry Association's International Technology Roadmap for

Semiconductors (SIA, 2005), discussed in detail earlier in this chapter, employs

millimeters (W/mm2). While these units may be quite intuitive when dealing with

centimeter- and millimeter-scale devices, they are not SI units as recognized by leading

publishing standards, such as ASME Guide SI-1, ASME Orientation and Guide for Use

of SI (Metric) Units Ninth Edition (ASME, 1982), and IEEE/ASTM SI 10™-2002,

American National Standard for Use of the International System of Units (SI): The

Modern Metric System (ASTM, 2002). Thus, heat flux values will be based on the SI unit

of watts per square meter (W/m2). However, in an attempt to provide intuitive and

physically meaningful descriptions of the presented research, key measurements provided

in standard SI units will often be repeated in parenthesis with alternate units.

While the SI unit of thermodynamic temperature is the kelvin (K), both of the standards

referenced above also allow the use of degree Celsius (°C) for temperature and

temperature interval measurements. Kelvin is used exclusively in derived units that

contain temperature. Therefore, the SI unit of thermal resistance is kelvins per watt

(K/W). Area-specific thermal resistance, commonly referred to as “thermal impedance,”

should be given SI units of thermal insulance, Km2/W.


The standards noted above include conversion factors as well as detailed usage and style

notes. Unit prefixes are discussed, and preference is given to multiples or submultiples of

units which result in numerical values ranging 0.1–1000. Furthermore, prefixes which

represent 10 raised to a multiple of 3 (e.g. milli and kilo) are especially recommended.

Thus, millimeter is preferred over centimeter for length. In the description of the

experimental apparatus, the majority of which appears in Chapter 3, length measurements

are also provided in inches, as most of the hardware was designed in inches and

fabricated using British machine tools.

21

CHAPTER

TWO

NATURAL CONVECTION BOILING IN VERTICAL

CHANNELS

As discussed in relation to Fig. 1.3, the flow configuration of interest is a narrow vertical

parallel plate channel submerged in an otherwise undisturbed liquid. Single phase natural

convection of parallel plate channels, which represents the minimum performance limit

for pool boiling, is discussed in detail in Chapter 6. Boiling activity from heated channel

walls can be expected to produce axial quality and vapor fraction gradients, leading to

distinct two phase flow regimes. The presence of this vapor will increase fluid buoyancy

in the channel. When this happens and the rate of fluid circulation increases, enhanced

and/or deteriorated thermal performance relative to undisturbed pool boiling may be

observed. As boiling activity increases, the growing vapor fraction may eventually lead to

dry out at the heated surfaces, beginning at or near the channel exit and causing severe

heat transfer degradation. An understanding of these phenomena and, ultimately, the

explicit influence of channel spacing on heat transfer is desirable for use in the design

and optimization of confined boiling structures.

Chapter 2: Natural Convection Boiling in Vertical Channels 22 2.1 LITERATURE REVIEW SUMMARY

In addition to immersion cooling of electronics, confined boiling occurs in a variety of

applications, including cryogenics (Guo and Zhu, 1997), nuclear reactor cooling (Kang,

2002), shell and tube heat exchangers (Ulke and Goldberg, 1990), and steam power

generation (Tieszen et al., 1987). As a result, it has garnered considerable attention over

the past half decade. Ishibashi and Nishikawa (1969) explored relative effects of

confinement on saturated water and alcohol boiling in narrow vertical annuli, under

natural circulation conditions. Since this landmark study, numerous researchers have

explored heat transfer enhancement in boiling channels, tubes, and other confined

geometries. Table 2.1 presents a representative summary of studies of natural convection

boiling in vertical, parallel plate channels. The majority of these studies deal with

nucleate boiling and CHF characteristics of saturated water or R-113 in channels formed

by one heated copper wall and one insulated wall (asymmetric heating). In addition, most

of the channels studied were longer (L) than they were deep (H), potentially resulting in

the inclusion of edge effects and exaggerating the importance of side periphery

conditions. While the body of work represented in Table 2.1 is still quite varied, some

general observations and conclusions may be drawn and summarized as follows:

• At large channel spacings, δ, boiling behavior proceeds as in unconfined pool

boiling (i.e. the limit as spacing→∞).

• At progressively smaller channel spacings, increasing heat transfer enhancement

is seen in the low heat flux region of the nucleate boiling curve, while the high

flux region and, in particular, CHF remain unchanged.

• With still smaller spacings, and/or channel aspect ratios larger than 10,

deteriorated heat transfer (relative to pool boiling) is observed at high heat fluxes,

and CHF tends to decrease with channel aspect ratio (height/spacing) in a roughly

hyperbolic fashion (Monde et al., 1982). Enhancement continues to increase at

low heat fluxes.

Chapter 2: Natural Convection Boiling in Vertical Channels 23

• Eventually, enhancement in the low heat flux region reaches a maximum, after

which further reductions in channel spacing lead to reduced enhancement and,

subsequently, deteriorated heat transfer relative to unconfined pool boiling.

These studies are now discussed in detail.


Table 2.1: Summary of representative studies of natural convection boiling in vertical channels.

Length Depth Spacing Aspect Ratio Pressure

L (mm) H (mm) δ (mm) L /δ (kW/m2) (MPa)

Monde et al . (1982)

water ethanol R113

benzene

copper A 20, 35, 50 10 0.45–7.0 0–111 open all ONB – CHF 0.1 sat

Bar-Cohen and Schweitzer (1985b) water copper A, S 240 66 2–20 12–120 closed sides 60–224 0.1 sat

Fujita et al . (1987, 1988) water copper A 30, 120 30 0.15–5 6–800 open all, closed sides and bottom 15–400 0.1 sat

Xia et al . (1996) R113 semiconductive oxide S 56, 88,

128, 197 45 0.8–5 0–160 open all, closed sides

0.1 to CHF 0.1 sat

Guo and Zhu (1997) helium copper A 150, 220 35 0.4–1.5 100–440 closed sides 0.01–4 0.1 sat

Bonjour and Lallemand (1997, 1998) R113 copper A 50, 120 20, 60 0.3–2.5 0–167 open all 0–300 0.1–0.3 sat

Chien and Chen (2000) methanol HFC4310 copper3 A 1, 2, 25 2.2–55 open all 30–160 sat 75.5°C

Fluid(s)StudySym / Asym1 Peripheral

Boundary

Heat FluxHeater Surface

Material

SystemChannel Details2

55 mm diameter circular disk

Temp.

Notes: 1. Relates to heating condition: Symmetric = both channel walls heated, Asymmetric = one wall heated, one insulated 2. See Fig. 1.3 for an illustration of the channel geometry and definition of geometrical parameters. 3. The authors explored various surface treatments, including: ground, sanded, horizontal and vertical V-shaped grooves, and a #80

mesh cover.


2.2 MONDE et al. (1982)

Monde et al. (1982) performed an extensive study of and developed a generalized

correlation for Critical Heat Flux (CHF) in asymmetrically heated vertical parallel plate

channels. CHF data was obtained for water, ethanol, R113, and benzene in 10 mm deep

rectangular channels formed by a copper heater and an opposing glass plate. Channel

lengths of 20, 35, and 50 mm and spacings in the range of 0.45–7.0 mm were

investigated, providing channel aspect ratios, L/δ, from 3 to 120.

Nucleate boiling data showed a slight enhancement of boiling heat transfer with

decreasing channel spacing. This enhancement was most prominent at low heat fluxes, as

the boiling curves tended to merge in the high flux region approaching CHF. For all

liquids and channel configurations, CHF remained relatively constant for channel aspect

ratios, L/δ, less than 10. As channel aspect ratios increased, CHF values decreased in a

roughly hyperbolic fashion. The authors observed that CHF occurred when a dry patch

formed near the channel exit and grew toward the channel entrance.

Based on the forms of a number of CHF correlations available in the literature, Monde et

al. (1982) developed the following correlation for CHF during natural convection boiling

in vertical rectangular channels submerged in saturated liquid when L/δ > 10.

( )( )16.0

g

f441gfgfgCHF 107.61g

−

−

×+−=′′

δρρρρσρ LKhq (2.1)

Clearly, as the channel aspect ratio goes to zero (unconfined, isolated heater), this

equation reduces to the form of the well-known Kutateladze-Zuber (Zuber, 1958)

correlation for pool boiling critical heat flux (CHF), Eq. (1.5), with K = π/24 = 0.13.

Monde et al. (1982) found that K was roughly scattered between 0.12 and 0.17 for the

data considered and uses an “average” value of 0.16.


Figure 2.1 contains a graph of Eq. (2.1) for the various fluids listed in Table 2.2. The

thermophysical properties of R113 and R12 are quite close, and, therefore, R12 results

were omitted from the graph. Here heat flux for a given channel aspect ratio has been

normalized by its value in the limit where L/δ→0 to better show the relative effects for

each fluid. The correlation agrees with the majority of the authors’ data for all four fluids

studied within ± 20%. The authors also compared their correlation to the experimental

data of Ogata et al. (1969) for liquid helium. The correlation overpredicted this

experimental data by approximately 50%. It is argued that the inability of Eq. (2.1) to

predict the liquid helium data comes from the fact the values of the parameter grouping

under the fourth root and the density ratio ρf/ρg for helium are far outside the range of the

four fluids used for the development of the correlation. However, as shown in Table 2.2,

while these quantities are relatively similar for ethanol, R113, and benzene, water and

helium both stand out as having properties significantly different from the rest of the

group, though at opposite parametric ends. Regardless, Eq. (2.1) appears to be quite

suitable for typical organic refrigerant fluids in near-room temperature applications.

Table 2.2: Comparison of property groupings used in the Monde et al. (1982) correlation

for CHF in vertical rectangular channels, Eq. (2.1), for various fluids at saturated

conditions.

h fg ρ f ρ g σ

×103

(kJ/kgK) (kg/m3) (kg/m3) (kg/s2)FC-72 85 1620 13.4 8.3 3.4 121ethanol 846 757 1.44 18 3.4 526R113 147 1511 7.38 16 3.9 205R12 165 1488 6.32 16 3.9 235benzene 393 877 2.7 23 3.8 325water 2257 958 0.6 59 4.8 1608helium 24 125 16.89 0.35 0.8 7

ρ f/ρ gFluid ( )( ) 41gfg ρρσ −


0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100

Channel Aspect Ratio, L /δ

Red

uced

Cha

nnel

CH

F R

atio

heliumFC-72R113benzeneethanolwater

Figure 2.1: Effect of channel aspect ratio on CHF—Monde et al. (1982) correlation,

Eq. (2.1), normalized by wide channel limit (L/δ→0).

2.3 BAR-COHEN AND SCHWEITZER (1985b)

In flow boiling heat transfer, the two phase heat transfer coefficient is typically

correlated, following Chen (1963), as

bc hhhTP γφ += (2.2)

where the heat transfer coefficients hb and hc are obtained from standard nucleate boiling

and forced convection correlations, respectively. The enhancement factor φ represents the

increase in heat transfer due to the high-velocity flow of the vapor core. Likewise, a

suppression factor γ is used to represent the suppression of nucleate boiling in high-

quality annular flows as the liquid layer thins at the wall. These factors were obtained

empirically by Chen (1963) for water/steam mixtures.


Unlike traditional forced flow boiling situations, in the case at hand channel flow arises

from density differences between the two phase mixture in the channel and the ambient

liquid. Despite this phenomenological difference, Bar-Cohen and Schweitzer (1985b)

sought an analytical model for boiling heat transfer and buoyancy-induced flow in

vertical, isoflux, parallel plate channels in the form of Eq. (2.2). The authors based their

correlation on experimental data for a 240 mm high by 66 mm wide channel in saturated

water. Symmetric and asymmetric heating conditions were explored for channel spacings

ranging from 2 to 15 mm.

In developing their analytical model for thermosyphon boiling in vertical, parallel plate

channels, Bar-Cohen and Schweitzer (1985b) set the boiling suppression factor, γ in

Eq. (2.2), equal to 1 (i.e. no suppression), based on experimental observations of the

presence of nucleate boiling throughout the parametric ranges investigated. The authors

then sought a correlation for the forced convection correction factor, φ. In their forced

convection model, the thermosyphonic mass flux, G, is determined by equating the in-

channel pressure drop for saturated two phase flow in a uniformly heated channel, a

combination of shear stress, fluid acceleration, and hydrostatic terms, expressed as

( ) ( )

( )

( )gLgL

xxLg

SxSxG

Lx

x

DGC

P

LL

LL

L

L

e

fr

g

f

gff

g

f2

g

f

g

fgf

f

g

f

gf

2

f

g

3

f

g

f2

channel

S1

11S

lnS

1

S

11S

1S

1

1S

3

11S

12

υυρρ

ρ

υυ

υυ

υυρρ

υυ

υυ

υ

υυυ

υυ

+

−−+

+

−

−

−+

−+

−+

−−+

−

−

−+

=∆

(2.3)


with the static pressure difference between fluid inside and outside the channel

( )( )[ ]gLP fgggfstatic 1 ραραρ −+−=∆ (2.4)

Here the hydraulic diameter for a wide, rectangular channel is De = 2δ. The exit flow

quality for a channel of length L with saturated incoming liquid is

fg

2hGLqxL δ′′

= (2.5)

and

fghG

LqxL δ′′

= (2.6)

for symmetric (both walls heated) and asymmetric (one wall heated, one wall insulated)

channels, respectively.

One of the major assumptions of the Bar-Cohen and Schweitzer (1985b) formulation is

that two phase flow in the channel could be represented by an axially invariant slip ratio,

S, defined as the ratio between the average velocities of the vapor and liquid phases.

f

g

uu

S ≡ (2.7)

Bar-Cohen and Schweitzer (1985b) found that a slip ratio of 17 best correlated their

experimental results. Given this definition of S, the vapor fraction at a location z in the

channel can be expressed as

1

g

fg 111

−

−+=

zxS

υυα (2.8)

This equation can be integrated to yield the height-averaged vapor fraction

L

dzzq

hGS

L

∫−

−

′′+

= 0

1

fg

g

f

g

12

1δ

υυ

α (2.9)

for a symmetrically-heated channel, or


L

dzzqhG

SL

∫−

−

′′+

= 0

1

fg

g

f

g

11δ

υυ

α (2.10)

for the asymmetric case. Flow quality and void fraction are key parameters in

determining the thermosyphon dry-out limit as the channel spacing narrows or the heat

flux increases.

With a method for determining the thermosyphonic mass flux, G, in hand, Bar-Cohen and

Schweitzer (1985b) were able to develop an appropriate forced convection heat transfer

coefficient and experimentally correlate its associated correction factor, φ. Based on the

similarity of the near-uniform velocity in the core and sharply changing gradient in the

thin liquid film near the wall to the single phase fully developed turbulent velocity

profile, Bar-Cohen and Schweitzer (1985b) employed a conventional (single phase)

forced convection correlation with a newly-defined two phase Reynolds number. This

two phase Reynolds number is based on the average fluid velocity in the channel,

expressed as

( )ffg υυυ +== xGGu (2.11)

yielding

+≡

ff

fgTP

21Reµδ

υυ

xG (2.12)

Consistent with the notion that the wall shear stress is governed by the liquid film

properties, the dynamic viscosity of the liquid phase, µf, is used in Eq. (2.12). Inserting

this definition of the two phase Reynolds number in the standard McAdams correlation

for turbulent convection, the height-averaged heat transfer coefficient becomes

8.0

fgf

4.0f

fc

4Pr00640

′′=

hLqk.h

µδ (2.13)

and


8.0

fgf

4.0f

fc Pr00640

′′=

hLqk.h

µδ (2.14)

for symmetrically and asymmetrically heated channels, respectively.

Then, Bar-Cohen and Schweitzer (1985b) sought a correlation for the forced convection

correction factor, φ, of the form

( )[ ] D

L

CB

xLgA

−=

δδρρσ

φ21

gf (2.15)

where A, B, C, and D are arbitrary constants. The correction factor was determined to be

independent of the channel aspect ratio L/δ, and the authors then fit values of the

remaining correlating constants. Unfortunately, the original correlation development

contains previously undetected errors. A closer inspection of the reduced data

(Schweitzer, 1983) reveals, among other errors, an order-of-magnitude over-reporting of

experimental φ values. Taking the corrected data and recorrelating the forced convection

correction factor yields the following:

( )367.0

f

55.0

2gf

253.08336.0−

−

−=

µδ

δρρσφ G

gxL (2.16)

An additional factor of (Gδ/µf) has been included to better capture the effect of wall heat

flux throughout the range of channel spacings. Figure 2.2 shows how this new correlation

compares with the corrected experimental data of Schweitzer (1983).

Thus, the updated forced convection correction factor, Eq. (2.16), can be substituted into

Eq. (2.2) (with γ=1) to provide the full two phase heat transfer coefficient relation.

( )

( ) ( ) 11satw

1

fg

pgffgf

c

367.0

f

55.0

2gf

253.0TP

Pr

8336.0

−

−−

−

−+

−=

r

r

sfs

L

TTCh

cgh

hGg

xh

σρρ

µ

µδ

δρρσ

(2.17)


0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 2 4 6 8 10 12 14 16

Channel Spacing, δδδδ

(mm)

φφφφ

4171109131175207Eq. (2.16)

q " (kW/m2)

Figure 2.2: Comparison of forced convection correction factors: Schweitzer (1983) data

and Eq. (2.16).

where hc is obtained from Eq. (2.13) or (2.14), and the second term on the right comes

from the familiar Rohsenow (1952) correlation for nucleate pool boiling, Eq. (1.4).

Figure 2.3 shows how this two phase heat transfer coefficient correlation, Eq. (2.17),

compares with the experimental two phase heat transfer coefficients reported by Bar-

Cohen and Schweitzer (1985b) for the symmetrically heated channel. While the

agreement between Eq. (2.17), and the experimental data shown in Fig. 2.3 is imperfect,

the correlation does follow the general trends of unenhanced pool boiling at large channel

spacings and increasing two phase heat transfer coefficient with decreasing channel

spacing. At small channel spacings, the correlation appears to be increasingly accurate, as

the various assumptions adopted in the development of the forced convection heat


transfer equations become more appropriate. It is this region which is of primary interest,

as heat transfer enhancement is obtained while, at the same time, channel volume is

minimized. Bar-Cohen and Schweitzer (1985b) showed that the Chen (1963) correlation

does not display the general trend seen in the data, and the Bjorge et al. (1982)

correlation severely under predicts heat transfer, even in the large channel spacing limit.

0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5 6 7

Channel Spacing, δδδδ (mm)

Hea

t Tra

nsfe

r Coe

ffici

ent,

h (k

W/m

2 K)

19360Eq. (2.17)

q " (kW/m2)

Figure 2.3: Comparison of two phase heat transfer coefficient correlation, Eq. (2.17),

with the experimental data of Bar-Cohen and Schweitzer (1985b) for symmetrically-

heated 240 mm high by 66 mm wide channels submerged in saturated water.


2.4 FUJITA et al. (1987, 1988)

Fujita et al. (1988) present the results and analysis of a wide variety of experimental

investigations of natural convection boiling of saturated water at atmospheric pressure in

asymmetrically heated rectangular parallel plate channels. These channels were formed

between a 30 mm wide heated copper surface and an opposing unheated glass plate.

Channels, 30 and 120 mm in length with spacings of 0.15, 0.6, 2.0, and 5.0 mm, were

characterized with a variety of periphery conditions.

With decreasing channel spacing for large and intermediate spacings, Fujita et al. (1988)

observed a distinct shift of the experimental boiling curves toward smaller superheats.

However, at heat fluxes approaching CHF this enhancement was less evident as the

boiling curves tended to merge. In the case of the 0.6 mm spacing for the 120 mm long

channel with closed side and bottom periphery and the 0.15 mm spacing (all lengths and

periphery conditions) some enhancement was evident at low heat fluxes. However, at

intermediate and high heat fluxes, the restriction of liquid and vapor flow in the channel

led to deteriorated heat transfer performance (compared to unconfined pool boiling). CHF

occurred at significantly larger superheats and severely reduced heat flux levels.

Fujita et al. (1988) saw no significant effect of channel height on boiling heat transfer

performance for channels with an open periphery. For channels with closed sides and

bottom, the longer, 120 mm channels showed deteriorated heat transfer performance,

when compared to the 30 mm long channels, only for 0.6 mm and 0.15 mm spacings.

Results for the heater length effect on channels with only closed sides were not given.

The effect of channel inclination on heat transfer performance was explored for close-

sided, 120 mm long channels. No significant difference was observed between vertical

channels (inclined 90°) and those inclined 150°, regardless of channel spacing. The 5 mm

spaced channel inclined 175° (nearly horizontal), with the heated surface facing down,

showed significant enhancement in heat transfer, as buoyancy forces pressed bubbles


against the heated surface. Evaporation of the thin liquid film between the bubble and

heated wall is assumed to provide the enhancement. This heat transfer mechanism is

discussed and quantified below in the context of the 0.6 mm and 2.0 mm spaced vertical

channels. For channel spacings less than 5 mm, channel inclination of 175° leads to

slower moving bubbles, more vapor accumulation, and, subsequently, deteriorated heat

transfer performance.

Based on photographic evidence of the different types of bubble behavior present for

large (5.0 mm), moderate (2.0 mm, 0.6 mm), and small (0.15 mm) channel spacings,

Fujita et al. (1988) sought to correlate the results of these experiments separately by

bubble flow regime. Fujita et al. (1987) presented a predictive methodology for “large”

spacings, where bubble size is smaller than the channel spacing. In this case, bubble

behavior and the shape of the boiling curves appear as in unconfined nucleate boiling.

Their correlation is based on a horizontal tube bundle model that combines the individual

contributions of bubble generation and bubble motion to wall heat transfer near bubble

nucleation sites and on the remaining surface area, respectively. As a result, the relevant

equations depend on bubble generation frequency and departure diameter which must be

evaluated experimentally for a given surface. Further, in order to apply this correlation,

the heater surface must be divided up into a large number of horizontal segments,

approximating a tightly packed stack of horizontal tubes. The heat transfer at each

segment is calculated separately as a combination of bubble generation at that segment

and convection produced by rising bubbles from the segments below. The authors

achieved good agreement for the open periphery channel by dividing the heater surface

into 100 calculation segments. The closed periphery (sides and bottom) channel showed

evidence of additional convective enhancement, due to the three-dimensional nature of

fluid and vapor flow in the confined space.

At channel spacings of 2.0 and 0.6 mm, isolated bubbles were larger than the channel

spacing and were deformed by the channel walls. The high levels of heat transfer


enhancement attainable in this regime were attributed to thin film evaporation taking

place between the flattened bubble and heater surface. This explanation is further

supported by the visual observation that bubbles grew rapidly as they proceeded up the

channel. At high heat fluxes, vapor accumulated near the channel exit, reducing the effect

of this enhancement. For a given location in the channel, in the short amount of time

between bubble passage events, τf, the sensible heat removed by the liquid phase may be

calculated as one-dimensional transient conduction into the semi-infinite liquid

ff

satff

2τπaTkq ∆=′′ (2.18)

where kf and af are the thermal conductivity and diffusivity of the liquid, respectively.

Equation (2.18) is strictly only applicable when transient conduction in the solid heater is

significantly more effective than conduction in the liquid. Given that the diffusivity of

copper is nearly 700 times that of water, this is a reasonable assumption. During the

bubble passage time, τg, the thin film between the bubble and heater surface evaporates.

This evaporative heat transfer can be expected to be dominated by conduction through

the film, expressible as

satf

g Tdkq ∆=′′ (2.19)

where d is the thickness of the liquid film. Thus, the time-averaged heat flux from the

heater surface can be expressed as

( ) gfgf

ggff 1 qqqq

q ′′+′′−=+

′′+′′=′′ αα

ττττ

(2.20)

where α is the void fraction in the channel.

Fujita et al. (1988) measured film thicknesses between a non-heated surface and rising air

bubbles. In addition, electrical resistivity probes were used to measure τg and τf at three,

vertically-spaced locations in the heated channel. With these quantities determined

experimentally, the researchers were able to use the equations above to predict their

experimental data for 0.6 mm and 2.0 mm spaced channels. Decent agreement (± 30%)


was obtained for the 2 mm spacing, while the data was severely over predicted for δ =

0.6 mm. These results agree with the visual observation that there were some spots on the

heater at the smaller spacing where the liquid film between the bubble and heater surface

had completely evaporated, leading to deteriorated heat transfer.

For channel spacings of 0.15 mm, the majority of the heated surface was covered by

vapor with wetted areas only near the open edges. Fujita et al. (1987) showed that the

large copper block heater surface was quite isothermal, even with such drastically

different heat transfer mechanisms taking place in the dry and wetted areas. The authors

do not attempt to predict heat transfer rates for this small channel spacing.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

0 2 4 6 8 10 12 14 16


∆∆ ∆∆T

sat/ ∆∆ ∆∆

Tsa

t( δδ δδ→∞

)

207

162

92

207

162

92

q " (kW/m2)

Schweitzer (1983)

Fujita et al . (1988)

Figure 2.4: Comparison of Schweitzer (1983) and Fujita et al. (1988) experimental data

for boiling of water in asymmetric channels, showing variation of normalized boiling

surface superheat with channel spacing.


Figure 2.4 shows a comparison the experimental data for asymmetrically heated, closed

side channels obtained by Schweitzer (1983) and Fujita et al. (1988). In this graph, the

boiling surface superheat, Tw-Tsat, is normalized by the superheat observed for

unrestricted nucleate boiling, i.e. ∆Tsat(δ = 15 mm). Presenting the data in this manner

factors out the individual nucleate boiling behaviors of these systems (very much

dependent on heater surface characteristics) and allows for direct comparison of the

enhancements observed. With the exception of the low heat flux data near δ = 5 mm, both

sets of data show the same type and level of boiling enhancement. It is interesting to note

that the channels employed in the Schweitzer (1983) study are twice as long as that used

to obtain the Fujita et al. (1988) data, L = 240 mm and 120 mm, respectively. Thus, a

comparison similar to that of Fig. 2.4 based on channel aspect ratio rather than channel

spacing would not show good agreement between the two sets of data. A similar lack of

dependence on channel length was also observed by Fujita et al. (1988) while comparing

open side channels 120 mm and 30 mm in length. However, given the open side

condition and fact that the 120 mm long channel is only 30 mm deep, significant

inflow/outflow at the periphery can be expected, and the observed independence on

channel length is not unexpected. Closed side channel data was not available for the

shorter, 30 mm long channels.

2.5 GUO AND ZHU (1997)

Guo and Zhu (1997) measured enhanced boiling of liquid helium at atmospheric pressure

in narrow, vertical, asymmetrically heated channels formed between heated copper

blocks and opposing acrylic plates. Channels 150 and 220 mm in length and 35 mm deep

were characterized, and channel spacing was varied from 0.4 to 1.5 mm. The copper

boiling surfaces were treated with 600 mesh emery paper and washed with alcohol prior

to each experimental run.


The authors observed significantly enhanced boiling at heat fluxes less than 1 kW/m2. At

larger channel spacings, enhancement was attributed to confined bubbles sweeping the

heated surface and prematurely releasing smaller growing bubbles in their path. At

channel spacings smaller than characteristic bubble departure diameters, flattened

bubbles were presumed to fuse with adjacent bubbles as well as depart from their

nucleation sites earlier than if unconfined, leading to higher departure frequencies and

enhanced heat transfer. The authors expect thin film evaporation was dominant at the

smallest spacings and highest heat fluxes.

A distinct dependence on channel length was observed across the entire range of heat

flux. CHF trends identified elsewhere in the literature were confirmed. Channel dry-out

occurred at lower heat fluxes for longer channels and with reduced channel spacing. At

low heat fluxes, higher heat transfer rates were obtained with the longer channels.

However, the authors defined the relevant temperature difference as that between the

surface and the local fluid in the channel, rather than the inlet saturation temperature.

They reported that local fluid temperatures were elevated with respect to saturation and

unstable, though quantitative data is not provided.

2.6 XIA et al. (1996)

Xia et al. (1996) investigated confinement effects on natural convection boiling in

symmetrically heated vertical parallel plate channels. Degassed saturated R113 (at

atmospheric pressure) was employed as the working fluid. Channel walls were formed by

plating the surface of two different types of substrates with an extremely thin (< 1 µm)

transparent layer of a semi conductive oxide. Transparent quartz substrates were

employed to facilitate flow visualization, while porcelain (95% Al2O3) substrates were

required for the measurement of boiling surface temperatures. Films were created in

lengths of 56, 88, 128, and 197 mm on 45 mm wide substrates. Spacers 0.8, 1.5, 3.0, and


5.0 mm thick defined the available channel spacings. In addition, experiments were run

with a single heated surface and a 10 mm gap, which the authors refer to as unconfined

pool boiling and denote as δ = ∞. Both closed and open side periphery conditions were

explored.

Enhanced heat transfer was observed with decreasing channel spacing at heat fluxes

below 30 kW/m2. Channel length effects on low flux boiling enhancement are presented

for a channel spacing of 1.5 mm. While boiling curves for the 88 mm and longer channels

are relatively coincident, 56 mm long channels show a greater than 10% increase in heat

flux compare to the other channels at a given wall superheat. Unfortunately, it is unclear

whether these results are for open or closed side channels. At high heat fluxes, CHF is

observed to decrease with decreasing channel spacing and increasing channel length. The

authors fit a correlation similar to that of Monde et al. (1982), Eq. (2.1), CHF, to their

experimental results with a stated accuracy of ±10%. Unfortunately, there are some

inconsistencies in their CHF data. First, the highest value of CHF obtained, 380 kW/m2

(38 W/cm2) with a 56 mm long heater and 10 mm gap, is 90% higher than CHF predicted

for R113 using the Kutateladze-Zuber CHF correlation, Eq. (1.5). In addition, as

discussed in detail Chapter 4, the extreme thinness of the heater and low thermal

conductivity of the substrates should, if anything, lead to CHF less than that predicted by

Eq. (1.5). Furthermore, the few CHF data points shown for channels with aspect ratios

near or below 10 have widely different values, suggesting that asymptotic, unconfined

behavior was not achieved. All of these issues call into question the experimental

apparatus and, potentially, procedure. Characteristics of the unique heater construction

deserve further scrutiny.


2.7 BONJOUR AND LALLEMAND (1997, 1998)

Bonjour and Lallemand (1997), expanding on the work of Monde et al. (1982), explored

CHF of R113 in asymmetrically heated, 50 mm long by 20 mm deep channels over a

pressure range of 0.1–0.3 MPa and channel aspect ratios approaching 170. In addition to

the channel spacing and aspect ratio trends observed by Monde et al. (1982), the authors

observed an increase in CHF with increasing pressure. For unrestricted pool boiling of

the vertical heater, increasing pressure from 0.1 to 0.3 MPa produced an increase in CHF

of 40%. This increase is identical to that predicted using the Kutateladze-Zuber

correlation, Eq. (1.5). For the smallest channel spacing investigated, δ = 0.3 mm, L/δ =

167, CHF increases by only 20% at 0.3 MPa. Thus, the pressure effect on CHF was

observed to be less effective in narrow channels, and increasing pressure could not

compensate for the decrease in CHF at small channel spacings.

In order to account for observed pressure effects, Bonjour and Lallemand (1997)

introduce a corrective term based on the reduced pressure, Pr = P/Pcrit, and present their

recorrelation of Eq. (2.1) as

( )

1517.1343.1

g

f541

2g

gffgg

CHF

252.0

1039.61g

−

−

×+=

−

′′δρ

ρ

ρρρσ

ρ

L

hK

qrP

(2.21)

The authors found an average value of K = 0.134, well in accordance with the

Kutateladze-Zuber (Zuber, 1958) correlation. The new correlation agrees with the authors

own data within ± 5% and that considered by Monde et al. (1982) for ethanol, R113, and

Benzene within ± 12%. The authors did not compare Eq. (2.21) with the Monde et al.

(1982) results for water, claiming there was too much scatter in this set of data.

Figure 2.5 shows a graph of Eq. (2.21) for the same fluids considered in Fig. 2.1.


0.0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100

Channel Aspect Ratio, L /δ

Red

uced

Cha

nnel

CH

F R

atio

heliumFC-72R113benzeneethanolwater

Figure 2.5: Effect of channel aspect ratio on CHF—Bonjour and Lallemand (1997)

correlation, Eq. (2.21).

In a subsequent study, Bonjour and Lallemand (1998) considered flow patterns and

boiling regimes in somewhat longer channels, 120 mm vs. 50 mm previously. Boiling

regimes were mapped based on Bond number, Bo, and the ratio of heat flux to CHF at a

given spacing, q”/q”CHF,δ. The Bond number is a function of the difference in density

between liquid and vapor phases and surface tension and relates channel spacing to the

bubble departure diameter. The Bond number is discussed in detail in Section 5.4. For

reduced heat flux q”/q”CHF,δ less than 0.2, Bonjour and Lallemand (1998) observed small

isolated bubbles. As channel spacing was decreased, corresponding to Bond numbers

near and below 1, individual bubbles were flattened and deformed but remained isolated

from each other. When the reduced heat flux was between 0.2 and 0.7, larger bubbles

were observed during unconfined boiling than at lower fluxes. For narrow channels

(Bo ≤ 1) at these intermediate heat fluxes, these larger bubbles interfere and become even

larger coalesced bubbles. At high heat fluxes near CHF, q”/q”CHF,δ greater than 0.7, large


bubbles or vapor mushrooms observed during unconfined boiling led to partial dry-out at

narrow channel spacings.

2.8 CHIEN AND CHEN (2000)

Chien and Chen (2000) investigated pool boiling from a vertical 55 mm diameter copper

disk in saturated methanol and HFC4310 at 75.5°C. To achieve saturated conditions,

system pressure was set at 160 and 201 kPa for methanol and HFC4310, respectively.

Channels were formed using an opposing glass plate, with spacings of 1, 2, and 25 mm.

The authors explored various surface treatments, including polishing with a grinding

wheel, sanding with #1200 emery paper, horizontal and vertical V-shaped grooves, and a

#80 mesh cover. The V-shaped grooves were 0.5 mm deep and had a 45° included angle.

Angle pitch was 1.25 mm, providing a 27% area increase over the ungrooved surface.

Boiling results for the mesh covered surfaces were in inconsistent, due to varying degrees

of contact between the mesh and copper surface. However, it is clear that with proper

attachment, some enhancement could be achieved. During unconfined pool boiling

(δ = 25 mm), the surface with the horizontal V-shaped grooves performed best, followed

closely by the surface with the vertical grooves. The sanded and ground surfaces showed

similar performance to each other below approximately 70 kW/m2, while at higher heat

fluxes the sanded surface performed better. At the highest heat fluxes investigated, near

160 kW/m2, the sanded surface was comparable to the surface with the horizontal

grooves.

The general trends discussed in the previous paragraph were similar for both fluids. The

surface with horizontal grooves provided very similar performance in both fluids, while

the ungrooved surfaces performed better in HFC4310. While not discussed by the

authors, if the measured heat fluxes are modified to account for the additional surface


area provided by the grooves, HFC4310 boiling curves for the grooved surfaces fall right

in line with the flat ground surface. In methanol, however, the surface with the horizontal

grooves still outperformed the flat surfaces at all but the highest heat fluxes.

Unlike the other channel studies discussed in this chapter, inclusion of the opposing glass

plate, with 1 and 2 mm spacings, yielded consistently, though subtly degraded

performance compared to unconfined boiling, for all surfaces and at all heat fluxes.

Degradation was more significant for the grooved surfaces. Overall module effects may

be the reason for this degradation. The internal dimensions of the liquid-filled apparatus

were 30 × 80 × 120 mm, and the opposing glass plate appears to be significantly longer

than (approaching twice) the boiling surface, according to the illustration of Chien and

Chen (2000). If the glass plate was, indeed, nearly as large as the internal space, gross

circulation of liquid in the module may have been impeded.

With a 1 mm spacing in methanol, coalesced bubbles were observed over much of the

heat flux range. Coalesced bubbles were never observed in HFC4310. Dry-out/CHF was

not observed in any of the experiments. Saturated fluid properties for methanol appear in

Table 2.3. Using the Kutateladze-Zuber correlation, Eq. (1.5), CHF of 643 kW/m2 is

predicted for saturated methanol at 75.5°C. Thus, the highest heat fluxes obtained in the

experiments were only 25% of CHF. Bond number, calculated with Eq. (5.3) at a variety

of different channel gap spacings, δ, also appear in Table 2.3. In addition to Bonjour and

Lallemand (1998), as previously mentioned, Yao and Chang (1983) and Kew and

Cornwell (1997) also identify Bo = 1 as the transition between confined and unconfined

behaviors. Based on the results shown in Table 2.3, it would appear that this transition

occurs in the methanol experiments of Chien and Chen (2000) between the 1 and 2 mm

gap sizes employed. Thus, it is not surprising that coalesced bubbles were observed with

a 1 mm spacing even in this low heat flux range, 5–25% of unconfined pool boiling CHF.

Still, it is interesting that no enhancement of boiling heat transfer was observed.


Table 2.3: Saturated fluid properties and Bond number results for methanol and

HFC4310.

methanol HFC4310

Pressure (MPa) 0.154 0.101 methanol HFC4310Saturation Temperature (°C) 75.5 40.2 0.5 0.1 0.3Liquid Density (kg/m3) 737 1580 1 0.4 1.1Surface Tension (N/m) 0.018 0.014 2 1.6 4.4Vapor Density (kg/m3) 1.82 5 10 27Heat of Vaporization (kJ/kg) 1079 130 25 251 687

Gap Size (mm)

Bond Number

Unfortunately, HFC4310 liquid properties at elevated pressures and vapor density at any

pressure were not available. However, assuming that the vapor density is small relative to

the liquid density so that the difference between them is approximately equal to the liquid

density, Bond number is calculated at 0.1 MPa (1 atm), and results appear in Table 2.3.

Even if operated at atmospheric pressure, the HFC4310 experiments of Chien and Chen

(2000) would be expected to behave similar to unconfined pool boiling. At nearly twice

this system pressure, 201 kPa, bubbles would be expected to be smaller, even more so

ensuring unconfined behavior. The authors observed smaller bubbles in HFC4310 than

methanol. It is clear from the Bond number trends shown in Table 2.3 that this is an

effect of the elevated pressure. Thus, no confinement-driven boiling enhancement would

be expected in these experiments.

46

CHAPTER

THREE

EXPERIMENTAL DESIGN

Unconfined pool boiling and channel experiments will be required to elucidate the

phenomenological aspects of channel boiling and provide heat transfer data and

correlations with which to design and predict the performance of boiling structures in

confined geometries. As the parametric domain of interest is focused on applications in

the thermal management of electronic devices, an experimental system was constructed

to facilitate the investigation of boiling heat transfer in parallel plate channels of typical

microelectronics dimensions. The basic foundation of the various experiments is the

same, and the following conditions should be assumed except where otherwise noted.

Tests were performed with degassed FC-72 at atmospheric pressure, with particular

attention paid to saturated conditions (Tbulk = 56.6°C). Heat transfer behavior will be

investigated from natural convection through CHF.

This chapter begins with a description of the liquid-filled module in which the

experiments were conducted. The construction and function of the silicon and aluminum

boiling surfaces are discussed next, followed by an overview of the entire experimental

system. This chapter ends with a description of the experimental measurements obtained

and estimates of experimental uncertainties.

Chapter 3: Experimental Design 47 3.1 EXPERIMENTAL MODULE

Figure 3.1 shows two views of the experimental module. The liquid-filled module was

formed from a 102 × 140 × 44 mm (4” × 5.5” × 1.75”) aluminum block. An 80 mm

(3.15”) square hole was machined through the thickness of the block to accommodate the

liquid volume. The enclosure is completed by 108 mm square, 6 mm thick (4.25” × 4.25”

× 0.25”) transparent polycarbonate walls bolted to the module and sealed with o-ring

gaskets. These walls served as the mounting surfaces for the various heater assemblies

used in the experiments. Figure 3.1a is a close-up of the module with a single, stationary

2 × 3 mm silicon heater. Figure 3.1b shows the support legs and condensers and includes

an adjustable heater positioning assembly, described in Section 3.2. Detailed schematics

and additional photographs appear in Appendix C.

Four 8 mm (0.332”) diameter water channels, two passing through each end of the

aluminum module, accept heated water to help maintain saturated liquid conditions.

Subcooled boiling experiments employed a water cooled heat sink replacing one of the

polycarbonate module walls. A 26 × 24 array of 2 × 2 mm square aluminum pin fins

extends 13.5 mm from the water cooled base into the module to aid in controlling the

bulk liquid temperature. Fin spacing is 1 mm. A few fins were removed from each corner

of the array to accommodate the radius of the internal module corners. Cooling water

from the module side wall channels is directed through a serpentine channel in the base

of this heat sink. The water cooled heat sink/wall is shown in Fig. 3.2.

Chapter 3: Experimental Design 48

Figure 3.1: The experimental module.

Figure 3.2: Photograph of the finned water cooled heat sink/module wall.

a b

Chapter 3: Experimental Design 49 The entire module is supported by two 305 mm (12”) high legs, 305 mm (12”) wide at

the base, with 4 adjustable feet to provide for leveling. Four 1.6 mm (0.062”) sheath

diameter bulk liquid thermocouples (type-T, Omega model TMQSS-062U-6) pass

through the end of the module via Swagelok pipe fittings with Teflon ferrules to allow for

positioning and subsequent repositioning within the module. Additional thermocouples

were installed in the water lines to monitor incoming and outgoing temperatures.

Fluid sampling and drainage ports were installed in the bottom of the module to facilitate

filling and draining the module and dissolved gas content measurements. The dissolved

gas content of the module liquid was measured using a Seaton-Wilson Aire-Ometer

(model AD-4003) air measuring instrument, with a measurement range of 4–100% by

volume. The FC-72 liquid could be degassed well below 4% by increasing the

temperature of the module control water above the saturation temperature and applying

power to the heaters. In order to prevent vapor losses (both during degassing as well as

normal operation), two 300 mm water cooled Allihn condensers were connected to nylon

pipe fittings installed in the top of the module via 150 mm (6”) long sections of 19 mm

(3/4”) I.D. Tygon C-544-A I.B. hose. This type of hose is recommended in Fluorinert™

materials compatibility literature (3M, 2002).

3.2 SILICON HEATERS

Silicon heaters, 20 × 20 mm and 20 × 30 mm in size, were employed in both single

surface and parallel plate channel experiments. The silicon heaters were fabricated out of

675 µm thick, double-side polished, doped silicon wafer with a measured electrical

resistivity of 0.0121 Ωm. In order to provide for adequate electrical contact, 10 µm thick

aluminum layers were deposited on opposing edges via DC sputtering performed in the

Microtechnology Laboratory (MTL) at the University of Minnesota. Custom holders

were fabricated out of aluminum to support stacks of silicon dies with only one edge

Chapter 3: Experimental Design 50 exposed. Thus, two sputtering runs were required to create aluminum electrodes on each

side. Pictures of the holders appear in Figs. C.12 through C.14.

The silicon heaters were secured to polycarbonate substrates (k = 0.2 W/mK) with quick-

setting epoxy. Small pockets, approximately 1 mm in from each heater edge, were

machined into the polycarbonate substrates in the area below the heaters to minimize heat

loss and accommodate a thin foil thermocouple (type-T, Omega model CO2-T) attached

in the center of the backside of the silicon with thermally conductive epoxy (Omegabond

101, k = 1.04 W/mK). Electrical contact was made between the edges of the silicon and

pairs of 0.3 mm (0.010”) thick brass electrodes via electrically conductive silver epoxy

(Epo-Tek H20S). The brass electrodes pass through the back of the polycarbonate

substrates and were connected to a DC power supply with 12-gauge copper wire.

Exposed edges of the heaters and brass electrodes were covered with quick-setting epoxy

to restrict heat loss to the top surface of the heaters and to prevent fluid leakage into the

substrate pockets.

Figure 3.3 shows one of the 20 × 20 mm heaters mounted on a module wall. While

current delivery was provided by crimp-on ring terminals bolted to the brass electrodes,

separate voltage measurement leads were soldered directly to the brass to eliminate

current carrier voltage drops from the measurement. Foil thermocouple leads were

covered with black heat shrink material to provide mechanical support and electrical

insulation. A subminiature connector mounted on the polycarbonate wall joined the

delicate foil leads to bulk thermocouple lead wire.


Figure 3.3: A 20 × 20 mm heater mounted on a polycarbonate module wall.

Figure 3.4: Silicon heater for moveable shaft assembly, 20 × 30 mm.


Figure 3.5: Experimental apparatus photograph including heater support shaft and

positioning screw assembly.

To create the desired parallel plate channel in a liquid medium, heaters were attached

directly to one of the fixed polycarbonate module walls, as well as to the end of a

moveable shaft shown in Figs. 3.4 and 3.5. A 102 mm (4”) long, 51 mm (2”) diameter

polycarbonate shaft passed through a 64 mm (2.5”) square block mounted on the outside

of the opposing wall. A pair of o-ring grooves and gaskets located in the middle of the

shaft maintained a tight liquid seal. A screw assembly facilitated precise positioning of

the shaft to create parallel plate channels with variable spacing. Channel spacings were

calculated from measurements of the shaft position. Reported channel spacings are

estimated to be accurate within ± 0.1 mm, based on numerous measurements from

various module reference surfaces as well as digital photographs of the interior of the

module taken through an observation window located on the bottom side, as shown in

Fig. 3.6.


Figure 3.6: View from underside of experimental module, 2 mm heater spacing.

In order to accommodate the bulky aluminum heater assemblies discussed in the next

section, some asymmetric channels were formed by using a single fixed heated surface

and a 20 mm high piece of polycarbonate. Its distance from the boiling surface was set by

layers of polyimide tape placed at the ends of its width. This arrangement was used for a

number of the asymmetric silicon channel experiments as well. All subcooled

experiments required this alternate channel arrangement due to the presence of the water

cooled heat sink discussed in the previous section. Identical results for asymmetric silicon

channels in saturated liquid were obtained when using a polycarbonate plate and a silicon

heater as the unheated opposing channel wall. Consequently, performance of experiments

using the polycarbonate wall also provided an additional means of validating the

accuracy of shaft position and channel spacing measurements.

Chapter 3: Experimental Design 54 3.3 ALUMINUM HEATER ASSEMBLIES

In addition to the silicon heaters described in the previous section, boiling experiments

were also performed on aluminum surfaces. Aluminum heater assemblies were fabricated

via electrical discharge machining (EDM). Figure 3.7 shows the two part heater

assembly. The heater unit was fabricated in two parts to allow the heater section to mate

with a variety of boiling surfaces. The boiling surface portion of the assembly consisted

of a 20 × 20 × 10 mm block of aluminum with a pair of short flanges for attachment to

the heater section. The boiling surface and heater sections were bolted together. Power

was supplied by a small cartridge heater (Watlow G1E99, 9.5 mm diameter, 31.8 mm

long, 39 Ω) which fit snugly into a deep hole in the heater section. Thermally-conductive

grease was applied to the surface of the cartridge heater as well as the interface between

the boiling surface and heater section. A thin foil thermocouple was attached to the side

of the assembly with thermally conductive epoxy (Omegabond 101, k = 1.04 W/mK),

with the sensing tip very near the boiling surface.

Figure 3.7: Aluminum heater assembly parts: a) boiling surface (EDM finish) with foil

thermocouple, and b) shaft with cartridge heater.

a. b.


Figure 3.8: Polished aluminum heater assembly in polycarbonate wall.

The heater assembly was epoxied into a square opening in one of the polycarbonate

module walls (Fig. 3.8). The bolt flanges helped align the boiling surface with the interior

of the module wall. Due to the physical size of the aluminum heater assembly the

aluminum heater experiments were limited to asymmetric heating and employed the

opposing polycarbonate channel wall discussed in the previous section. Unlike the silicon

heaters, most of the aluminum heater assembly was external to the module. The exposed

heater section was covered with two layers of 6.35 mm (1/4”) thick polyethylene foam

insulation (Owens Corning FoamSealR). Parasitic heat losses from both the silicon and

aluminum heaters are evaluated in Section 3.6.

Chapter 3: Experimental Design 56 3.4 EXPERIMENTAL SYSTEM

Figure 3.9 provides a pictorial representation of the entire experimental system. In

addition to the module and heater components already described, Fig. 3.9 also shows the

power delivery and signal gathering components. Cold facility water was supplied to the

pair of vapor condensers, while a user-controlled mixture of hot and cold water was

directed to the channels in the module edges. An in-line electric water heater was

required to increase the temperature of the hot facility water up to the saturation

temperature of the FC-72 in the module (56.6°C).

All thermocouples connect to screw terminals mounted on a pair of 100 × 150 × 6 mm

(4” × 6” × 0.25”) aluminum plates. Copper leads connect the screw terminals to a multi-

channel digital multimeter (Keithley, model 2000-20). The aluminum plates were bolted

together (using 30 mm standoffs) with the terminal sides facing each other. The terminal

sides of the plates were spray-painted black (ε ≈ 0.95) and the entire structure was

enclosed in multiple layers of thick insulation.

digital multimeter

computer w/data

acquisition software

digital multimeter

isothermalblock

thermocouples

ice bath

electric water heater

DC power suppliescold water to condensers

hot waterto module wall

immersionmodule scanner

shunt resistors

digital multimeter

computer w/data

acquisition software

digital multimeter

isothermalblock

thermocouples

ice bath

electric water heater

DC power suppliescold water to condensers

hot waterto module wall

immersionmodule scanner

shunt resistors

Figure 3.9: Pictorial representation of overall experimental system.


Figure 3.10: Photograph of the thermocouple terminal block.

The purpose of this terminal arrangement (shown in Fig. 3.10 with most of the insulation

removed) was to create an isothermal structure to maintain a uniform temperature for all

thermocouple connections and allow the use of a single 0°C ice bath reference. A pair of

thermocouples connected in series were secured to opposing corners of the structure.

Throughout all of the experiments performed, the differential temperature read by this

pair of thermocouples was less than 0.15°C, well within the manufacturer-specified

accuracy of all the thermocouples used in the experiment, ± 0.5°C.

When two heaters were used at the same time to provide a symmetrically heated channel,

each was powered separately. Thus, the experimental system included two DC power

supplies (Hewlett-Packard, models 6643A and 6032A). Heater voltage drop

measurements were made via sense leads discussed previously. Shunt resistors (Empro

Shunts models HA-5-50 and HA-2-50, 0.010 Ω and 0.025 Ω, respectively) were

connected to the ground side of the heater circuit to measure heater current. Heater power

is calculated as

senseshuntheater VIP ⋅= (3.1)

Chapter 3: Experimental Design 58 where

shunt

shuntshunt R

VI = (3.2)

Heater and shunt resistor voltage measurements were made through a multi-channel

scanner (Keithley, model 705) connected to a digital multimeter (Keithley, model 196).

Voltage and current measurements were verified by internal power supply readings.

Shunt resistors are guaranteed to be accurate within ± 0.25%, as long as they are installed

according to the following manufacturer guidelines. Shunt resistors were

• connected to the ground side of the heater circuit

• continuously operated at no more than two-thirds the rated current

• adequately ventilated and monitored to insure the managanin shunt strips stay

within an operating temperature range of 10 to 85°C

While joule heating will occur within the shunt resistors, and their resistance will vary to

some degree over the operating temperature range, the change in resistance is negligible

compared to the shunt resistor's overall accuracy (Empro, 2002).

Appendix D contains a detailed discussion of experimental techniques used for bubble

detection and other two phase flow measurements. Table D.1 is a qualitative comparison

of these techniques when applied to two phase flow. From this table as well as the

surrounding discussion, it is clear that thermal anemometry is a leading option for two

phase flow measurements in dielectric liquids. As a result, thermal anemometry was

explored as a method to measured flow characteristics in the boiling channel.

Proof-of-principle thermal anemometry experiments were performed using a TSI model

1210-60W hot film probe and model 1053b constant temperature anemometer. This

probe was recommended by TSI for liquid flows based on its relative durability. In order

to provide a consistent stream of bubbles, a common aquarium pump was used to

discharge air from the end of a tube located at the bottom of a pool of room temperature

Chapter 3: Experimental Design 59 FC-72. The inner diameter of the tube was approximately 2 mm, and the resulting bubble

diameter was on the same order, approximately three times larger than expected for

boiling-produced vapor bubbles (see Appendix F for bubble departure diameter

predictions). Pump speed was adjusted to provide a bubble period of approximately 1 s.

The probe was positioned 20 mm above the end of the tube, directly in the path of rising

bubbles.

Numerous difficulties were encountered during these preliminary anemometry

experiments. First of all, the hot film probe did not penetrate the bubbles. Oncoming

bubbles were simply deflected to one side or another. As a result, the anemometer bridge

output voltage signal did not match the typical bubble detection scenario described in

Appendix D. While fluctuations were produced in the anemometer signal, as shown in

Fig. 3.11, the peaks—corresponding to the passage of each bubble—reflected enhanced

heat transfer at the probe surface, due to enhanced liquid convection and/or thin film

evaporation, rather than a steep decrease in the heat transfer rate due to direct contact

with the vapor phase. While the probe was able to identify the passage of relatively large

bubbles in an undisturbed pool, the probability of quantitatively characterizing small

vapor bubbles in a highly agitated two phase mixture was deemed low. In order to get

discernable signals, it was also necessary to set the probe overheat ratio so that the probe

temperature was relatively high compared to the liquid saturation temperature. This led to

occasional film boiling events—accompanied by large temperature fluctuations—on the

probe itself which eventually damaged the probe sensor.


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 1 2 3 4 5 6 7 8 9 10

Time (s)

Brid

ge O

utpu

t Vol

tage

(V)

Figure 3.11: Output signal from a constant temperature hot film anemometer, with each

peak representing a bubble passage event.

In addition to the issues discussed above, the best available probes were relatively large

compared to the existing fluid enclosure. It was, thus, concluded that this technique could

not be employed in the current study, without significant modification of the

experimental apparatus and deviation from the system conditions and geometry of

interest. As a result, it was not possible to achieve an experimental determination of

bubble and/or flow characteristics, and the theoretical analysis, including advanced two

phase CFD simulations discussed in Chapter 5 and detailed in Appendix F, were relied on

for this aspect of the research.

Chapter 3: Experimental Design 61 3.5 EXPERIMENTAL MEASUREMENTS

Table 3.1 shows a list of all experimental measurements performed. Only a few were

obtained manually. Dissolved gas content measurements were taken at the beginning and

end of each experiment. Heater shaft location was measured multiple times throughout

the course of each channel experiment. However, the power supplies, multimeters, and

scanner discussed in the previous section were all accessed through a Pentium-class

computer running the Linux operating system. Data acquisition and reduction was

automated through the use of a C program written specifically for these experiments and

discussed in Appendix E. The automated acquisition system obtained a complete set of

readings every 3–4 s. The output file created by the data acquisition program contains

raw measurements (6-digit precision) as well as various derived quantities. In addition to

displaying textual measurement data at the end of each cycle, the data acquisition

program also launches the Gnuplot plotting program for real-time graphical display of the

output file.

Table 3.1: Experimental Measurements

Automated Readings Manual Readingsthermocouple voltages: dissolved gas content

ice bath shaft position/channel spacingheatersbulk liquid (4) Derived Quantitiesmodule control water, in & out thermocouple temperaturesshunt resistors shunt resistor/heater currentisothermal block differential heater powerlaboratory ambient heater resistance

heater voltagesshunt resistor voltagespower supply voltagespower supply currents


Figure 3.12: Example of real-time data acquisition graph of temperature measurements.

Sample real-time data acquisition graphs are shown in Figs. 3.12 and 3.13. This

capability provides a convenient view of how each experiment is progressing. In the

experimental run of Figs. 3.12 and 3.13, the data acquisition program was initiated with

no power applied to the heaters, allowing the hot water circulating in the module walls to

raise the liquid temperature to values close to its saturation temperature. Heater power

was turned on after nearly 1000 s. For the following 1000 s, the primary heater was held

at approximately 29 W, with the secondary heater near 22.5 W (well into nucleate boiling

on both). This heating time allowed the bulk liquid to reach its saturation temperature

while simultaneously facilitating degassing of the liquid. In the experimental run of Figs.

3.12 and 3.13, dissolved gas content was measured to be less than 4% at approximately

1900 s.


Figure 3.13: Example of real-time data acquisition graph of heater electrical parameters

Between the 2000 s and 3000 s marks in Figs. 3.12 and 3.13, heater power was gradually

increased to find CHF for each heater. CHF events are readily identified in these graphs

by rapidly increasing temperatures and discontinuities in the electrical parameters

resulting from the automatic interruption in heater power when the heater temperature

exceeded 100°C (see Appendix E for a discussion of the data acquisition program and

this feature). After the 4000 s mark, heater power was gradually reduced to trace out the

boiling curve. The graphs allow identification of when steady-state conditions have been

reached for each power setting. After reaching steady-state, the data acquisition program

was allowed to cycle through more than 30 sets of readings to capture a good statistical

sampling of data before moving to the next power setting.

Chapter 3: Experimental Design 64 Table 3.2: Keithley 2000 DMM 1-year DC voltage measurement accuracy when operated

in a 23°C ± 5°C environment (Keithley, 1999).

Range Resolution(V) (µV) %reading %range min. max.0.1 0.1 0.0050 0.0035 ± 3.5 ± 8.51 1 0.0030 0.0007 ± 10 ± 3710 10 0.0030 0.0005 ± 80 ± 350100 100 0.0045 0.0006 ± 1100 ± 5100

Accuracy Zeroth Order Bias Limits (µV)

3.6 UNCERTAINTY ESTIMATES

3.6.1 Zeroth Order Temperature Measurement Uncertainties

Zeroth order bias error limits for the Keithley 2000 DMM used for the thermocouple

measurements may be calculated as

( )22

accuracy deviceLSD21 +

± (3.3)

where the first term is one-half the device resolution (or Least Significant Digit), and the

device accuracy may be taken from manufacturer specifications. Table 3.2 contains DC

voltage measurement accuracy specifications for the Keithley 2000 DMM. As shown in

the table, overall accuracy is calculated by adding a specified percentage of the reading to

a (different) specified percentage of the device measurement range.

( )rangerange%readingreading% ×+×± (3.4)

Compared to the device accuracy, device resolution contributes only slightly to the total

uncertainty. Minimum and maximum possible values for the limits of each reading range

also appear in Table 3.2.

For type-T thermocouples operated over a differential temperature range of 25° to 100°C,

raw voltage measurements range from 1 to 4 mV. With the differential thermopile

arrangement of Fig. 3.10, all differential thermocouple measurements reference the

Chapter 3: Experimental Design 65 thermopile at room temperature (typically 20–25°C). As a result, ice bath thermocouple

voltages are on the order of 1 mV, while other thermocouple voltages range from 0 to

3 mV over an absolute temperature measurement range of 25°C to 100°C. Given these

low voltages, and the 0.1 V range accuracy specifications shown in Table 3.2, the range

contribution to the accuracy is large compared to the reading component and dominates

the measurement accuracy. Therefore, zeroth order bias limits for the thermocouple

voltage measurements are approximately ± 3.5 µV. When propagated through the

temperature conversion calculation discussed in Appendix E, the resulting uncertainty in

reported temperatures due to device accuracy is less than an order of magnitude smaller

than the manufacturer-stated thermocouple accuracy of ± 0.5°C. This value includes the

physical quality of the probe itself, as well as the voltage-to-temperature conversion.

As discussed in Section 3.5, more than 30 sets of readings were obtained for each steady-

state condition to minimize precision errors. First order precision uncertainty may be

calculated as (Moffat, 1985)

nst± (3.5)

where s is the standard deviation of the sample, n is the number of elements in the

sample, and t is taken from the t-distribution. (At 95% confidence with 30 degrees of

freedom (n-1), t = 2.04.) Very little scatter was observed in the raw voltage readings from

the ice bath thermocouple. Ice bath voltage precision uncertainty calculated via Eq. (3.5)

was typically ± 0.02%. Heater thermocouple readings were least precise for the narrowest

silicon heater channels at the lowest heat fluxes. For 0.3 mm wide channels, raw voltage

uncertainty was in the range of ± 1% at low heat flux to ± 0.5% at high heat flux. Over an

absolute temperature measurement range of 50°C to 100°C, these voltage fluctuations

translate to a temperature uncertainty of ± 0.3°C. Precision uncertainty for wider channels

and the other thermocouples in the system was significantly less. First order bias errors

associated with the physical installation of heater thermocouple probes are discussed in

Section 3.6.3, and total first order uncertainty estimates are presented in Section 3.6.4.

Chapter 3: Experimental Design 66 3.6.2 Zeroth Order Heater Power Measurement Uncertainties

The Keithley 196 DMM used for heater power measurements was calibrated using the

Keithley 2000 DMM discussed in the previous section. This calibration was performed to

account for potential measurement errors introduced by the various devices included in

the measurement chain, including the scanner, wiring, connectors, and protective fuses

and to eliminate the cost of having the manufacturer calibrate a second instrument.

Separate calibration experiments were performed over the ranges of expected voltages

encountered in the heater and shunt voltage measurements. The relationship between

voltages measured with the two instruments was highly linear, as might be expected.

There was noticeable scatter in the data, though it is not presumed that these fluctuations

were due to random phenomena in the instruments themselves. A silicon heater immersed

in highly subcooled FC-72 was used as the load in the test circuit. Random temperature

fluctuations inherent to the boiling process produce instantaneous fluctuations in the

electrical resistance and, therefore, current draw, of the heater. When fluctuations occur

during the fraction of a second that elapses between multimeter readings, the readings

from each instrument will vary slightly. This explanation is well supported by the data, as

much less scatter was evident before the onset of nucleate boiling compared to voltages

measured during boiling.

A least-squares curve fit performed using Microsoft Excel software regression utilities

produced the following relationship between shunt resistor voltage drops (Vshunt)

measured by the Keithley 2000 and 196 DMMs (at 95% confidence).

( ) ( ) 61962000 103.12.600011.099993.0 −×±+±= VV (3.6)

Similarly, the following relationship was determined for heater voltage drops (Vsense).

( ) ( ) 41962000 100.25.30000008.09993640.0 −×±+±= VV (3.7)

The absolute difference between readings is larger for the heater voltage measurements.

However, heater voltages are three orders of magnitude higher than shunt resistor

Chapter 3: Experimental Design 67 voltages. As a result, the heater voltage correlation is more precise than the shunt resistor

correlation. Unlike the current-driven voltage fluctuations across the shunt resistor, the

heater power supply is voltage-controlled and, as a result, more stable. Fortunately, the

uncertainties in these correlations are well within the device accuracy of the Keithley

2000 DMM itself. Thus, zeroth order bias error limits for the heater and shunt resistor

voltage measurements are only slightly larger than those shown in Table 3.2. Given the

range of heater and shunt resistor voltages encountered in the experiment, these

uncertainties evaluate to approximately ± 0.05% and ± 1%, respectively. The calibration

represented by Eqs. (3.6) and (3.7) were included in the data acquisition software, though

both raw and corrected values were written to the output file so data integrity could be

maintained and later verified, if necessary.

When typical heater and shunt resistor voltage readings are considered in the context of

Eq. (3.5), it is found that first order precision uncertainties are typically on the order of

± 0.2% and ± 1%, respectively. The square root of the sum of the squares of the zeroth

order bias and first order precision uncertainties

( ) ( )2st2th precisionorder 1biasorder 0 +± (3.8)

evaluate to ± 0.21% and ± 1.4%. Strictly speaking, uncertainty estimates should not be

reported to more than one significant digit. However, intermediate values such as these

will be maintained to two significant figures for the purposes of subsequent first order

uncertainty calculations. Uncertainty estimates will not be rounded to one significant

digit until reporting of the final total values.

Heater power is a derived quantity, based on measured heater and shunt resistor voltages.

Combining Eqs. (3.1) and (3.2), heater power may be expressed as

shunt

senseshuntheater R

VVP ⋅= (3.9)

Chapter 3: Experimental Design 68 Generally speaking, the percent uncertainty in the product of a number of factors is equal

to the square root of the sum of the squares of the percent uncertainty of the individual

factors, weighted by their exponents (Moffat, 1985).

( ) ...,...,,

222

+

+

+

=zzc

yyb

xxa

zyxff δδδδ (3.10)

where

...cba zyxf =

As previously discussed, shunt resistor resistance is accurate to within ± 0.25%. When

combined with the uncertainties calculated in the previous paragraph for Vshunt and Vsense,

Eq. (3.10) yields ± 1.4% for the uncertainty in heater power (dominated by shunt resistor

measurements). First order bias errors related to parasitic heat losses from the heaters are

considered in the next section, and complete first order uncertainty estimates are

presented in Section 3.6.4.

3.6.3 First Order Bias Errors: Parasitic Heat Losses and Thermocouple Placement

With zeroth order bias and first order precision errors evaluated in previous sections, first

order bias errors including parasitic heat losses and thermocouple installation and

placement are now considered. Due to conduction heat transfer to the heater supports and

convective heat transfer from the back of the apparatus, the heat transferred to the liquid

from the boiling surface is necessarily some reduced fraction of the electrical power

supplied to the heater. In addition, first order bias considerations must include the

discrepancy between actual thermocouple junction and reported average boiling surface

temperatures. Though the methodology will be the same, given the significant physical

differences between the silicon and aluminum heaters, these errors must be estimated

separately for each.


Y

XZ

Air Spacewith top, bottom, and rear openings

Hollow Block

Module Wall

Y

XZ


Hollow Block

Module Wall

Figure 3.14: Isometric view of silicon heater Icepak model.

3.6.3.1 Silicon Heater First Order Bias Errors

The commercial computational fluid dynamics (CFD) software Icepak™ (version 4.1.16)

was used to perform a steady-state analysis of natural convection heat losses from the

backside of the experimental apparatus to the ambient environment. Figure 3.14 shows an

isometric view of the Icepak model. The entire model is 254 × 254 × 101.6 mm in size

(X × Y × Z, or width × height × depth). An Icepak hollow block object 25.4 mm thick (Z-

direction) is used to remove the portion of the computational domain representing the

interior of the apparatus. Icepak does not mesh or solve for temperature or flow within

the empty space of a hollow block object. However, the software will perform

calculations for meshed objects that intersect or lie inside the hollow block.

Chapter 3: Experimental Design 70 The space available for air flow and convective heat transfer is 254 × 254 × 76.2 mm in

size and is bounded by openings at the top, bottom, and rear sides (maximum Y,

minimum Y and Z). A 20°C ambient air temperature boundary condition is specified at

each of these openings. The minimum and maximum X-direction boundaries of the air

space are adiabatic walls by default. The computational domain was set to be large

enough to prevent boundary effects from affecting the solution. The gravity vector was

defined with a magnitude of 9.80665 m/s2 in the negative Y-direction.

Solid objects included in the model are summarized in Table 3.3 and shown in

Figure 3.15. The polycarbonate module wall is located in the air space but shares a

common boundary with the hollow block object previously described. The heater and

substrate lie within the hollow block, while the brass electrodes penetrate through the

wall and substrate to meet the edges of the heater. A uniform heat generation is specified

in the silicon heater. Object surfaces within the hollow block are adiabatic by default. A

boiling heat transfer coefficient, in the range of 500 W/m2K to 4000 W/m2K, based on

experimental data presented in Chapter 4 and appropriate for each heat generation setting,

is specified on the boiling surface of the heater. In addition, a liquid natural convection

heat transfer coefficient of 20 W/m2K is applied to the external surfaces of the heater

substrate and module wall. An “ambient” temperature of 56.6°C, corresponding to the

saturation temperature of FC-72, is set for each of these convective boundary conditions

representing conditions in the interior of the module.

Table 3.3: Solid objects included in the silicon heater Icepak model.

X Y Zmodule wall polycarbonate 100 100 6.35heater substrate polycarbonate 40 26 6.35substrate pocket air 16 16 2.85heater silicon 20 20 0.675electrodes brass 0.254 20 38

Dimensions (mm)Object Material


ElectrodesModule Wall

Heater Air Pocket

Substrate

Hollow BlockBoundary

YX

Z

ElectrodesModule Wall

Heater Air Pocket

Substrate


YX

Z

Figure 3.15: Top view of silicon heater assembly model.

The air pocket in the heater substrate is modeled as a solid block with the thermal

conductivity of air. This construction relieves the software from solving flow equations in

this small insulating region of non-circulating air. The thin layers of high thermal

conductivity, electrically conducting epoxy used to bond the brass electrodes to the

silicon heater were not included in the model because of their relatively high thermal

conductance. Material properties used in the analysis are shown in Table 3.4. Laminar

flow was assumed for the flow calculations in the air space. The Icepak objects shown in

Figure 3.15 are grouped as an assembly to allow independent meshing of these objects

within the larger computational domain, using Icepak’s non-conformal meshing

capabilities. Mesh refinement was pursued to ensure mesh independence of reported

results. The final mesh contained slightly less than 60,000 elements and required solution

run times of several minutes on a 3 GHz Pentium-based PC.

Table 3.4: Material properties used in the Icepak analyses.

density 1.1614 kg/m3

specific heat 1005 J/kgKpolycarbonite 0.2 thermal conductivity 0.0261 W/mKsilicon 145 volumetric expansion 0.00333 1/Kbrass 130 viscosity 1.84E-05 kg/m·s

diffusivity 1 m2/smolecular weight 28.966 kg/kmol

Air PropertiesSolid Material Thermal Conductivity

(W/mK)

Chapter 3: Experimental Design 72 Figure 3.16 contains sample temperature and velocity results for a heat generation of

45 W and associated boiling heat transfer coefficient of 8000 W/m2K. In addition to the

minimum, maximum, and average temperatures of the boiling surface, Icepak is capable

of reporting the heat flow through this side of the heater block object. In this example,

96.8% of the total 45 W of heat generated in the silicon heater was dissipated through the

boiling surface, and, therefore, 3.2% of the heat was lost to the ambient, primarily via

conduction through and convection from the brass electrodes. Similar analyses were

performed for the 30 mm wide silicon heaters. In addition to extending the heater object

5 mm in both the positive and negative X-directions, the substrate air pocket was

widened to a total length of 26 mm. The models were otherwise identical.

By stepping the analysis through various power settings, the percent heat loss could be

evaluated over the experimental range. Figure 3.17 shows the results of this exercise for

both sizes of silicon heaters. As the main heat flow path for parasitic heat loss is the brass

electrodes at the edges of the heater, it should come as no surprise that these losses are

proportionately greater for the smaller 20 × 20 mm heater. Heat loss is most significant

(as a percentage of total power) at low power, where boiling heat transfer coefficients are

weakest. Analysis results were fit to high-order polynomials using Microsoft Excel,

yielding the following correlations for the ratio of heat transferred via boiling to total

heater power as a function of total heater power.

4736.0109144104113

10201110600.210367.1

heater22

heater3

3heater

44heater

65heater

8

mm20heater

+×+×−

×+×−×=

−−

−−−

P.P.

P.PPPQb

(3.11)

6914.0105134102043102021

10434.210515.210038.1

heater22

heater33

heater4

4heater

65heater

86heater

10

mm30heater

+×+×−×+

×−×+×−=

−−−

−−−

P.P.P.

PPPPQb

(3.12)


Figure 3.16: Sample temperature and velocity results for silicon heater Icepak model

(Pheater = 45 W, hb = 8000 W/m2).


0%

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

0 10 20 30 40 50 60 70

Heater Power (W)

Par

asiti

c H

eat L

oss

20 x 20 mm heater20 x 30 mm heater

Figure 3.17: Results of parasitic heat loss analysis for silicon heaters.

All experimental silicon heater boiling flows were corrected to account for non-boiling

parasitic heat losses using Eq. (3.11) or (3.12). Despite the steep slope of these curves at

low power, a first order bias error for this correction of ± 2% will be assumed to

adequately represent the analysis assumptions and approximations over the experimental

range.

Various supplementary models were created to explore the impact of the foil

thermocouple on heater temperatures. The thermocouple and attaching epoxy were

modeled in detail and included in analyses similar to those discussed above. Fortunately,

the heat flow path provided by the thin foil thermocouple leads (0.05 mm thick) is

insufficient to significantly depress the temperature at the thermocouple junction. As

might be expected, the effect of the presence of the thermocouple on the backside of the

silicon heaters was an order of magnitude less than the variation in heater surface

Chapter 3: Experimental Design 75 temperature due to the heat flow path presented by the brass electrodes. As a result, the

center of the 20 × 20 mm heater was consistently 0.2°C above the edges, while the effect

was twice as strong (0.4°C) for the 20 × 30 mm heater. Thus, uncertainties of ± 0.1°C and

± 0.2°C will be assumed to cover these and any other first order bias effects in silicon

heater temperature due to thermocouple attachment, heater temperature nonuniformity,

and the like.

3.6.3.2 Aluminum Heater First Order Bias Errors

Analyses similar to those discussed in the preceding section were performed for the

aluminum heater assembly. The air space was extended an additional 50.8 mm in the

negative Z-direction to accommodate the length of the aluminum heater shaft. The

module wall, hollow block, and openings otherwise remained the same. Figure 3.18

shows an isometric view of the Icepak model with the aluminum heater assembly.

Y

XZ


Hollow Block

Module Wall

Y

XZ


Hollow Block

Module Wall

Figure 3.18: Isometric view of silicon heater Icepak model.

Chapter 3: Experimental Design 76 Icepak objects comprising the aluminum heater assembly and insulation are summarized

in Table 3.5 and shown in Figure 3.19. The last row of Table 3.5 has dimensions for a

small block used to represent the thermally conductive epoxy which secures the

thermocouple to the edge of the boiling surface. Temperature variations in this block are

used to evaluate first order bias errors associated with this measurement, discussed

below. In addition to the air and polycarbonate material properties shown in Table 3.4,

thermal conductivities of 177, 1.04, and 0.6 W/mK are used for the aluminum, epoxy,

and insulation, respectively.

Table 3.5: Solid objects included in the aluminum heater Icepak model.

X Y Zsurface block aluminum 20 20 8surface block flange aluminum 34 20 2heater shaft aluminum 20 20 47shaft flange aluminum 34 20 3insulation polyethylene foam 36 36 60thermocouple epoxy Omegabond 101 4 0.5 6.35

Object MaterialDimensions (mm)

Insulation

Module Wall

Boiling Surface

Thermal Interface

Shaft


YX

Z

Cartridge Heater Chamber

Thermocouple Epoxy

Insulation

Module Wall

Boiling Surface

Thermal Interface

Shaft


YX

Z

Cartridge Heater Chamber

Thermocouple Epoxy

Figure 3.19: Top view of aluminum heater assembly model.

Chapter 3: Experimental Design 77 A hollow cylinder, 40 mm long and 10 mm in diameter, was used to represent the

cartridge heater chamber inside the aluminum heater shaft. A uniform heat load is applied

to the cylindrical surface of this object to supply heat to the assembly. A fluid block

object, 20 × 20 × 10 mm is included at the end of the heater shaft to override this portion

of the insulation block and expose the very end of the shaft to ambient air, as it was

during the experiments.

As with the silicon heater analyses, a boiling heat transfer coefficient, based on

experimental data presented in Chapter 4 and appropriate for each heat load setting, is

specified on the boiling surface. A liquid natural convection heat transfer coefficient of

20 W/m2K and 56.6°C “ambient” temperature are specified on the interior side of the

module wall. Based on the results of an auxiliary experiment employing a cold plate and

several thin foil thermocouples located around the heater shaft and boiling surface block,

a planar resistance equal to 0.02°C/W is included to represent the thermal interface

resistance at this bolted joint. A parametric sensitivity analysis of this resistance

determined that it has a relatively insignificant effect on resulting heater power

corrections.

The final meshed Icepak model contained just over 120,000 elements. Solution run times

were on the order of 10 minutes on a 3 GHz Pentium-based PC. Figure 3.20 shows

sample temperature and velocity results for a heat generation of 60 W and associated

boiling heat transfer coefficient of 5578 W/m2K. Figure 3.21 shows parasitic heat loss

results generated using experimental heat transfer coefficients obtained for each of the

three aluminum boiling surfaces discussed in Chapter 4. Similar to the results of the

silicon heater analyses, heat loss is most significant (as a percentage of total power) at

low power, where boiling heat transfer coefficients are weakest.


Figure 3.20: Sample temperature and velocity results for aluminum heater Icepak model

(Pheater = 60 W, hb = 5578 W/m2).


0%

3%

6%

9%

12%

15%

18%

21%

24%

27%

0 10 20 30 40 50 60 70

Heater Power (W)

Para

sitic

Hea

t Los

s600 grit surface400 grit surfaceEDM surface

Figure 3.21: Results of aluminum heater assembly parasitic heat loss analysis.

It is clear from the graph of Fig. 3.21 that heat loss results were very similar for all three

boiling surfaces, disagreeing by less than ± 1% over most of the experimental range. This

variation is well within the accuracy of the analysis assumptions, and any one of these

curves might as well represent all three. Regardless, data for each type of surface is

corrected separately. Analysis results were fit to high-order polynomials using Microsoft

Excel yielding the following equations for the ratio of boiling heat transfer to total heater

power as a function of total heater power.

5780.010699.510279.4107191

10780.310286.410959.1

heater22

heater33

heater4

4heater

65heater

86heater

10

EDMheater

+×+×−×+

×−×+×−=

−−−

−−−

PPP.

PPPPQb

(3.13)


5704.010504.510020.4105801

10404.310778.310687.1

heater22

heater33

heater4

4heater

65heater

86heater

10

grit400heater

+×+×−×+

×−×+×−=

−−−

−−−

PPP.

PPPPQb

(3.14)

5438.010852.510243.4106541

10531.310886.310722.1

heater22

heater33

heater4

4heater

65heater

86heater

10

grit600heater

+×+×−×+

×−×+×−=

−−−

−−−

PPP.

PPPPQb

(3.15)

All experimental aluminum heater boiling heat flows were corrected to account for

parasitic heat losses using one of these equations. Despite the steep slope of the curves at

low power, a first order bias error of ± 3% will be assumed to adequately represent the

analysis assumptions and approximations over the experimental range.

Given the position of the thermocouple located at the side of the boiling surface (shown

in Fig. 3.7), one might expect measured temperatures to be somewhat lower than average

boiling surface temperatures. Fortunately, the polycarbonate wall, which supports the

aluminum heater assembly, has a very low thermal conductivity (0.2 W/mK). Across the

range of simulations represented by Fig. 3.21, the difference between the average boiling

surface temperature and the front end of the thermocouple epoxy block was less than

0.2°C. Given this simplified model of the thermocouple installation, an uncertainty of

± 0.2°C will be assumed for the first order bias error of aluminum boiling surface

temperature measurements.

3.6.4 Complete First Order Uncertainty Estimates

Table 3.6 summarizes zeroth order bias, first order precision, and first order bias errors

evaluated earlier in this chapter for the various heaters. Total first order estimates of

absolute temperature measurement uncertainty may be calculated as the square root of the

sum of the squares of these individual uncertainties.

( ) ( ) ( )2st2st2th biasorder 1precisionorder 1biasorder 0 ++± (3.16)

Chapter 3: Experimental Design 81 Taking the data of Table 3.6 and Eq. (3.16), first order uncertainty can be shown to be

equal to ± 0.6°C for all heaters. This result is dominated by the ± 0.5°C accuracy inherent

to the thermocouples, as provided by the manufacturer. Fortunately, thermocouple bias

errors are eliminated from the combined uncertainty in the difference between

temperatures measured using the same probe. Thus, improvements in thermocouple

accuracy would not improve the accuracy of observed channel spacing effects on

temperature. However, when considering temperature differences, precision errors from

both measurements must be combined (square root of the sum of the squares) to calculate

the uncertainty of the result. Based on the ± 0.3°C precision error shown in Table 3.6,

first order uncertainty for temperature differences measured using the same thermocouple

is ± 0.4°C, solely due to random temperature fluctuations inherent to the boiling process

itself. Thus, it is concluded that the temperature measurement instrumentation,

differential thermopile arrangement, thermocouple probe installation, and experimental

procedure were all adequate to minimize temperature uncertainty to an appropriate level.

Table 3.6: Summary of temperature measurement uncertainty contributions.

Uncertainty 20 mm silicon 30 mm silicon aluminum0th order bias ± 0.5°C ± 0.5°C ± 0.5°C1st order precision ± 0.3°C ± 0.3°C ± 0.3°C1st order bias ± 0.1°C ± 0.2°C ± 0.2°C

Boiling heat flows have a combination zeroth order bias and first order precision

uncertainty of ± 1.4% along with estimated ± 2% and ± 3% first order bias errors for the

silicon and aluminum heaters, respectively. The square root of the sum of the squares of

these contributions yields ± 2.4% and ± 3.3%. However, boiling heat flux is typically

reported throughout this dissertation. Boiling heat flux is a derived quantity calculated

from the boiling heat flow and heat transfer surface area.

1b

−==′′ AQA

Qq bb (3.17)

Thus, the total percent uncertainty in reported heat fluxes may be calculated using

Eq. (3.10). Based on physical measurements, surface area for each of the heaters is taken

Chapter 3: Experimental Design 82 to be accurate with ± 1%. Nominal dimensions (20 × 20 mm) were used to calculate area

and, subsequently, heat flux, for the aluminum and smaller silicon heaters. The larger,

20 × 30 mm heaters, however, had a somewhat reduced area for boiling heat transfer

(560 mm2, nearly 7% smaller), due to the presence of quick-setting epoxy around the

edges that found its way to the top surface from the edges during assembly.

With appropriate rounding of final uncertainty results to a single digit, total heat flux

uncertainty estimates are conveniently ± 3% for all heaters. The majority of this

uncertainty is from the parasitic heat loss, captured by the derived correlations, with the

remainder primarily attributable to shunt resistor voltage fluctuations.

Thus, in summary, the ranges of the primary measurements and their estimated

uncertainties at 95% confidence are:

• Temperature: 20–100°C ± 0.6°C absolute, ± 0.4°C difference

• Boiling Heat Flux: 5–160 kW/m2 ± 3%

• Channel Spacing: 0.3–20 mm ± 0.1 mm

83

CHAPTER

FOUR

POOL BOILING CHARACTERIZATION

Basic characterization experiments were performed to quantify the nucleate boiling

performance of various vertical surfaces. These results provide a baseline for subsequent

channel and heat sink experiments discussed in Chapter 5. The difference between these

and the channel experiments will show the magnitude and nature of confinement-driven

enhancement. This chapter contains a presentation of results, discussion of observed

trends, and comparisons with previously published pool boiling correlations.

4.1 BASIC SATURATED POOL BOILING EXPERIMENTS

Saturated pool boiling data obtained at atmospheric pressure for silicon heaters are shown

in Fig. 4.1 for a large heater separation (channel spacing) of approximately 20 mm and

increasing heat flux. The time interval between each data point was 3–4 s, and the self-

heating silicon plate responded very quickly to changes in power dissipation. For the

experimental run of Fig. 4.1, the data acquisition program was set to cut power when the

Chapter 4: Pool Boiling Characterization 84

0

20

40

60

80

100

120

0 20 40 60 80 100

∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )

CHF

power cut

cool down

ONB

Figure 4.1: Pool boiling curve for polished silicon heater in saturated FC-72.

heater temperature went above an absolute temperature of 100°C (∆Tsat = 43°C). Thus,

the 128°C (∆Tsat = 71°C) reading shown in Fig. 4.1 triggered heater shutoff. As

temperature readings were taken at the beginning of the measurement loop and power

readings at the end, the heater achieved a temperature in excess of 140°C before quickly

cooling down to the bulk liquid temperature (saturation). While the power supply output

voltage was held constant, the electrical resistance of the silicon heater increased with

increasing temperature. This explains why the heat flux dropped below 80 kW/m2 at the

first elevated film boiling data point in Fig. 4.1.

The low heat flux data of Fig. 4.1 show an extreme example of the temperature overshoot

observed at boiling incipience, or the Onset of Nucleate Boiling (ONB). The overshoot at

ONB varied significantly across experimental runs, often reaching values in excess of

10°C, but once boiling was initiated across the heater surface, data obtained with

increasing and decreasing heat flux were indistinguishable. Figure 4.2 contains a


0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )Current StudyRohsenow FitMcNeil (1992)Watwe (1996)

Figure 4.2: Comparison of pool boiling curves for silicon heaters in saturated FC-72.

conglomeration of unconfined saturated pool boiling data obtained from 20 × 20 mm and

20 × 30 mm silicon heaters. Boiling heat transfer coefficients range from 2 to 4 kW/m2K

for the majority of the fully developed nucleate boiling region. The thick solid line in

Fig. 4.2 represents the Rohsenow (1952) correlation, Eq. (1.4), with 1/r = 2.6 and

Csf = 0.0056 chosen to fit the data. Two additional curves for pool boiling of FC-72 at

atmospheric pressure from silicon surfaces from the literature are included for

comparison.

The thin solid line in Fig. 4.2 is the Rohsenow correlation, Eq. (1.4), with s = 1.7, 1/r = 3,

and Csf = 0.00478, and represents the empirical boiling curve of McNeil (1992) obtained

for 10 × 10 mm silicon heaters somewhat similar to those of the current study. The

Chapter 4: Pool Boiling Characterization 86 heaters were fabricated from 565 µm thick silicon plates doped to provide an electrical

resistance of approximately 1.7 Ω. Copper wires 0.05 mm in diameter were attached to

opposing edges using an ultrasonic soldering iron and indium solder. The rate of change

of the electrical resistance of the silicon heaters with temperature was characterized in

separate calibration experiments. Heater temperatures during pool boiling experiments

were then calculated in real time from a measurement of the heater electrical resistance.

With a rate of change of resistance with temperature of 0.003 Ω/°C, heater temperature

uncertainty was estimated to be quite large at ± 5°C. Thus, heater temperature calibration

uncertainty may be at least partially responsible for the wall superheats being somewhat

lower than observed for silicon heaters in the current study at a given heat flux. Estimated

heat flux uncertainty was ± 2%.

The high CHF values obtained by McNeil (1992), approaching 180 kW/m2 (18 W/cm2),

are well in excess of the base value of 137 kW/m2 (13.7 W/cm2) predicted by the

Kutateladze-Zuber correlation, Eq. (1.5), and even more so those of the current study.

(The average CHF value of 114 kW/m2 obtained for the silicon heaters of the current

study is discussed later in Section 4.3.) The McNeil (1992) boiling curve was verified for

similarly constructed heaters by Geisler et al. (1996) in a study of the thermal

performance of a passive immersion cooled multichip module. However, boiling activity

was observed on the exposed surfaces of the lead wires and solder interface in that

experimental apparatus. This behavior would be expected to produce both reduced

superheats and elevated heat fluxes.

The dashed line in Fig. 4.2 is the Rohsenow correlation, Eq. (1.4), with s = 1.7,

1/r = 7.47, and Csf = 0.0075, and represents the empirical boiling curve of Watwe (1996)

generated using an exposed-die test chip PPGA package fabricated by Motorola, Inc. The

silicon die was 10 × 10 mm in size and 0.38 mm thick and included integrated heating

and temperature sensing circuitry. Estimated wall superheat and heat flux uncertainties

were estimated to be ± 1.3°C and ± 8 kW/m2, respectively. CHF values varied by as

much as 25% between different test chips, but the average value for saturated conditions

Chapter 4: Pool Boiling Characterization 87 at atmospheric pressure, 151 kW/m2 (15.1 W/cm2), matched the Kutateladze-Zuber

correlation within the stated experimental uncertainty after correction for heater length

scale effects discussed in Section 4.3. The comparisons of Fig. 4.2 clearly illustrate the

need to characterize the basic pool boiling performance of any heated surface before

exploring additional parametric effects or behaviors.

Figure 4.3 shows raw saturated pool boiling data obtained for the 20 × 20 mm aluminum

heater of the current study, before correcting for parasitic heat losses per Eq. (3.13). Due

to the thermal mass of the cartridge heater and aluminum heater assembly, the surface

temperature reading responded slowly to changes in heater power. The interval between

the data points shown in Fig. 4.3 is approximately 18 s. Only one out of every five

readings is included in the graph to show the transient behavior more clearly. As a result,

a few minutes were required to reach steady-state at each power setting. No temperature

overshoot was observed at ONB for any of the aluminum heater experiments, with

nucleation sites activating quite readily with increasing heat flux. The transition to film

boiling was clearly identified by visual observation of a wavy layer of vapor blanketing

the heater surface and a gradual, yet persistent increase in temperature, as shown in

Fig. 4.3.

Steady-state data comprising the pool boiling curve for the EDM aluminum surface is

shown in Fig. 4.4. The solid line again represents the Rohsenow (1952) correlation,

Eq. (1.4), this time with s = 1.7, 1/r = 2.2, and Csf = 0.0026. The steepness of the boiling

curve shows very high heat transfer coefficients compared to the silicon curve, 3–

8 kW/m2K in the fully-developed nucleate boiling region. Thus, the rough and pitted

aluminum surface created via wire EDM yields significantly increased boiling heat

transfer performance compared to polished silicon. In general, nucleation sites were

distributed quite evenly across the aluminum surfaces, and many were active, throughout

the entire range of heat flux. This is in stark contrast to the silicon surfaces which had a

significantly less uniform nucleation site distribution, particularly at low fluxes where

only a few were active.


0

20

40

60

80

100

120

140

0 5 10 15 20

∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 K)

powercut

manually

Figure 4.3: Transient pool boiling data for aluminum heater in saturated FC-72.

0

20

40

60

80

100

120

140

0 5 10 15 20∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )

Figure 4.4: Pool boiling curve for rough aluminum EDM surface.

Chapter 4: Pool Boiling Characterization 89 4.2 EFFECT OF SURFACE ROUGHNESS

The nucleate boiling results presented in the preceding section for aluminum and silicon

surfaces were obtained in the same experimental apparatus, with the same fluid, under the

same conditions, and yet, very different boiling heat transfer coefficients were obtained.

While the three empirically determined constants in the Rohsenow correlation, Eq. (1.4),

may be fit to account for various surface materials and conditions, the trends are not

clear. Cooper (1984) presented an empirical correlation based on three properties, which

may be written as:

( )( ) 235.055.010

log2.012.0 log55 10 TMPPh rR

rbp ∆−= −−− (4.1)

where Pr is the reduced system pressure (P/Pcrit), M is the molecular weight of the fluid

(g/mol), and Rp is the RMS surface roughness in microns (µm). The surface roughness

factor is based on one suggested by Nishikawa et al. (1982) and includes the observed

trend that boiling is more dependent on roughness at low reduced pressure than at high

reduced pressure. Reduced pressure is employed to represent the dominant property

variations of a given fluid, while molecular weight was shown to capture the general

behavior of multi-property correlations evaluated for a variety of fluids. Given the limits

of experimental control, measurement accuracy, and experiment-to-experiment variation

typically associated with boiling heat transfer, Eq. (4.1) is no less accurate than

significantly more complex, multi-property correlations (Cooper, 1984). The primary

advantage of Eq. (4.1) is that one is not required to characterize boiling performance and

correlate multiple empirical parameters before further boiling predictions can be pursued.

It should be noted that the experimental data on which Eq. (4.1) is based covered a fluid

molecular weight range of 2–200 g/mol. While the molecular weight of FC-72 is

338 g/mol, the relative flatness of the M-0.5 dependence at the higher end of this range

makes extrapolation of Eq. (4.1) for FC-72 predictions less troublesome.

The Cooper (1984) correlation suggests that the dominant effect leading to different

boiling heat transfer coefficients for different surfaces is the RMS surface roughness.

Chapter 4: Pool Boiling Characterization 90 Electrical discharge machining (EDM) of aluminum can produce a wide range of surface

finishes depending on the process, from mirror-like to visibly rough and pitted. The

magnified photographs of Fig. 4.5 show the relatively rough surface of the aluminum

heater. The roughness of a polished silicon surface is, relatively speaking, difficult to

measure, though it can be expected to be on the order of 1 µm (Teichert et al., 1995).

In an attempt to bridge the gap between the results obtained for the silicon and aluminum

surfaces, the original heater surfaces were modified and their boiling performance re-

characterized. The EDM aluminum surface was polished in two stages. First, the

aluminum was sanded with 400 grit sandpaper. Secondly, a wet 600 grit paper was used

to obtain a smoother appearance, as shown in Fig. 4.6. The silicon surface was scratched

with 60 grit sandpaper to a cloudy appearance, as shown in Fig. 4.7. Figure 4.8 includes

saturated pool boiling results for all the surfaces, and shows a general trend of smoother

surfaces producing lower heat transfer coefficients and, hence, higher superheats at a

given heat flux. Nucleate boiling heat transfer coefficients for the modified surfaces

ranged from 2 to 5 kW/m2K.


Figure 4.5: Magnified photographs of aluminum heater surface formed by wire EDM.


Figure 4.6: Magnified photographs of aluminum surface after sanding with 600 grit sandpaper.


Figure 4.7: Magnified photographs of scratched silicon heater surface.


0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )

Eq. (4.1), Rp = 20 micronsEq. (4.1), Rp = 5 microns

Eq. (4.1), Rp = 2 micronsEq. (4.1), Rp = 1 micron

Aluminum, EDMAluminum, 400 grit

Aluminum, 600 gritSilicon, Scratched

Silicon, Polished

Figure 4.8: Unconfined pool boiling curves for various silicon and aluminum surface,

comparison of surface roughness effect and Cooper (1984) correlation, Eq. (4.1).

As can be seen in Fig. 4.8, while the fully-developed nucleate boiling portion of the

polished silicon data matches quite well with Eq. (4.1), the scratched silicon surface data

varies between predictions for Rp = 2 µm at low flux to 5 µm at high flux. Aluminum

results fit the slope of the Cooper predictions significantly better than the scratched

silicon, however the superheat is consistently underpredicted at high heat flux.

Regardless, the results shown in Fig. 4.8 support the general surface roughness trends of

Eq. (4.1).

Chapter 4: Pool Boiling Characterization 95 4.3 CRITICAL HEAT FLUX

The boiling curves in Fig. 4.8 show that surface treatment does not have a significant

effect on the maximum heat flux levels obtained for these heaters. However, a clear

difference in CHF was observed between the aluminum and silicon heaters, 137

vs. 114 kW/m2 (13.7 vs. 11.4 W/cm2), respectively, averaged over all unconfined boiling

experiments. Arik and Bar-Cohen (2003) expanded the Kutateladze-Zuber correlation to

allow for prediction of pool boiling CHF for a wider variety of situations. Using relations

from the literature (Ivey and Morris, 1966) (Dhir and Lienhard, 1973), their correlation

modifies Eq. (1.5) by parametric factors which take into account effects of heater

properties, the heater length in the flow direction, and bulk liquid subcooling.

( )

∆

+−+⋅

+−=′′

subp

p

Thc

L'..

kct

kctghq

fg

f,

75.0

g

f

hhp,h

hh,h4/1gffgfgCHF

03.01015070301401

1.0)]([

24

ρρ

ρρ

ρρσρπ

(4.2)

where

f

gf )('

σρρ −

=g

LL

The subcooling factor appearing at the end of Eq. (4.2) is discussed in Section 4.5. The

quantity <0.3014-0.01507L’> reflects the increase in CHF observed for small heaters. It

is included only when positive, corresponding to heater lengths below approximately

14 mm for FC-72 and 50 mm for water, both at a system pressure of 101 kPa (1 atm).

The effusivity factor appearing in Eq. (4.2) is based on heater thickness, density, specific

heat, and thermal conductivity. Silicon properties typically put traditional microelectronic

IC devices at the “thick heater” limit. CHF for a 130 µm thick silicon heater would be

within 5% of the asymptotic limit, while the 5% thickness for an aluminum boiling

surface would be 175 µm. For the 675 µm silicon and greater than 10 mm thick

aluminum heaters employed in this study, the effusivity factor evaluates to 0.990 and

Chapter 4: Pool Boiling Characterization 96 0.9995, respectively. The variation of this factor across a wide range of thicknesses is

shown in Fig. 4.9 for silicon and aluminum.

The difference in CHF observed between the aluminum and silicon heaters, 137

vs. 114 kW/m2 (13.7 vs. 11.4 W/cm2), can not be explained by any of the parametric

effects considered by Eq. (4.2). However, the CHF values obtained are well within the

accuracy stated by Arik and Bar-Cohen (2003), ± 25% at 95% confidence, from the base

value of 137 kW/m2 (13.7 W/cm2). It is suspected that nonuniform doping of and/or

current delivery to the silicon heaters (and, therefore, nonuniform Joule heating) led to

somewhat lower CHF values for the doped silicon.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.001 0.01 0.1 1 10

Heater Thickness (mm)

Effu

sivi

ty T

erm

siliconaluminum

Figure 4.9: Variation of effusivity term of Eq. (4.2) with heater thickness for silicon and

aluminum.

Chapter 4: Pool Boiling Characterization 97 4.4 SATURATED POOL BOILING DATA SUMMARY

The saturated pool boiling curves of the surfaces discussed in this chapter, displayed

graphically in Fig. 4.8, are now summarized for comparison and reference. Results of

subsequent channel experiments will be compared to these data to quantify channel

confinement effects. Silicon data was obtained on three different heaters, two

20 × 30 mm and one 20 × 20 mm. The aluminum results are all from the same heater

block (20 × 20 mm) that was sanded to modify its surface roughness. Table 4.1

summarizes the experimental runs and correlating parameters of Eqs. (1.4) and (4.1) fit

for each surface. In addition to these correlating parameters, boiling curves were fit with

sixth-order polynomial functions of the form

∑=

∆=′′6

0i

isati TCq (4.3)

using Microsoft Excel. These polynomial functions fit the experimental data to a high

degree, and their use will facilitate subsequent data comparisons while minimizing

correlation errors. Table 4.2 contains the coefficients of Eq. (4.3) determined for each

surface.

Pool boiling Critical Heat Flux data is summarized in Table 4.3. On average, CHF was

137 kW/m2 (13.7 W/cm2) for the aluminum heaters and 114 kW/m2 (11.4 W/cm2) for

silicon, averaged over all unconfined boiling experiments. CHF for the silicon heaters

varied ± 6%, and the aluminum data points are within ± 2% of their average, with a

predicted value of 137 kW/m2.


Table 4.1: Experimental run and correlating parameter summary.

Eq. (4.1)s 1/r Csf Rp (µm)

0 2x3 60 2x2 4

19 2x2 1 1.7 1.5 0.004332 2x2 1 1.7 1.2 0.0034

scratched 0 2x2 1 1.7 5.0 0.0042 2–5EDM 0 2x2 2 1.7 2.2 0.0026 20

400 grit 0 2x2 2 1.7 2.4 0.0039 5600 grit 0 2x2 2 1.7 2.5 0.0046 2

Correlating ParametersEq. (1.4)

1.7 2.6

Surface Size # runsSubcooling (°C)

1polished

0.0056

Table 4.2: Saturated boiling curve polynomial curve fit coefficients of Eq. (4.3).

polished scratched EDM 400 grit 600 gritC 0 -1.32116E+00 4.59502E+05 2.16218E+05 -4.81193E+05 -6.58506E+04C 1 3.24792E+03 -2.36443E+05 -1.54704E+05 2.21928E+05 4.23647E+04C 2 -1.27411E+03 4.17424E+04 4.40238E+04 -4.00059E+04 -8.37929E+03C 3 2.13777E+02 -2.71191E+03 -6.27069E+03 3.64895E+03 7.61717E+02C 4 -1.53010E+01 -8.48559E+00 4.95624E+02 -1.74121E+02 -3.31637E+01C 5 5.16678E-01 7.52506E+00 -2.01781E+01 4.18396E+00 7.00706E-01C 6 -6.54589E-03 -2.09528E-01 3.26788E-01 -4.00883E-02 -5.83670E-03

Si Al

Table 4.3: Pool boiling Critical Heat Flux data summary.

2x2 117 EDM 2x2 1352x2 122 400 grit 2x2 138

2x3 #1 115 600 grit 2x2 1392x3 #2 1132x3 #2 1082x3 #2 111

scratched 2x2 115

polished

CHF (kW/m2)

CHF (kW/m2)

Silicon Surface Size Size

Aluminum Surface

Chapter 4: Pool Boiling Characterization 99 4.5 SUBCOOLED POOL BOILING

Subcooled pool boiling data were obtained for 20 × 20 mm polished silicon heaters. A

water cooled pin fin heat sink was used in place of one of the polycarbonate module walls

to aid in controlling the bulk liquid temperature, as discussed in Chapter 3. As a result, it

was possible to maintain the temperature of the liquid below the heaters at the stated

subcooled temperature within ± 0.5°C. Because the module was open to the atmosphere,

it was not possible to have the liquid both subcooled and degassed simultaneously. The

liquid in the subcooled experiments contained approximately 30% gas (by volume), thus

making comparisons with the saturated and degassed data somewhat convoluted.

Subcooled pool boiling data obtained for 20 × 20 mm polished silicon heaters are shown

in Fig. 4.10. Rohsenow constants for these data are included in Table 4.1, while Table 4.4

contains the coefficients of Eq. (4.3) determined to fit each subcooled boiling curve.

0

20

40

60

80

100

120

140

160

180

0 5 10 15 20 25 30 35

∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )

saturated19°C subcooling32°C subcooling

Figure 4.10: Polished silicon heater pool boiling curves for 19 and 32°C subcooled liquid.

Chapter 4: Pool Boiling Characterization 100 Table 4.4: Subcooled boiling curve polynomial curve fit coefficients of Eq. (4.3) for

polished silicon heaters.

0°C 19°C 32°CC 0 -1.32116E+00 8.61989E+02 1.32885E+04C 1 3.24792E+03 5.78185E+03 2.45396E+03C 2 -1.27411E+03 -8.67690E+02 2.21422E+02C 3 2.13777E+02 1.03902E+02 -2.91442E+01C 4 -1.53010E+01 -5.81830E+00 2.14428E+00C 5 5.16678E-01 1.64328E-01 -6.57450E-02C 6 -6.54589E-03 -1.83307E-03 7.07819E-04

Subcooling

In addition to shifting the boiling curves to the right, the data of Fig. 4.10 show that CHF

increases with increasing subcooling, from 114 kW/m2 (11.4 W/cm2) at saturated

conditions to 147 kW/m2 (14.7 W/cm2) and 162 kW/m2 (16.2 W/cm2) with 19°C and

32°C of subcooling, respectively. In addition, CHF was observed at 126 kW/m2

(12.6 W/cm2) with 10°C of subcooling. This enhancement of CHF with subcooling may

be correlated by the subcooling factor of Eq. (4.2).

subp T

hc

qq

∆

+=

′′′′

fg

f,

75.0

g

f

TEDCHF,SATURA

SUBCOOLED CHF, 03.01ρρ (4.4)

Table 4.5 shows the effect of system pressure and bulk liquid subcooling on CHF

predictions based on Eq. (4.2). Figure 4.11 demonstrates that the enhancement of CHF

with subcooling observed in the present data is correlated very well by Eq. (4.4), with a

maximum absolute deviation of 3.2%. While manipulation of pressure or subcooling can

provide significant increases in CHF, the benefits are not linearly additive. For FC-72 for

example, increasing subcooling from 0°C to 30°C yields a 42% CHF enhancement.

Increasing the system pressure from 101 kPa (1 atm) to 304 kPa (3 atm) yields a 31%

increase. However, the combined enhancement of CHF with 30°C of subcooling and a

pressure of 304 kPa (3 atm) is only 59% above saturated, 101 kPa (1 atm) performance.

Chapter 4: Pool Boiling Characterization 101 Table 4.5: Effects of liquid subcooling and system pressure on CHF for various

Fluorinert liquids, relative to saturated, 101 kPa (1 atm) conditions.

Subcooling (ºC) 101 kPa 203 kPa 304 kPa

0 1.00 1.20 1.3110 1.14 1.31 1.4020 1.28 1.42 1.5030 1.42 1.54 1.590 1.00 1.27

10 1.12 1.3620 1.24 1.4630 1.36 1.560 1.00

10 1.1220 1.2330 1.35

FC-72

FC-84

FC-77

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 5 10 15 20 25 30 35

∆∆∆∆T sub (°C)

CH

F Su

bcoo

ling

Enha

ncem

ent F

acto

r

Figure 4.11: Subcooling enhancement of CHF for polished silicon heaters, compared to

subcooling factor from Arik and Bar-Cohen (2003) CHF correlation, Eq. (4.4).

102

CHAPTER

FIVE

CHANNEL BOILING

As stated in the introductory chapters, the focus of this work is confinement-driven

enhancement of nucleate boiling, and the configuration of interest is a narrow vertical

parallel plate channel submerged in FC-72. This chapter contains a presentation of results

obtained during boiling experiments conducted at atmospheric pressure for silicon

(20 × 20 mm and 20 × 30 mm) and aluminum (20 × 20 mm) heaters. Channel spacing

was varied down to 0.3 mm, providing channel aspect ratios (height/spacing) as high as

67. Experiments were performed with equal heat dissipated from both channel walls

(symmetric heating) as well as with one side heated and the other either an unpowered

silicon heater or polycarbonate plate (asymmetric heating). Presentation of data is

followed by analysis of observed trends and heat transfer correlations. Channel boiling

curves displayed graphically in this chapter are provided in tabular form in Appendix I.

Chapter 5: Channel Boiling 103 5.1 SILICON CHANNEL EXPERIMENTS

Despite shifts in the absolute values observed, all silicon heater channels showed

behaviors and trends similar to those discussed in the literature and Chapter 2. Visual

observation of bubble behavior and two phase flow was possible for asymmetrically

heated channels with the polycarbonate opposing wall. At moderate heat fluxes and

spacings, individual nucleation sites and bubbles were visible near the channel inlet,

while bubbles coalesced and formed columns as they approached the channel exit. At the

smallest channel spacing of 0.3 mm, there was no significant visible difference in void

fraction or bubble behavior along the length of the channel. Large coalesced bubbles

were flattened between the heater and opposing wall. The view across the entire heater

surface was quite homogeneous in these cases.

5.1.1 Polished Silicon Channels

Figures 5.1 and 5.2 show decreasing flux boiling curves for 20 × 30 mm symmetrically

and asymmetrically heated polished silicon channels. Each symbol in these graphs

represents an average of at least 30 data points. The qualitative trends observed agree

well with those identified in the literature and discussed in Chapter 2. As channel spacing

is decreased below 2 mm, and the channel walls begin to interact, boiling curves shift

slightly to the left, signifying lower superheats and enhanced heat transfer. With further

decreases in channel spacing, heat transfer at low heat fluxes is greatly enhanced, while

CHF values and boiling data in the high flux region show deteriorated performance.

Chapter 5: Channel Boiling 104

0

20

40

60

80

100

120

0 5 10 15 20 25 30

∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )0.3 mm0.7 mm1.0 mm1.5 mmLarge Spacing Limit

Figure 5.1: Boiling curves for symmetric 20 × 30 mm polished silicon heater channels.

0

20

40

60

80

100

120

0 5 10 15 20 25 30

∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )

0.3 mm spacing0.7 mm spacing1.5 mm spacing1.6 mm spacingLarge Spacing Limit

Figure 5.2: Boiling curves for asymmetric 20 × 30 mm polished silicon heater channels.

Chapter 5: Channel Boiling 105 Narrow silicon channels, both symmetric and asymmetric, show significantly reduced

surface temperatures compared to unconfined pool boiling up to heat fluxes of 40–

50 kW/m2 (4–5 W/cm2). At this point, the symmetric channel boiling curves flatten out,

sooner than the asymmetric data, as small increases in heat flux lead to increasingly

higher increases in wall temperature. The intersection of narrow channel boiling curves

with the wide channel pool boiling limit, signifying the transition from enhanced to

deteriorated heat transfer performance, occurs at heat fluxes ranging from 40 to

60 kW/m2 (4–6 W/cm2) for symmetrically heated channels as compared to 50 to

70 kW/m2 (5–7 W/cm2) for asymmetrically heated channels. The observation that

channel spacing effects are more pronounced for symmetric channels is expected, since at

a given heat flux twice as much heat is being dissipated from the combined surface area

of both channel walls.

Figure 5.3 contains asymmetric channel boiling data for a 20 × 20 mm polished silicon

heater. The data show a shift to lower temperatures at low flux compared to the

20 × 30 mm asymmetric channel data of Fig. 5.2. This shift is presumably due to edge

effects, as the channel sides are not blocked, providing additional paths for flow to enter

and exit the channel. At heat fluxes above 30 kW/m2 (3 W/cm2), the channel data for the

two different size heaters is very comparable. As noted in Chapter 4, the large spacing

pool boiling limit for the 20 × 20 mm and 20 × 30 mm polished silicon heaters were

indistinguishable.


0

20

40

60

80

100

120

0 5 10 15 20 25 30

∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )0.3 mm spacing0.6 mm spacingLarge Spacing Limit

Figure 5.3: Boiling curves for asymmetric 20 × 20 mm polished silicon heater channels.

Chapter 5: Channel Boiling 107 5.1.2 Scratched Silicon Channels

Asymmetric channel data obtained for the 20 × 20 mm scratched silicon surface appears

in Fig. 5.4. Comparing Figs. 5.2 and 5.4 or considering Fig. 4.8, it is clear that the large

spacing pool boiling curves for the scratched and polished silicon heaters have very

different slopes above 20 kW/m2 (2 W/cm2). However, relative channel enhancement for

similar plate spacings is quite comparable. Figure 5.5 shows the ratio of the wall

superheat at the stated spacing to the wall superheat for the isolated plate vs. heat flux.

Normalizing the superheat in this manner factors out the individual nucleate boiling

behaviors of the two surfaces and allows for direct comparison of the observed

enhancements. The superheat ratio is seen to be lower for the smaller gap than for the

larger gap—signifying greater enhancement—and displays superheat values as low as

20% of the unconfined boiling curves. As heat flux increases, the superheat ratio

approaches and then exceeds unity, due to the progressive deterioration in boiling

performance in this part of the nucleate boiling regime.

0

20

40

60

80

100

120

0 5 10 15 20 25 30∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )

0.3 mm spacing0.7 mm spacing1.0 mm spacingLarge Spacing Limit

Figure 5.4: Boiling curves for asymmetric 20 × 20 mm scratched silicon heater channels.


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 10 20 30 40 50 60 70 80 90 100

Heat Flux (kW/m2)

∆∆ ∆∆T

sat (( (( δδ δδ

)) ))/ ∆∆ ∆∆T

sat (∞

)(∞

)(∞

)(∞

)

polished, 0.3 mm spacingpolished, 0.6 mm spacingscratched, 0.3 mm spacingscratched, 0.7 mm spacing

Figure 5.5: Enhancement ratios for asymmetric 20 × 20 mm scratched and polished

silicon heater channels.

5.1.3 Subcooled Silicon Channels

As discussed in Chapters 3 and 4, a water cooled pin fin heat sink was used in place of

one of the module walls to aid in controlling subcooled bulk liquid temperatures. Without

these water cooled fins, it was not possible to maintain nominally constant levels of bulk

liquid subcooling. As a result, subcooled boiling curves could only be obtained for

asymmetric channels. Unfortunately, visual observation of bubble behavior and two

phase flow was impeded by the presence of the water cooled heat sink during these

experiments. Figure 5.6 contains boiling data for 0.3 mm and 1.0 mm asymmetrically

heated channels immersed in 33°C ± 0.5°C subcooled liquid (measured at the channel

inlet). As with the subcooled pool boiling data of Section 4.5, the bulk liquid contained

approximately 30% gas by volume.


0

20

40

60

80

100

120

140

160

180

-10 -5 0 5 10 15 20 25 30∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )0.3 mm spacing1.0 mm spacingLarge Spacing Limit

Figure 5.6: 30°C subcooled boiling curves for asymmetric polished silicon heater

channels.

Figure 5.6 also contains the unconfined pool boiling curve (large spacing limit) for 32°C

of subcooling discussed in Section 4.5. Unlike the saturated channel data discussed thus

far, it is clear that these subcooled data show no confinement-driven enhancement of

boiling heat transfer in the low flux region. Further, the 1.0 mm channel appears to show

more of the same type of high flux enhancement seen with saturated liquid at channel

spacings of 1.5 mm and 1.6 mm in Fig. 5.2. Subcooled liquid should result in smaller

channel void fractions as bubbles are condensed in the flow stream, so it is not unlikely

that the behavior of smaller channels in subcooled conditions would be similar to larger

channels in saturated liquid. Exploration of channels with spacing less than 0.3 mm

would require a different heater/channel design with significantly tighter spacing

tolerances and was beyond the scope of the present effort.

Chapter 5: Channel Boiling 110 5.2 ALUMINUM CHANNEL EXPERIMENTS

Boiling curves for asymmetric 20 × 20 mm aluminum heater channels are shown in

Fig. 5.7. Decreased channel spacing led to deteriorated high flux performance and

decreased CHF, as was seen in the case of the silicon heaters. At lower heat fluxes,

however, no reductions in wall superheat were observed, regardless of channel spacing

and surface finish. The visual appearance of bubbles and flow in the aluminum channels

was similar to the silicon patterns discussed at the start of the previous section. However,

at comparable heat flux levels there appeared to be a larger number of smaller bubbles

emanating from the aluminum heaters. Further, their distribution across the heater surface

was noticeably more uniform. Unlike the highly polished silicon heaters, the aluminum

surfaces contained a wide variety of pits and cavities, as shown in Figs. 4.5 and 4.6.

0

20

40

60

80

100

120

140

0 5 10 15 20 25 30 35 40

∆∆∆∆T sat (°C)

Hea

t Flu

x (k

W/m

2 )

EDM pool boiling limitEDM, 1.0 mmEDM, 0.5 mm400 grit pool boiling limit400 grit, 0.5 mm600 grit pool boiling limit600 grit, 0.7 mm600 grit, 0.4 mm

Figure 5.7: Boiling curves for asymmetric aluminum heater channels.

Chapter 5: Channel Boiling 111 5.3 EFFECT OF CONFINEMENT ON CHF

CHF data obtained in the current study were normalized by the average CHF observed

for each type of heater material at large channel spacings (δ > 3 mm, L/δ < 5) for

comparison with the Bonjour and Lallemand (1997) correlation for CHF in

asymmetrically heated channels, Eq. (2.21) discussed in Section 2.7, and restated here as

Eq. (5.1).

( ) ( )[ ] 1517.1343.1gf

5

)0/(

CHF 252.0r1039.61

−−

=

×+=′′′′

δρρδ

Lq

q P

L

(5.1)

For the most part, the asymmetric channel data, shown in Fig. 5.8, agree with the Bonjour

and Lallemand (1997) correlation within its previously-stated accuracy of ± 12%. There

are a few outliers, particularly at high aspect ratio. However, given the channel spacing

uncertainty of ± 0.1 mm discussed in Chapter 3, a measured channel aspect of ratio of 67

(δ = 0.3 mm) could in reality range from 50 to 100. The horizontal error bars included in

Fig. 5.8 represent this uncertainty. All of the CHF data presented in Fig. 5.8 appear in

tabular form in Table I.7.

As should be expected, the effect of channel spacing on CHF is stronger for

symmetrically heated channels, and Eq. (5.1) does not apply. Further, due to differing

flow conditions, it is not possible to represent a symmetric channel as a simple

superposition of two asymmetric channels (Xia et al., 1996). As a first-order attempt at

achieving similitude between symmetric and asymmetrically heated channels, CHF data

obtained in the current study for symmetrically heated channels were modified by

multiplying channel aspect ratios by the square root of two and compared to predictions

based on Eq. (5.1). Figure 5.9 shows how this modification of symmetric channel aspect

ratios brings the CHF data within ± 12% of Eq. (5.1).


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 10 20 30 40 50 60 70 80 90 100 110

Channel Aspect Ratio (L /δ )

CH

F/C

HF(

L/ δ

0)

Eq. (5.1), ± 12%Si, Asymmetric Heating, 2x3Si, Asymmetric Heating, 2x2Si, Asymmetric Heating, 2x2, ScratchedAl, Asymmetric Heating, 2x2 (all surface conditions)Si, Symmetric Heating, 2x3 (w/modified aspect ratio)

Figure 5.8: Dependence of CHF data on aspect ratio and comparison with correlation of

Bonjour and Lallemand (1997), Eq. (5.1).

The symmetric channel data with modified aspect ratios are included in Fig. 5.8 as well.

Given enough CHF data spanning the range of parameters on which it is based, a similar

correlation could be developed independently for symmetric channels to test this

approximation. However, in lieu of modifying the channel aspect ratio by the square root

of 2, Eq. (5.1) could be modified as

( ) ( )[ ] 1517.1343.1gf

4

)0/(

CHF 252.0r1008.11

−−

=

×+=′′′′

δρρδ

Lq

q P

L

(5.2)

for prediction of CHF in symmetrically heated channels. The only difference between

Eqs. (5.1) and (5.2) is that the 6.39×10-5 coefficient in Eq. (5.1) has been multiplied by a

constant (√2)1.517 from the aspect ratio factor.


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 10 20 30 40 50 60 70 80 90 100

Channel Aspect Ratio (L /δ )

CH

F(L

/ δ)/C

HF(

0)

Eq. (5.1), ± 12%

Si, Symmetric Heating, 2x3 (w/actual aspect ratio)Si, Symmetric Heating, 2x3 (w/modified aspect ratio)

Figure 5.9: Dependence of symmetric channel CHF data on aspect ratio and comparison

with correlation of Bonjour and Lallemand (1997), Eq. (5.1).

Chapter 5: Channel Boiling 114 5.4 LOW FLUX ENHANCEMENT

Heat transfer in the low flux region of the nucleate boiling curve, heat fluxes below 40–

50 kW/m2 or 40% of unconfined CHF, from the silicon surfaces was greatly enhanced

with decreases in channel spacing. Figures 5.10 and 5.11 show the reduction of boiling

superheat with channel spacing for symmetric and asymmetric heating, respectively, at a

variety of heat fluxes. It is clear that at large spacings the superheat ratio approaches

unity, signifying unconfined pool boiling performance. At ever smaller spacings, various

levels of enhancement and deteriorated heat transfer performance are observed,

depending on heat flux.

Maximum enhancement of channel boiling was observed in asymmetric channels at a

heat flux of 25 kW/m2 (2.5 W/cm2). Boiling superheat at this heat flux with a 0.3 mm

channel spacing decreased by nearly 60% compared to unconfined pool boiling.

Symmetric channels with heat fluxes ranging from 7.5 to 25 kW/m2 (0.75–2.5 W/cm2)

yielded the same maximum enhancement at all channel spacings. Above the points of

maximum enhancement, confinement benefits are reduced with increasing heat flux until

the transition between enhanced low flux and deteriorated high flux is made.


0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.25 0.50 0.75 1.00 1.25 1.50

δδδδ (mm)

∆∆ ∆∆T

sat (( (( δδ δδ

)) ))/ ∆∆ ∆∆T

sat (∞

)(∞

)(∞

)(∞

)

696152433425167.5

Figure 5.10: Enhancement ratios for symmetric polished silicon heater channels at

various heat fluxes (kW/m2).

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.25 0.50 0.75 1.00 1.25 1.50

δδδδ (mm)

∆∆ ∆∆T

sat (( (( δδ δδ

)) ))/ ∆∆ ∆∆T

sat (∞

)(∞

)(∞

)(∞

)

796152433425167.5

Figure 5.11: Enhancement ratios for asymmetric polished silicon heater channels at

various heat fluxes (kW/m2).


0.00.10.20.30.40.50.60.70.80.91.01.11.2

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0Bo

∆∆ ∆∆T

sat (( (( δδ δδ

)) ))/ ∆∆ ∆∆T

sat (∞

)(∞

)(∞

)(∞

)

Water (Fujita et al., 1988)Water (Schweitzer, 1983)R-113 (Xia et al., 1996)FC-72, current study

Figure 5.12: Bond number comparison of confinement-driven enhancement from

asymmetrically heated channels.

Many researchers have employed the Bond number to relate channel spacing to bubble

departure diameter (Monde et al., 1982).

( )

−=

f

gf2Boσ

ρρδ

g (5.3)

Subtle variations of this parameter grouping include use of the reciprocal of Eq. (5.3)

(Xia et al., 1996), its square root (Yao and Chang, 1983) (Bonjour and Lallemand, 1998),

and the combination square root of the reciprocal (Kew and Cornwell, 1997) though with

hydraulic diameter (2δ for a parallel plate channel) instead of the gap size/channel

spacing, δ. Given that this type of parametric grouping takes on significance only when

dealing with multiple fluids with different properties, select asymmetric channel boiling

data for water from Fujita et al. (1988) and Schweitzer (1983), R113 from Xia et al.

(1996), and FC-72 from the current research are compared in Fig. 5.12. In this graph, the

normalized boiling surface superheat is plotted vs. Bond number.

Chapter 5: Channel Boiling 117 Presenting the data in the manner of Fig. 5.12 factors out the idiosyncratic nucleate

boiling behaviors of the various surfaces and allows for a direct comparison of the heat

transfer enhancement observed. While these data cover a variety of conditions, the

general trend does suggest that the Bond number can capture many of the effects of

channel spacing. Yao and Chang (1983), Kew and Cornwell (1997), and Bonjour and

Lallemand (1998) all identify the equivalent of Bo = 1 as defined in Eq. (5.3) as the

general transition point between confined and unconfined behaviors. While some

enhancement is shown to begin somewhat before this point, perhaps around a Bond

number of 2, enhancement does not become significant until values of 1 or less,

particularly in relation to typical boiling correlation uncertainties of ±30%. Furthermore,

as previously noted, many researchers define Bond number as the square root of

Eq. (5.3). If the data of Fig. 5.12 were plotted using this alternate definition, it would

appear more tightly concentrated around a value of 1.

Clearly, a multifluid comparison similar to that of Fig. 5.12 based on channel spacing

alone would not provide satisfactory results, particularly at small channel spacings.

Table 5.1 shows how different fluids have significantly different spacings for a given

Bond number. Unfortunately, Bond number alone can not explain the heat flux trends left

unresolved by Fig. 5.12.

Table 5.1: Relationship between channel spacing and Bond number values for select

fluids, based on saturation properties at atmospheric pressure.

FC72 R113 H2O FC-72 R-113 H2O0.3 0.17 0.08 0.014 0.2 0.3 0.5 1.10.7 0.93 0.45 0.078 1 0.7 1.0 2.51 1.9 0.93 0.16 4 1.4 2.1 5.02 7.6 3.7 0.64 10 2.3 3.3 7.95 48 23 4.0 16 2.9 4.2 10

BoChannel Spacing, δδδδ (mm)

δδδδ (mm)Bo

Chapter 5: Channel Boiling 118 Yao and Chang (1983) developed a boiling regime map for R-113, acetone, and water at

atmospheric pressure in narrow annular gaps with closed bottoms based on Bond number

and the Boiling number

bgfg uh

LqBlδρ

′′= (5.4)

where ub is the characteristic bubble rise velocity, given as

( )

f

gfbb

gDu

ρρρ −

= (5.5)

The Boiling number represents the ratio of the bubble rise time through the channel (L/ub)

to the bubble expansion time (hfgρgδ/q”). At Bond numbers less than 1, Yao and Chang

(1983) visually observed isolated deformed bubbles at all Boiling numbers below CHF.

At Bond numbers near unity, coalesced deformed bubbles were observed, except at high

heat fluxes (Boiling number) where nucleation occurred under slightly deformed bubbles.

Given that the annulus of Yao and Chang (1983) was closed at the bottom, the identified

bubble regimes can be expected to be somewhat different from situations where fresh

liquid can flow into the confined space from the bottom. Furthermore, the bubble rise

velocity of Eq. (5.5) does not accurately represent the characteristic bubble velocity in the

accelerated two phase flow of an open-bottom channel.

The bubble regime trends identified by Bonjour and Lallemand (1998) were well

captured using the reduced heat flux, that is, heat flux normalized by CHF at that channel

spacing (q”/q”CHF,δ). However, its use in the context of the current study proved

unsuccessful. This lack of correlation can be demonstrated by considering the

enhancement data of Fig. 5.12. The channel boiling data from Xia et al. (1996)

corresponds to reduced heat fluxes well below 0.2. The water data from Fujita et al.

(1988) came from significantly higher reduced heat fluxes (0.3–0.8), while the FC-72

data was in between (0.1–0.45). Furthermore, the reduced heat flux ratio also fails to

bridge the gap between the symmetric and asymmetric FC-72 channel data of Figs. 5.1

and 5.2.


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 5 10 15 20 25 30

∆∆∆∆T sat (°C)

Hea

t Flu

x R

atio

, q"/

q"C

HF,

δδ δδ

sym, 0.3 mmsym, 0.7 mmsym, 1.5 mmasym, 0.3 mmasym, 0.7 mmasym, 1.5 mmLarge Spacing Limit

Figure 5.13: Comparison of FC-72 symmetric and asymmetric channel boiling curves

from Figs. 5.1 and 5.2 based on reduced heat flux.

This comparison is shown in Fig. 5.13 for δ = 0.3, 0.7, and 1.5 mm. Clearly, correlation

of confinement-driven enhancement will require significantly more sophisticated

analysis.

5.4.1 Convective Enhancement

As discussed in Section 2.3, flow boiling two phase heat transfer coefficients are

typically expressed as a summation of convective and boiling contributions, often with

empirically or theoretically determined enhancement and suppression factors multiplying

the individual terms, e.g. (Chen, 1963). If it is assumed that the boiling contribution

remains unchanged, while the convective contribution increases with decreasing channel

spacing, convective heat transfer coefficients can be calculated by subtracting the large

Chapter 5: Channel Boiling 120 spacing pool boiling heat transfer coefficients from the overall heat transfer coefficient at

a given spacing, i.e.:

( ) ( )∞−= hhh δconvective (5.6)

Figure 5.14 shows the difference between experimental asymmetric channel and

unconfined pool boiling heat transfer coefficients. The additional contribution above

unconfined boiling due to confinement effects is significant—in some cases 2 or 3 times

larger than the corresponding large spacing pool boiling heat transfer coefficients.

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30

∆∆∆∆T sat (°C)

h(( (( δδ δδ

)) )) −− −− h

(∞)

(∞)

(∞)

(∞)

(W/m

2 K)

0.3 mm data0.7 mm data1.5 mm data1.6 mm dataEq. (2.17) 0.3 mm, S=3Eq. (2.17) 0.3 mm, S=17Eq. (2.17) 0.3 mm, S=30Eq. (2.17) 0.7 mm, S=17Eq. (2.17) 1.5 mm, S=17

Figure 5.14: Confinement contribution to experimental heat transfer coefficients for

asymmetric polished silicon heater channels compared to Bar-Cohen and Schweitzer

(1985b) thermosyphon boiling model, Eq. (2.17).

Chapter 5: Channel Boiling 121 Single phase natural convection cooling of parallel plate channels is investigated in detail

in Chapter 6. Results presented in Table 6.2 for comparable channels immersed in FC-72

show single phase natural convection heat transfer coefficients on the order of

200 W/m2K. While moderate enhancement of single phase natural convection by

secondary effects, due to temperature gradients and 3-dimensional flow, might, thus, be

sufficient to explain the heat transfer coefficients observed at the larger, 1.5 and 1.6 mm,

channel spacings in the data of Fig. 5.14, the order-of-magnitude enhancement observed

at the smaller spacings is far to large to explain in this way.

The Bar-Cohen and Schweitzer (1985b) thermosyphon boiling model discussed in detail

in Chapter 2 considers buoyancy-induced “forced convective” enhancement of heat

transfer in narrow vertical channels. Figure 5.14 also shows how predictions based on

this model compared to the difference between asymmetric channel and unconfined pool

boiling heat transfer coefficients. Figure 5.15 shows a similar comparison between the

Bar-Cohen and Schweitzer (1985b) model and the present experiments for the symmetric

channel temperature enhancement ratios of Fig. 5.10. The major assumption herein is that

the slip ratio value of 17 obtained by Bar-Cohen and Schweitzer (1985b) for water

applies equally as well to FC-72. Calculated two phase flow parameters like void

fraction, exit quality, mass flow rate are highly dependent on the assumed value of slip

ratio. Fortunately, the ultimate prediction of two phase heat transfer coefficient is

relatively insensitive to slip ratio over a wide range (particularly at low heat fluxes), and

trends are unaffected. Figure 5.14 includes predictions based on S values equal to 3 and

30 at a channel spacing of 0.3 mm to demonstrate this behavior. Predicted heat transfer

coefficients are significantly less dependent on slip ratio at larger channel spacings.


0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.25 0.50 0.75 1.00 1.25 1.50

δδδδ (mm)

∆∆ ∆∆T

sat (( (( δδ δδ

)) ))/∆∆ ∆∆

Tsa

t (∞)

(∞)

(∞)

(∞)

6943257.5

prediction

Figure 5.15: Enhancement ratios for symmetric polished silicon heater channels

compared to Bar-Cohen and Schweitzer (1985b) model at various heat fluxes (kW/m2).

Clearly the theoretical predictions shown in Figs. 5.14 and 5.15 do not match the trends

observed in the data. The experimental data on which the correlation is based were

obtained at very low heat fluxes compared to CHF for water. However, the model is

based on an annular flow assumption, suggesting the model should be appropriate for

very narrow channels, where relatively little bubble generation is sufficient to create

significant channel void fractions. The Bar-Cohen and Schweitzer (1985b) model does

not predict significant enhancement as early as seen in the data. In fact, it tends to predict

drastically increasing enhancement only as the experimental curves approach CHF. If

convective enhancement is indeed present, the comparisons of Figs. 5.14 and 5.15

suggest that an alternate enhancement mechanism comes into play and dominates before

the forced convection enhancement component is significant.

Chapter 5: Channel Boiling 123 Fortunately, we are at the beginning of an era when computational tools and computing

resources can adequately simulate two phase flow and heat transfer in bubble-sized

geometries. Given that bubble motion can affect the motion of the liquid phase as much

as the liquid phase affects bubble motion, an Euler-Euler multiphase approach, such as

the volume of fluid (VOF) method (Harlow and Welch, 1965) (Hirt and Nichols, 1981) is

required. While the literature contains many direct numerical simulation studies of

idealized individual bubble nucleation and motion in unconfined pools, see (Dhir, 2006),

examples of confined nucleate boiling problems are quite scarce.

Khalij et al. (2006) performed a VOF-based numerical study of subcooled forced flow

boiling of FC-72 in asymmetrically heated horizontal channels. A simple evaporation and

condensation model was employed, using a vapor source term dependent on the

difference between the fluid mixture temperature in a computation cell and the saturation

temperature of the liquid. Thus, finer details of individual bubble nucleation, growth,

departure, and coalescence are not included. Further, the channel dimensions were

relatively large (2.5 × 5 × 110 mm) compared to typical FC-72 bubbles (D ≈ 0.5–1 mm),

with computational cells 0.125 × 0.125 × 0.5 mm in size. The authors report satisfactory

agreement with experimental vapor visualizations from the literature. While the effect of

vapor distribution on wall temperature distributions is displayed, general heat transfer

performance is not discussed.

Appendix F contains an effort pursued in the context of the current research to execute

VOF multiphase simulations of buoyancy-driven saturated boiling in narrow vertical

channels using the commercially-available Fluent CFD software package. Unfortunately,

as discussed further in Appendix F, available computing resources were not adequate to

provide workable 3-D solution run times. However, results from 2-D simulations suggest

that enhanced natural convection already accounts for a large portion of the unconfined

pool boiling heat flux. While the increased buoyancy from larger vapor fractions in the

narrow channels leads to an order of magnitude increase in channel mass flux, convective

enhancement is found to be greater for 0.7 mm wide channels than narrower 0.3 mm

Chapter 5: Channel Boiling 124 channels. Even so, the enhancement is only on the order of 20%. These results further

suggest an alternate enhancement mechanism not based solely on increased convection of

the liquid phase.

5.4.2 Thin Film Evaporation and Transient Conduction

In the literature it is almost exclusively assumed that forced flow boiling heat transfer is

governed by forced convection and nucleate boiling (Zhang et al., 2004). However, the

majority of forced flow studies employ high mass flow rates and subcooled liquid. Even

so, flow boiling studies in small channels (Bo < 1) are still relatively scarce (Cheng and

Mewes, 2006).

When investigating buoyancy-driven flows in narrow vertical channels, numerous

researchers have considered evaporation of the thin film between compressed bubbles

and the heated wall, transient conduction to the liquid phase in the bubble slug wake, or

some combination of these two mechanisms, e.g. (Ishibashi and Nishikawa, 1969) (Fujita

et al., 1987) (Monde, 1988). However, detailed knowledge of many two phase flow

parameters (void fraction, film thickness, bubble passage times, etc.) is required for these

types of predictions. Even when two phase flow parameters are carefully estimated or

even measured directly, these models have met with only limited success (Zhao et al.,

2003).

Transient conduction to the liquid phase is, of course, included in the CFD simulations

discussed in the previous section. With extension of the VOF CFD model discussed in

Appendix F, it would be possible to include mass transfer between the phases and

investigate thin film evaporation in addition to transient conduction and convective

enhancement mechanisms. This would require the creation of a custom user-defined

function (UDF) in addition to significant refinement of the mesh near heater surface to

resolve thin evaporating liquid films. Predictions of the liquid film thickness will most

definitely require experimental validation.

Chapter 5: Channel Boiling 125 If transient conduction, either into the bulk liquid or through a thin film, was indeed the

dominant enhancement mechanism occurring in the current study, the silicon and

aluminum heaters should have shown the same behavior. While the thermal diffusivity of

aluminum is 50% larger than that of silicon (9.5×10−5 and 6.3×10−5 m2/s at 100°C,

respectively), both are three orders of magnitude greater than that of FC-72

(2.9×10−8 m2/s).

5.4.3 Vapor and Nucleation Site Interactions

None of the enhancement mechanisms discussed thus far would appear to explain the

differences observed in low flux behavior between the silicon and aluminum channels.

The prevalence of low flux enhancement in silicon channels and its absence in aluminum

channels suggests an enhancement mechanism linked to surface characteristics. Attempts

to achieve similitude by polishing and roughening the surfaces were unsuccessful, despite

significant shifts in the boiling curves. However, it has been demonstrated that simple

polishing techniques do not necessarily affect cavity size distributions, and,

fundamentally, surface roughness effects and nucleation site dynamics are quite complex

(Kandlikar and Spiesman, 1998).

It is relatively unusual to publish studies that show a lack of interesting phenomena (i.e. a

lack of expected enhancement). However, in addition to the methanol experiments of

Chien and Chen (2000) discussed in Section 2.8, Feroz MD and Kaminaga (2002) also

note a lack of enhancement at sub-unity Bond numbers. Their experimental study

considered buoyancy-driven boiling of R-113 in a vertical stainless steel tube with a

1.45 mm inner diameter. Effective confinement was varied by changing the system

pressure and, as a result, characteristic bubble sizes. Contrary to the authors’ expectation,

no enhancement was observed, despite achieving equivalent Bond numbers as low as 0.4.

Unfortunately, no description of the internal surface characteristics of the tube is

provided.

Chapter 5: Channel Boiling 126 In the context of the present study, it is unknown what characteristics of the nucleation

sites and their distribution across the aluminum surfaces preclude the enhancement of

confined boiling. Presumably the aluminum surfaces possess a large number of

nucleation site cavities with a wide variety of shapes and sizes. In addition to the polished

silicon surface, even the scratched silicon surface would be expected to be limited in

variety of potential nucleation sites. In at least a notional sense, the potential for

enhancement should be higher. Thus, it is proposed that in these experiments confined

bubbles interact with the silicon surfaces in a manner not available to the diverse,

nucleation-rich aluminum surfaces that modified bubble nucleation, growth, and

departure, leading to increased heat transfer. This is also consistent with the observation

of no enhancement in the highly subcooled silicon channels, where, presumably, bubble

condensation and collapse would tend to lessen these interactions.

Nucleation site interaction effects have been well documented in a wide variety of forms.

Judd and Chopra (1993), for example, studied the ability of growing or passing bubbles

to deposit bubble embryos and initiate nucleation at adjacent sites. In this highly detailed,

data acquisition-intensive experiment, bubble departure diameters and growth and

waiting times were measured at randomly located natural nucleation sites on a large

heated surface. Chai et al. (2000) theoretically considered additional effects of heat

conduction in the boiling surface as well as thermodynamic aspects of bubble fluctuations

on the stability of adjacent bubble nuclei. Bonjour et al. (2000) investigated the effects of

bubble coalescence on bubble growth and heat transfer from artificial nucleation sites

with various separation distances and demonstrated that moderate coalescence increases

heat transfer. Enhancement was attributed to vaporization of the relatively large

supplementary microlayer formed between bubble stems.

During unconfined boiling experiments of pentane, Bonjour and Lallemand (2001)

measured void fraction profiles normal to the vertical heated surface. It was observed that

at high heat fluxes bubbles tend to stay close to the surface and coalesce. On the other

hand, at low and moderate heat fluxes bubble detachment provides a force which propels

Chapter 5: Channel Boiling 127 bubbles away from the surface, creating a rising bubble column approximately 2 to 2.5

bubble diameters away from the surface. This behavior not only helps explain the

increased bubble/surface interactions proposed by Guo and Zhu (1997), discussed in

Chapter 2, but it may also explain the trends in the channel boiling data of Figs. 5.1 and

5.2. Subtle confinement effects were observed for channel spacings less than 2 mm,

where the opposing wall would start to interfere with the rising bubble column at low

heat fluxes. At higher heat fluxes, boiling heat transfer rates may be equivalent to

unconfined performance, as the bubble column moves closer to the heater surface.

These insights highlight the need to investigate surface characteristics in addition to two

phase flow phenomena in confined boiling systems. Generalized physics-based prediction

of low flux confinement-driven enhancement should be expected to be extremely

complicated and involve the consideration of a wide variety of fluid, surface, material,

and geometric parameters.

128

CHAPTER

SIX

PASSIVE IMMERSION COOLING OF 3-D STACKED DIES

Given the experimental data and analytical treatments presented in the preceding

chapters, attention is now turned to the design and optimization of confined boiling

structures in electronics cooling applications. This chapter considers both single phase

natural convection and boiling heat transfer between stacked dies. In Chapter 7, channel

CHF limits and boiling heat transfer coefficients are combined with fin conduction

analyses to evaluate and maximize the heat dissipation capability of longitudinal

rectangular plate fin boiling heat sinks.

As discussed in Chapter 1, 3-D stacked die packages are an emerging technology.

Conduction cooling of a stack of heat sources separated by electrically insulating and

relatively low thermal conductivity materials can be expected to yield large temperature

gradients. On the other hand, immersion cooling techniques which provide fluid flow

between stacked dies and high heat transfer coefficients directly on the die surfaces could

be very efficient in producing a relatively isothermal die stack. Design-level heat transfer

calculations are now performed for various geometries, based on the geometry illustrated

in Fig. 1.3. Details of particular interconnect technologies (wire bonds, through-silicon

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 129 vias, etc.) will not be considered, as there is currently no clear leader for next generation

3-D packages (Arunasalam et al., 2006). Fortunately, in addition to being scalable to any

number of dies, the direct liquid cooling approach can easily accommodate a wide variety

of interconnect schemes.

6.1 SINGLE PHASE NATURAL CONVECTION COOLING OF 3-D

STACKED DIES

Despite increasing performance demands and advances in thermal management

technology, single phase convective cooling of electronic equipment (most often with air)

dominates the product landscape. Single phase natural convection is the quietest, least

expensive, easiest to implement, and most reliable implementation of direct fluid cooling.

In addition, single phase natural convection liquid cooling provides a convenient lower

bound for boiling and a benchmark solution for other advanced cooling approaches.

6.1.1 The Heat Transfer Coefficient

Convective heat transfer from a surface to a fluid in motion is often expressed as a linear

function of the heat transfer surface area, A, and the temperature difference between the

fluid and the surface.

)( fluidsurface TThAQ −= (6.1)

It should be noted that while commonly referred to as Newton’s Law of Cooling,

evidence suggests that it was, in fact, Fourier who first proposed the heat transfer

coefficient and form of Eq. (6.1) (Adiutori, 1990). The differences between convection to

a rapidly moving fluid, a slowly flowing or stagnant fluid, as well as variations in the

convective heat transfer rate among various fluids, are reflected in the heat transfer

coefficient, h. For a particular geometry and flow regime, h may be obtained from

empirical correlations and/or theoretical relations. Note that for a symmetrically heated

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 130 channel, the appropriate area to use in Eq. (6.1) is twice the area of a single wall, 2LH,

while for an asymmetrically heated channel, A = LH.

Some common dimensionless quantities that are used in the correlation of natural

convection heat transfer data are the Nusselt number, Nu, which relates the convective

heat transfer coefficient to the conduction in the fluid,

f

NukhL

L ≡ (6.2)

the Prandtl number, Pr, which is a fluid property parameter relating the diffusion of

momentum to the conduction of heat,

f

Prk

cpµ≡ (6.3)

and the Grashof number, Gr, which accounts for the buoyancy effect produced by the

volumetric expansion of the fluid,

2

32

Grµ

βρ TgLL

∆≡ (6.4)

In natural convection, fluid motion is induced by density differences resulting from

temperature gradients in the fluid. The heat transfer coefficient for this regime can be

related to the buoyancy and the thermal properties of the fluid through the Rayleigh

number, Ra, which is the product of the Grashof and Prandtl numbers,

TLkgc p

L ∆≡ 3

f

2

Raµβρ

(6.5)

where the fluid properties are evaluated at the film temperature (the average temperature

between the surface and bulk liquid) and ∆T is the temperature difference between them.

Empirical correlations for the natural convection heat transfer coefficient generally take

the form

( )mC RaNu = (6.6)

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 131 where m is found to be typically 1/4 for 103 < Ra < 109, representing laminar flow, 1/3

for 109 < Ra < 1012, the region associated with the transition to turbulent flow, and 1/2.5

for Ra > 1012 when strong turbulent flow prevails. The precise value of the correlating

coefficient, C, depends on the thermophysical properties of the fluid, the geometry of the

surface, and the Rayleigh number range.

6.1.2 Natural Convection Correlations

Vertical parallel plate channels are a frequently encountered configuration in natural

convection cooling of electronic equipment. The historical work of Elenbaas (1942), a

milestone of experimental results and empirical correlations, was the first to document a

detailed study of natural convection in smooth, isothermal parallel plate channels. In

subsequent years, this work was confirmed and expanded both experimentally and

numerically by a number of researchers, including Bodoia (1964), Sobel et al. (1966),

Aung (1972), Aung et al. (1972), Miyatake and Fujii (1972), Miyatake et al. (1973), and

Geisler and Bar-Cohen (1997).

These studies revealed that channel Nusselt numbers lie between two extremes associated

with the separation between the plates (channel spacing, δ). At wide spacings, the plates

appear to have little influence upon one another and the Nusselt number in this case

achieves its isolated plate limit. On the other hand, for closely spaced plates or relatively

long channels, the fluid attains its fully developed velocity profile, and the Nusselt

number reaches its fully developed limit. Intermediate values of the Nusselt number can

be obtained from a family of composite expressions developed by Bar-Cohen and

Rohsenow (1984) and verified by comparison to numerous experimental and numerical

studies.

For an isothermal channel, at the fully developed limit, the Nusselt number takes the form

fd,

isothermal ElNuTC

=δ (6.7)

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 132 where El is the Elenbaas number, defined as

( )

LkTTgc

Lp

Lf

4ambw

2

4

4

RaElµ

δβρδ −=≡ (6.8)

where δ is the channel spacing, L is the channel length, and (Tw – Tamb) is the temperature

difference between the channel wall and the ambient, or channel inlet. For an asymmetric

channel, one in which one wall is heated and the other is insulated, the appropriate value

of CT,fd is 12, while for symmetrically heated channels, CT,fd = 24.

For an isoflux channel, at the fully developed limit, the Nusselt number has been shown

to take the form

fd,

isoflux lENuq

x

C ′′

′=δ (6.9)

where the modified Elenbaas number, El’, is defined as

zkqgcp

2f

52

lEµ

δβρ ′′≡′ (6.10)

where q” is the heat flux leaving the channel wall(s). To calculate the maximum wall

temperature, the modified Elenbaas number should be based on the channel exit (z = L).

In this case, the appropriate values of Cq”,fd are 24 and 48 for asymmetric and symmetric

heating, respectively. When the channel mid-height (z = L/2) wall temperature is of

interest, the asymmetric and symmetric Cq”,fd values are 6 and 12, respectively.

In the limit where the channel spacing is very large, the opposing channel walls do not

influence each other hydrodynamically or thermally. This situation may be accurately

modeled as heat transfer from an isolated vertical surface in an infinite medium. Natural

convection from an isothermal plate is typically expressed as

41ip, ElNu TC=δ (6.11)

McAdams (1954) suggests a CT,ip value of 0.59 for air. Bar-Cohen and Schweitzer

(1985a) reinterpreted McAdams’ (1954) results to provide the following Prandtl number

correction to accommodate other fluids.

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 133

41

ip, Pr861.0Pr72.0

+=TC (6.12)

Note that for saturated FC-72 at atmospheric pressure, Pr = 9.55 yielding CT,ip = 0.705.

Further, as shown in Table A.1, FC-84 and FC-77 have Prandtl number values of 8.03

and 8.64, yielding CT,ip values of 0.702 and 0.703, respectively—a difference of less than

0.5%.

Natural convection from an isoflux isolated plate may be expressed as

51ip, lENu ′= ′′qCδ (6.13)

For air, leading coefficients of 0.63 when based on the maximum (z = L) wall

temperature and 0.73 when based on the mid-height (z = L/2) wall temperature are

appropriate (Bar-Cohen and Rohsenow, 1984). Likewise, Bar-Cohen and Schweitzer

(1985a) employed Cq”,ip values of 0.60 and 0.69 for water when z = L and L/2,

respectively. Table 6.1 summarizes the various C coefficient values discussed in this

section.

Table 6.1: Summary of C coefficient values for various cases.

Symmetric Asymmetric

24 12

0.63 - Air0.60 - H2O0.73 - Air

0.69 - H2O

Fully Developed Channel Limit

Isoflux

Isothermal

Isolated Plate Limit

Maximum TemperatureMid-Height

Temperature

48 24

612

41

Pr861.0Pr72.0

+

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 134 6.1.3 Composite Equations for Vertical Channels

When a function is expected to vary smoothly between two limiting expressions, which

are themselves well defined, and when intermediate values are difficult to obtain, an

approximate composite relation can be obtained by appropriately summing the two

limiting expressions. Using the Churchill and Usagi1 (1972) method, Bar-Cohen and

Rohsenow (1981) developed composite Nusselt number relations for natural convection

in parallel plate channels of the form

( ) ( )[ ] nnn 1ipfdcomposite NuNuNu

−−− += (6.14)

where Nufd and Nuip are Nusselt numbers for the fully developed and isolated plate limits,

respectively. The correlating exponent n was given a value of 2 to offer good agreement

with Elenbaas’ (1942) experimental results.

For an isothermal channel, combining Eqs. (6.7) and (6.11) yields a composite relation of

the form

212

ip,2

2fd,isothermal

ElElNu

−−

+= TT CC

δ (6.15)

while for an isoflux channel, Eqs. (6.9) and (6.13) yield a result of the form

21

52

2ip,fd,isoflux

lElENu

−−′′′′

′+

′= qq CC

δ (6.16)

Figures 6.1 through 6.4 contain graphs of these composite relations for symmetric and

asymmetric heating conditions along with the fully developed and isolated plate limits.

Predictions based on Eq. (6.15) were compared to the single phase asymmetric channel

simulations of Appendix F and agree within 5% (see Table F.2).


0.1

1

10

1 10 100 1000 10000 100000

El

Nu

CompositeFully DevelopedIsolated Plate99% MaximumOptimum

Figure 6.1: Isothermal Nusselt number correlations, symmetric heating, CT,ip = 0.705.

0.1

1

10

1 10 100 1000 10000 100000

El

Nu


Figure 6.2: Isothermal Nusselt number correlations, asymmetric heating, CT,ip = 0.705.


0.1

1

10

1 10 100 1000 10000 100000

El'

Nu


Figure 6.3: Isoflux Nusselt number correlations, based on maximum temperature (z = L),

symmetric heating, Cq”,ip = 0.60.

0.1

1

10

1 10 100 1000 10000 100000

El'

Nu


Figure 6.4: Isoflux Nusselt number correlations, based on maximum temperature (z = L),

asymmetric heating, Cq”,ip = 0.60.

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 137 6.1.4 Maximizing Heat Transfer

In applications where volumetric concerns are not an issue, it is advantageous to space

channel walls sufficiently far apart to ensure that the isolated plate Nusselt number

prevails. In lieu of choosing an infinite channel spacing, the spacing which yields a

composite Nusselt number equal to 99% (or some other high fraction) of the asymptotic

isolated plate value can be selected.

For an isothermal channel, the channel spacing that maximizes heat transfer takes the

form

( )

( )41

61

2

22ip,

2fd,isothermal

max 99.0199.0 −

−= P

CC TTδ (6.17)

where

( )

4f

ambw2 El

δµβρ

=−

=Lk

TTgcP p (6.18)

while for an isoflux channel, the channel spacing that minimizes wall temperature for a

given heat flux takes the form

( )

( )51

31

2

22ip,fd,isoflux

max 99.0199.0 −′′′′ ′

−= P

CC qqδ (6.19)

where

52f

2 lEδµ

βρ ′=

′′=′

zkqgc

P p (6.20)

These points are included in the graphs of Figs. 6.1 through 6.4 and clearly lie well into

isolated plate behavior. Due to the presence and interaction of two opposing boundary

layers in symmetrically heated channels, isolated plate behavior occurs at larger channel

spacings and Elenbaas numbers (and modified Elenbaas numbers) 2.5–3 times that

required to come within 99% of the isolated plate limit with asymmetrically heated

channels.

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 138 6.1.5 Optimizing Channel Spacing

In addition to being used to predict heat transfer coefficients, the composite relations

presented may also be used to optimize the spacing between plates. For isothermal arrays,

the optimum spacing maximizes total heat transfer from a given base area or volume

assigned to an array of plates. In the case of isoflux parallel plate arrays, the total array

heat transfer for a given base area may be maximized by increasing the number of plates

indefinitely, though the plates will experience dramatic increases in temperature as the

spacing is reduced toward zero. Thus, it is more appropriate to define the optimum

channel spacing for an array of isoflux plates as the spacing that will yield the maximum

volumetric heat dissipation rate per unit temperature difference. Despite this distinction,

the optimum spacing is found in the same manner for both cases.

Combining Eqs. (6.1) and (6.2), the total heat transfer rate from an array of vertical,

double-sided plates (symmetric channel heating) can be written as

( )

+=

tδTLHWkQ

δNu

∆2T (6.21)

where the number of plates is W/(δ + t), t is the plate thickness, W is the width of the

entire array, and H is the depth of the channel. Expressions for the optimum spacing may

be found by substituting the appropriate composite Nusselt number equation into the

right-hand side of Eq. (6.21), taking the derivative of the resulting expression with

respect to δ, and setting the result equal to zero. Note that the expression for total heat

transfer from an array of single-sided plates (asymmetric channel heating) would differ

from Eq. (6.21) only by the absence of the factor of 2 multiplying the plate area LH in the

denominator of the left-hand side. Thus, the only impact of symmetric vs. asymmetric

heating comes in the C coefficients of the Nusselt number correlations. After

differentiation, use of the isothermal composite Nusselt number relation, Eq. (6.15), in

Eq. (6.21) yields a relation of the form

( )( ) 032opt

7232ip,fd, =−+ − δδ PCCt TT (6.22)

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 139 or

( ) 4131

ip,fd,isothermalopt 2 −= PCC TTδ (6.23)

in the limit where the plate thickness, t, is negligibly small. Combining Eqs. (6.23) and

(6.18) produces an expression for the optimum Elenbaas number in this limit

( ) 34

ip,fd,opt 2El TT CC= (6.24)

Similarly, the isoflux composite Nusselt number relation, Eq. (6.16), yields

( )( ) 023opt

45322ip,fd, =′−+ −

′′′′ δδ PCCt qq (6.25)

and the following thin plate isoflux optimum channel spacing and Elenbaas number

expressions

( ) 51

312ip,fd,isoflux

opt 2−′′′′ ′

= P

CC qqδ (6.26)

( ) 352

ip,fd,opt 2

lE

=′ ′′′′ qq CC

(6.27)

Optimum Elenbaas numbers in the thin plate limit, Eqs. (6.24) and (6.27) are included in

the graphs of Figs. 6.1 through 6.4. Optimum points are clearly shown to occur in the

transition region between the fully developed channel and isolated plate limits. The

effects of finite plate thickness on optimum spacing, represented by Eqs. (6.22) and

(6.25), are shown in Figs. 6.5 through 6.8 for the same conditions represented by

Figs. 6.1 through 6.4. As plate thickness increases, so does the optimum spacing. With

thicker plates, the inclusion of each additional channel in an array comes with an

increasingly larger channel spacing “cost,” which leads to deteriorated heat transfer.

Thus, with thicker plates, there is an advantage of slightly larger channel spacings, and

the optimum shifts in this manner. Optimum channel spacings for isothermal

symmetrically heated channels are consistently 1.2–1.3 times larger than asymmetric

channels for a given combination of t and P. In the isoflux case, optimum channel

spacings for isoflux symmetric channels are 1.4–1.6 times larger than corresponding

asymmetric channel results.


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.0 0.2 0.4 0.6 0.8 1.0

Plate Thickness, t (mm)

Opt

imum

Spa

cing

, δδ δδ (m

m)

1.E+131.E+141.E+151.E+161.E+171.E+18

P


symmetric heating, CT,ip = 0.705.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.0 0.2 0.4 0.6 0.8 1.0


Opt

imum

Spa

cing

, δδ δδ (m

m)

1.E+131.E+141.E+151.E+161.E+171.E+18

P


asymmetric heating, CT,ip = 0.705.


0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0.0 0.2 0.4 0.6 0.8 1.0


Opt

imum

Spa

cing

, δδ δδ (m

m)

1.E+161.E+171.E+181.E+191.E+201.E+21

P'

Figure 6.7: Optimum spacing as a function of plate thickness: isoflux plates, maximum

temperature (z = L), symmetric heating, Cq”,ip = 0.60.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.2 0.4 0.6 0.8 1.0


Opt

imum

Spa

cing

, δδ δδ (m

m)

1.E+161.E+171.E+181.E+191.E+201.E+21

P'

Figure 6.8: Optimum spacing as a function of plate thickness: isoflux plates, maximum

temperature (z = L), asymmetric heating, Cq”,ip = 0.60.

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 142 6.1.6 Sample Calculations for Die Stacks Immersed in FC-72

Table 6.2 contains the results of parametric calculations performed for single phase

natural convection cooling of 3-D die stacks at the optimum spacings calculated from

Eq. (6.22) for isothermal die, assuming symmetric heating. Geometric nomenclature used

in the table corresponds to that illustrated in Fig. 1.3. The bulk liquid is assumed to be at

56.6°C, and fluid properties were evaluated at the film temperature. As the results show,

over the parameter ranges of interest, t = 0.04–0.40 mm, L = 10–20 mm, and temperature

differences from 20 to 30°C, heat transfer coefficients range from 200 to 300 W/m2K.

Rayleigh numbers suggest operation at or near the upper range of laminar flow, and Biot

numbers (hL/k) based on the length of the die in the flow direction are less than 0.1,

validating the choice of heat transfer correlations employed. Optimum spacings are on

the order of 0.4 mm. At the upper range of plate thickness, roughly equal to the optimum

spacings, volumetric dissipation rates are nearly half those achievable with thinner plates,

8–23 MW/m3 vs. 14–43 MW/m3 (1 MW/m3 = 1 W/cm3). Volumetric heat dissipation is

calculated using Eq. (6.21).

Table 6.2: Results of example calculations for single phase natural convection cooling of

3-D die stacks immersed in saturated FC-72 at atmospheric pressure. t (mm) 0.40 0.40 0.40 0.40 0.04 0.04 0.04 0.04L (mm) 10 10 30 30 10 10 30 30∆T (°C) 20 30 20 30 20 30 20 30Ra 3.9E+07 5.9E+07 1.1E+09 1.6E+09 3.9E+07 5.9E+07 1.1E+09 1.6E+09δ opt (mm) 0.42 0.38 0.54 0.49 0.37 0.34 0.49 0.44δ max (mm) 0.62 0.56 0.82 0.74 0.62 0.56 0.82 0.74El 124 129 113 117 76 77 74 75Nui.p. 2.4 2.4 2.3 2.3 2.1 2.1 2.1 2.1Nuf.d. 5.2 5.4 4.7 4.9 3.2 3.2 3.1 3.1Nucomp. 2.1 2.2 2.1 2.1 1.7 1.7 1.7 1.7h i.p. (W/m2K) 291 322 221 245 291 322 221 245h f.d. (W/m2K) 640 728 454 515 443 494 331 369h comp. (W/m2K) 265 294 199 221 243 270 184 204q " (kW/m2) 5.30 8.83 3.97 6.63 4.86 8.09 3.68 6.12Q /V (MW/m3) 12.9 22.5 8.4 14.8 23.5 42.8 13.9 25.3

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 143 Figure 6.9 shows heat transfer coefficient and heat flux results for symmetric isothermal

parallel plate channels, 20 mm in length (L), immersed in saturated FC-72 at atmospheric

pressure. Curves are shown for channel spacing values of 5, 0.5, 0.4, and 0.2 mm,

corresponding Elenbaas number ranges >1×105, ≈100, 10–100, and <10, respectively. For

these results, δmax is below 1 mm for all but the smallest temperature differences.

Therefore, the 5 mm results are well into isolated plate behavior. In addition to

temperature, optimum channel spacings are also dependent die thickness but are typically

around 0.5 mm for these results. Below a spacing of 0.4 mm, heat transfer drops sharply,

and at a channel spacing of 0.2 mm, results are well into fully developed channel

behavior. These trends are quite obvious when the Elenbaas number ranges noted above

are compared to the Nusselt number curves of Fig. 6.1.

0

50

100

150

200

250

300

0 5 10 15 20 25 30 35

Wall Superheat, ∆∆∆∆T sat (°C)

Hea

t Tra

nsfe

r Coe

ffici

ent,

h (W

/m2 K

)

0

2000

4000

6000

8000

10000

12000

Hea

t Flu

x, q

" (W

/m2 )

h

q"

δ decreasing

Figure 6.9: Heat transfer coefficient and heat flux variations for isothermal die stacks,

immersed in saturated FC-72 at atmospheric pressure, 20 mm in length (L) with spacings

(δ) of 5, 0.5, 0.4, and 0.2 mm.

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 144 In Fig. 6.9, single phase natural convection heat transfer coefficients are shown to

increase with increasing wall temperature, decrease with decreasing channel spacing, and

generally range from 100 to 250 W/m2K for near-optimum channel spacings. The heat

flux curves of Fig. 6.9 may be considered to represent the lower bound of boiling heat

transfer, the natural convection portion of the boiling curve as heat flux is increased from

zero, before the onset of nucleate boiling.

Figures 6.10 and 6.11 contain composite, isolated plate, and fully developed heat transfer

coefficient curves as a function of channel spacing. In Fig. 6.10, two sets of curves are

shown, corresponding to superheats of 3 and 30°C. As should be expected in natural

convection, larger temperature differences produce larger heat transfer coefficients. In

Fig. 6.11, a superheat of 10°C is assumed, and points representing optimum volumetric

heat dissipation for a variety of plate thicknesses, t, are included.

0

50

100

150

200

250

300

0 0.2 0.4 0.6 0.8 1


Hea

t Tra

nsfe

r Coe

ffici

ent,

h (W

/m2 K

)

Isolated Plate LimitFully Developed LimitComposite Equation

∆T = 30°C

∆T = 3°C

Figure 6.10: Single phase natural convection heat transfer coefficients for isothermal die

stacks, 20 mm in length, in saturated FC-72 at atmospheric pressure.


0

50

100

150

200

250

0 0.2 0.4 0.6 0.8 1


Hea

t Tra

nsfe

r Coe

ffici

ent,

h (W

/m2 K

)

Isolated Plate LimitFully Developed LimitComposite Equation99% MaximumOptima

0.010.2 0.5

1t (mm)

Figure 6.11: Single phase natural convection heat transfer coefficients for isothermal die

stacks, 20 mm in length, in saturated FC-72 at atmospheric pressure, with ∆T = 10°C.

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 146 6.2 TWO PHASE PASSIVE IMMERSION COOLING OF 3-D

STACKED DIES

As discussed in the context of the fluid property comparison of Appendix A, the

electrical characteristics of candidate fluids that make them suitable for direct contact

with electronic devices also tend to be accompanied by relatively poor thermal properties.

For example, the thermal conductivity of FC-72 is an order of magnitude smaller than

that of water and only twice that of air. As a consequence, even the optimum natural

convection heat transfer coefficients of the previous section result in cooling rates of less

than one watt per square centimeter from the immersed die. These heat fluxes may be

adequate for memory chips, but are insufficient to meet the demanding requirements of

high performance microprocessor chips. Fortunately, the highly efficient nucleate boiling

process may be employed to maximize heat transfer rates from microelectronics

immersed in dielectric liquids. Further, the naturally generated agitation of the boiling

liquid, or “bubble pumping,” can assist in mixing and spreading of heat within a passive

immersion module.

6.2.1 Maximum Volumetric Heat Dissipation at CHF

The maximum volumetric boiling heat flow from an array of uniformly-heated dies may

be expressed as

( )tNLHNLHq

VAq

VQ

+′′

=′′

=δ

2CHF

array

surfaceCHFCHF (6.28)

where N is the number of dies and the factor of 2 comes from fact that boiling will occur

on both sides of a die. Channel CHF may be expressed by combining the Arik and Bar-

Cohen (2003) correlation for unconfined pool boiling, Eq. (4.2), which includes the base

Kutateladze-Zuber prediction and effusivity factor, and the channel correlation developed

in the current study for symmetrically heated channels, Eq. (5.2). Inserting these

expressions into Eq. (6.28) and simplifying yields


( )

+

++

−=

tkct

kct

L

ghV

Q p

δρ

ρ

δψ

ρρσρπ 21.01

)]([

24 hhp,h

hh,h

517.1

4/1gffgfgCHF (6.29)

where

( ) 252.0r343.1

gf41008.1 Pρρψ −×=

for symmetrically heated vertical channels in saturated liquid. For the purposes of these

design analyses, the length scale factor from Eq. (4.2) has not been included in

Eq. (6.29). This factor is unity when L is greater than 14 mm for FC-72 at near

atmospheric pressure and provides a correction of less than 10% as L approaches 10 mm.

Further, it is unclear how this phenomenon might be negated by channel aspect ratio

effects in confined geometries.

At vanishingly small channel spacings, CHF goes to zero, per Eq. (5.2), while the array

volume asymptotes to a constant V = NLHt. At large spacings, corresponding to L/δ < 10,

boiling channels achieve their large spacing CHF limit, and additional spacing increases

only continue to increase the array volume. Thus, there must exist an optimum channel

spacing in the range 0 < δ < L/10 where volumetric heat dissipation is maximized.

Figure 6.12 shows volumetric heat dissipation curves calculated using Eq. (6.29) for

20 mm long silicon dies immersed in saturated FC-72 at 101 kPa (1 atm), ψ = 0.002412.

Indeed, for a given die thickness, t, maximum volumetric heat dissipation occurs at a

channel spacing well below 2 mm (i.e. L/δ = 10). Similar curves may be generated for

different die lengths, L. According to the ITRS data shown in Table 1.1, die sizes are

expected to range between 10 and 30 mm for the foreseeable future. Figure 6.12 shows

peak volumetric heat dissipation in the range of 180 to 290 MW/m3 (1 MW/m3 =

1 W/cm3) for 20 mm long dies. Over this same range of die thickness, peak volumetric

heat dissipation is even greater for L = 10 mm, ranging from 260 to 520 MW/m3.

Alternatively, reduced volumetric heat dissipation, 140–200 MW/m3, is seen to occur

when L = 30 mm.


0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Die Spacing, δδδδ (mm)

Volu

met

ric

Hea

t Dis

sipa

tion

(MW

/m3 )

t = 0.04 mmt = 0.12 mmt = 0.20 mmt = 0.40 mm

Figure 6.12: Volumetric heat dissipation at CHF for stacked silicon dies immersed in

saturated FC-72: L = 20 mm, P = 101 kPa (1 atm).

6.2.2 Optimum Die Spacing

Optimum die spacings that maximize volumetric heat dissipation may be found by taking

the derivative of Eq. (6.29) with respect to channel spacing and setting it equal to zero.

After algebraic manipulation, the following equation may be obtained.

517.1

1

optopt

1517.1

−

−

+=

ψ

δψ

δtL

(6.30)

Solution of Eq. (6.30) for the optimum spacing requires iteration but is easily handled

with current equation solving software. If manual iteration is required, an initial guess of

channel spacing equal to die thickness on the right hand side will provide convergence to

within ± 5% in 3 iterations for ψ = 0.002–0.003. Figure 6.13 shows optimum spacing

results calculated using Eq. (6.30) over a range of die length and thickness with

ψ = 0.002412.


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.0 0.1 0.2 0.3 0.4 0.5

Die Thickness, t (mm)

Opt

imum

Spa

cing

, δδ δδ (m

m)

L = 30 mmL = 25 mmL = 20 mmL = 15 mmL = 10 mm

Figure 6.13: Optimum channel spacing calculated using Eq. (6.30) for saturated FC-72 at

101 kPa (1 atm), ψ = 0.002412.

The optimum spacing found with Eq. (6.30) can be used in Eq. (6.29) to find the

maximum volumetric heat dissipation for a given length and thickness (L and t). Figures

6.14 and 6.15 show loci of maxima found in this manner for silicon dies immersed in

saturated FC-72 at 101 kPa (1 atm) over an unrealistically wide die thickness range of

0.004–4 mm (for illustrative purposes). The peak in the L = 20 mm curve occurs at a

thickness of approximately 0.04 mm, while for die lengths of 10 and 30 mm, volumetric

heat dissipation is a maximum for t ≈ 0.03 and 0.05 mm, respectively. However, the

peaks are relatively broad. This behavior is shown graphically in Fig. 6.15, where the

data of Fig. 6.14 is plotted versus die spacing instead of thickness.


0

100

200

300

400

500

600

0.0 0.5 1.0 1.5Optimum Die Spacing, δδδδ opt (mm)

Volu

met

ric

Hea

t Dis

sipa

tion

(MW

/m3 )

L = 10 mmL = 20 mmL = 30 mm

Figure 6.14: Loci of maxima of volumetric heat dissipation for stacked silicon dies

immersed in saturated FC-72 at 101 kPa (1 atm).

0

100

200

300

400

500

600

0.00 0.02 0.04 0.06 0.08 0.10Die Thickness, t (mm)

Volu

met

ric

Hea

t Dis

sipa

tion

(MW

/m3 )

L = 10 mmL = 20 mmL = 30 mm

Figure 6.15: Volumetric heat dissipation variation with die thickness for stacked silicon

dies immersed in saturated FC-72 at 101 kPa (1 atm) at optimum channel spacings, δopt,

calculated using Eq. (6.30).

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 151 Die thickness impacts the volumetric heat dissipation of an array of stacked dies in two

different and counteracting ways. First, reductions in die thickness directly translate into

a reduction in the overall volume of a die stack. Secondly, boiling surface effusivity

effects, as represented by the thickness and material property factor included in

Eq. (6.29), can lead to deteriorated CHF performance for thin dies. According to the ITRS

(SIA, 2005), future vertical stacking technologies will rely on wafer thinning to meet

space constraints and/or accommodate through-silicon interconnect. Current technology

for “general product” includes dies as thin as 75–50 µm and is expected to go as low as

40 µm by 2012 and remain there through 2020 (SIA, 2005). Fortunately, these roadmap

targets are within in the optimum range of the data shown in Fig. 6.15. Figure 6.15

clearly shows that the effusivity effect does not significantly impact the volumetric

benefits of decreasing die thickness until t < 10 µm. Die thickness in extreme applications

is expected to drop to 10 µm in 2011 and 8 µm from 2015–2020 (SIA, 2005), but these

applications would not be expected to be accompanied by challenging heat dissipation

requirements.

6.2.3 Effect of System Pressure

The presence of the fluid density factor, ψ, as well as the inherent pressure dependence of

pool boiling CHF in the volumetric heat flow relation, Eq. (6.29), suggests that variations

in pressure may have a significant impact on the optimum and maximum channel boiling

cooling rates for stacked dies. As operating pressure increases, the ratio of liquid density

to vapor density goes down, while the reduced pressure goes up. Interestingly, over

pressures ranging from 101 to 355 kPa (1 to 3.5 atm), these effects counteract each other,

and, as a result, ψ and δopt are relatively constant. For FC-72, ψ equals 0.002412 at

pressures of both 101 and 355 kPa (1 and 3.5 atm) and has a peak value of 0.002529 at

193 kPa (1.9 atm). The resulting impact on optimum channel spacing is less than 3% over

channel lengths, L, from 10 to 30 mm and die thicknesses, t, from 0.01 to 1.0 mm.

However, pressure does have a significant impact on CHF, as discussed in Section 1.3.3.

Thus, while the geometry of an optimum boiling die stack, determined via Eq. (6.30),

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 152 will not change significantly with operating pressure, maximum heat dissipation will

increase with increasing pressure up to a reduced pressure of approximately 0.35 (Watwe,

1996), scaling with the base Kutateladze-Zuber values shown in Table 1.2. In addition, as

with unconfined pool boiling, operating pressure may be manipulated to set the liquid

saturation temperature and, therefore, boiling surface superheat at an acceptable level.

6.2.4 Sub-CHF Volumetric Heat Transfer Coefficients

As seen in the channel boiling curves of Chapter 5, once CHF occurs, it typically does so

at roughly the same boiling superheat regardless of channel spacing. Therefore, surface

temperature is not as important a factor in the volumetric optimization as it is, for

example, with isoflux parallel plates cooled by single phase natural convection, as

discussed at the beginning of Section 6.1.5. Naturally, reduced superheats will lead to

reduced heat fluxes and reduced volumetric heat dissipation of boiling die stacks. This

trend is displayed graphically in Fig. 6.16, where the symmetric channel boiling curves of

Fig. 5.1 have been multiplied by two (for symmetric heating) and divided by the width of

the channels, δ + t, assuming t = 0.1 mm for illustrative purposes.


0

50

100

150

200

250

0 5 10 15 20 25

∆∆∆∆T sat (°C)

Volu

met

ric H

eat D

issi

patio

n (M

W/m

3 )

0.3 mm0.7 mm1.0 mm1.5 mm2.0 mm

Figure 6.16: Die stack volumetric heat dissipation as a function of superheat, based on the

symmetric channel boiling data of Fig. 5.1, with t = 0.1 mm.

Alternatively, the efficiency of different channels at various superheats may be explored

by considering volumetric heat transfer coefficients, representing volumetric heat

dissipation per unit temperature difference. Figure 6.17 shows the result of dividing the

data of Fig. 6.16 by superheat to produce volumetric heat transfer coefficients. Clearly,

the sharp increase in boiling heat flux near a superheat of 5°C for the 0.3 mm channel

creates the observed peak in the volumetric heat transfer coefficient to a quite formidable

value of 19.8 MW/m3K. For thinner dies, the relative difference in volumetric

performance for different channel spacings is larger, though superheat trends remain the

same regardless of die thickness, as shown in Fig. 6.18. While the conditions yielding the

highest volumetric heat transfer coefficients should not be confused with those

maximizing the overall heat removal rate, the performance and reliability advantages that

could derive from operation at lower chip superheats may make this an attractive

operating point for stacked die designs.


0

5

10

15

20

0 5 10 15 20 25

∆∆∆∆T sat (°C)

Volu

met

ric H

eat T

rans

fer

Coe

ffici

ent (

MW

/m3 K

)

0.3 mm0.7 mm1.0 mm1.5 mm2.0 mm

Figure 6.17: Die stack volumetric heat transfer coefficient as a function of die superheat,

based on the symmetric channel boiling data of Fig. 5.1, assuming t = 0.1 mm.

0

5

10

15

20

25

0 5 10 15 20 25

∆∆∆∆T sat (°C)

Volu

met

ric H

eat T

rans

fer

Coe

ffici

ent (

MW

/m3 K

)

0.3 mm spacing, 0.04 mm thickness0.7 mm spacing, 0.04 mm thickness0.7 mm spacing, 0.4 mm thickness0.3 mm spacing, 0.4 mm thickness

Figure 6.18: Die stack volumetric heat transfer coefficient as a function of die superheat,

based on the symmetric channel boiling data of Fig. 5.1.

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 155 6.3 DIE STACK NOTES AND OBSERVATIONS

Saturated fluid properties for the Fluorinert™ liquids FC-77 and FC-84 are provided in

Table A.1. The fluid density factor ψ for these fluids evaluates to 0.002404 and

0.002222, respectively, at 101 kPa (1 atm). Thus, optimum geometries for these fluids

will be very similar to the FC-72 results discussed in the preceding sections, and

maximum heat dissipation will scale primarily with the base Kutateladze-Zuber values

shown in Table 1.2. Clearly, several hundred megawatts per cubic meter may be

dissipated from 3-D stacked dies immersed in candidate Fluorinert™ electronics cooling

liquids, under saturated operating conditions. Optimum single phase natural convection

cooled plate arrays were shown in Table 6.2 to dissipate on the order of 10 MW/m3

(10 W/cm3) over the same typical parameter ranges. The heat dissipation of the human

brain is on the order of 0.1 MW/m3 (0.1 W/cm3), albeit on a somewhat larger scale via

single phase forced convective cooling (Cochrane et al., 1995). Optimum volumetric heat

dissipation for an immersion cooled die stack, experiencing ebullient heat transfer, with a

length L comparable to the size of the human brain, i.e. 0.1 m, would range from 50 to

100 MW/m3 (50-100 W/cm3).

For applications that are not constrained by space, larger channel spacings maximize

achievable nucleate boiling heat flux until the pool boiling limit is reached. By choosing

channel aspect ratios equal to 10, it is possible to approach to within 5% of the large

spacing (pool boiling) CHF limit. However, the volumetric advantages of reduced

channel spacing are undeniable. For typical parameter ranges discussed in this chapter,

70–80% reductions in channel spacing reduce maximum total heat flow by only 30–50%,

yielding 50–150% increases in maximum volumetric heat dissipation.

Non-uniform chip-level heat generation is expected to provide one of the driving thermal

management challenges of next generation microprocessors (Yang et al., 2006). In

general, non-uniform heating will decrease the maximum allowable power dissipation of

a given device, as local dry out will occur earlier for areas of elevated heat flux than it

Chapter 6: Passive Immersion Cooling of 3-D Stacked Dies 156 would for the average device heat flux. Once even a small portion of the surface reaches

CHF, drastically increasing temperatures will spread the resulting vapor blanket across

the entire surface. This effect will be further exacerbated by die thinning. These and other

special cases should be predictable with a modified form of Eq. (6.29) once the

unconfined pool boiling CHF limit is known.

( )( )

++′′=

−

∞→ tLq

VQ

δδψδ

211517.1

,CHFCHF (6.31)

Equation (6.31) may be used for die stack design and optimization in a variety of

circumstances.

157

CHAPTER

SEVEN

DESIGN AND OPTIMIZATION OF BOILING HEAT SINKS

Various requirements for and approaches to enhancement techniques for increasing heat

dissipation from individual devices are discussed in Chapter 1. Longitudinal rectangular

plate fin heat sinks, based on the vertical channel geometry that is the focus of this

dissertation, are now considered. This heat sink configuration is illustrated in Fig. 7.1.

The nomenclature shown is the same as that employed in the parallel plate illustration of

Fig. 1.3, and the stacked die optimizations of Chapter 6. As before, the gravity vector is

assumed to lie parallel with the heat sink length, L. The heat load is assumed to be

distributed uniformly across the heat sink base area, L × W. Unlike studies which seek to

maximize the heat transfer from boiling fins by allowing film boiling at the fin base with

other (multiple) boiling regimes occurring along the length of the fin, e.g. Haley and

Westwater (1966), the following heat sinks will be limited to CHF at the fin base to

prevent base temperatures from exceeding typical operational limits of microelectronic

components.

Chapter 7: Design and Optimization of Boiling Heat Sinks 158

H

L

W

tδ

H

L

W

tδ

Figure 7.1: Longitudinal rectangular plate fin heat sink geometry with nomenclature.

Details of heat sink attachment and the resulting thermal interface between component

and heat sink will not be considered, though it is recognized that this interface is often

one of the most critical in the thermal design of an overall system. While it might be

possible to fabricate integrated circuitry and heat sink fins in a single, continuous piece of

silicon, this may not be viable when desired fin heights are on the order of or larger than

typical die thicknesses. It is perhaps more likely that one would seek to fabricate the heat

sink out of a separate piece of silicon or some other material with high thermal

conductivity and a coefficient of thermal expansion (CTE) close to that of silicon,

3 ppm/°C. This approach could minimize mechanical stresses induced by the differential

thermal expansion between the device and heat sink and allow for a very thin solid

adhesive interface, minimizing thermal interface resistance.

Chapter 7: Design and Optimization of Boiling Heat Sinks 159 7.1 FIN CONDUCTION ANALYSIS METHODOLOGY

Unlike the stacked die configuration explored in Chapter 6, where heat flux is assumed

be uniform across the boiling surfaces, temperature gradients in heat sink fins resulting

from heat conduction away from the base can be expected to lead to significant heat

transfer coefficient variations. Closed form analytical solutions for fin conduction with

temperature dependent boiling heat transfer coefficients have been pursued by numerous

researchers, including Unal (1987), Liaw and Yeh (1994a, 1994b), and Lin and Lee

(1996, 1999). An analytical study of longitudinal, rectangular plate fins by Yeh (1997)

and its drawbacks are discussed at the end of Appendix B. Numerical approaches include

the fourth order Runge-Kutta solution of a 1-D differential equation formulation (Haley

and Westwater, 1966) and a FORTRAN implemented cascade algorithm (Bu et al.,

2000). All of these techniques rely on certain simplifying assumptions, the most common

of which are:

• The thermal conductivity of the fin material is isotropic and constant, or at most a

simple (linear) function of temperature.

• Temperature gradients across the fin thickness are negligible.

• The tip of the fin is insulated.

• Boiling heat transfer coefficient may be accurately represented by a power-law

formula.

In the following design analyses, conductive transport in heat sink fins with temperature

dependent boiling heat transfer coefficients are evaluated using finite element analysis

(FEA) with the commercial software package ANSYS™. In addition to being free of the

assumptions listed above, batch processing capabilities and the computational power of

current computer workstations make this the simplest, most efficient, most accurate, and,

hence, most satisfying method currently available.

Chapter 7: Design and Optimization of Boiling Heat Sinks 160 Two-dimensional, half symmetry, steady-state conduction analyses are performed in

batch mode to facilitate the generation of a large number of solutions corresponding to a

large parametric space. Following Haley and Westwater (1966) and Nakayama et al.

(1984), localized boiling heat transfer coefficients on surfaces with non-uniform

temperature profiles will be assumed to be equal to boiling heat transfer coefficients

obtained from isothermal surfaces. The validity of this assumption has been supported by

Mudawar and Anderson (1993) among others. Thus, the numerical simulation of boiling

fin behavior employs temperature dependent boiling heat transfer coefficients based on

the experimental boiling curves presented in Chapters 4 and 5, provided in the form of

“look-up” heat transfer coefficient tables. A large number of table entries may be chosen

so that linear interpolation between them does not sacrifice accuracy.

Appendix G contains a listing of the ANSYS™ input file created for these analyses. Heat

flows entering the fin base and leaving the fin sides and tip are readily extracted from the

numerical results and automatically written in tabular form to an output text file. A heat

balance was performed on each solution to verify its accuracy. Elements were evenly

spaced so that nodal heat flux averages from each surface would be equivalent to area

averages (with appropriate consideration of corner nodes). Mesh refinement was

employed to insure heat balance agreement within 1%. In general, element aspect ratios

close to unity provided good heat balance. Element counts were typically on the order of

105 for most of the single fin analyses performed. Depending on the mesh and non-

linearity of the heat transfer coefficient, run times varied from tens of seconds to tens of

minutes using a 3 GHz, x86-based PC with the Windows XP operating system.

Given the nature of the 2-D analysis, fin heat dissipation results are provided in units of

watts per unit fin length. These values are multiplied by the sum of the fin length and

thickness, (L + t), to include the contribution from the area at the ends of the fins. This

approximation is inaccurate for fins that are not very long compared to their thickness,

but fortunately optimum fins are typically very long compared to their thickness. The

heat dissipation obtained from the FEA solution for a given fin geometry is analytically

Chapter 7: Design and Optimization of Boiling Heat Sinks 161 combined with the contribution of the exposed base area between fins to determine the

heat transfer capability of entire arrays. These calculations may be easily incorporated

into a spreadsheet. For a given fin thickness (t), number of fins (N), and array width (W),

fin spacing (δ) may be expressed as

1−

−=N

tNWδ (7.1)

The maximum heat flux (CHF limit) for a given fin spacing may be calculated using

Eq. (5.2), the CHF correlation developed for symmetric channels. This maximum heat

flux may be translated into maximum heat sink base temperature and base heat transfer

coefficient using curve fits of the boiling curve appropriate for a particular surface and

channel spacing (when spacing dependent). The total array heat dissipation is then

calculated as

( ) ( ) ( )satbbasefinsink 1 TTLhNqtLNQ −−+′+= δ (7.2)

The base heat transfer coefficient is taken from the same temperature dependent heat

transfer coefficient curve used on the fins, despite the fact that the bottom of a three-

walled U-shaped channel might experience somewhat modified performance relative to a

parallel plate channel.

The suitability of this approach was verified using experimental data obtained for an

aluminum heat sink tested in a precursor to the experimental module described in

Chapter 3 (see Appendix C for details), employing the same basic measurement system,

aluminum heater assembly, and cartridge heater. The aluminum heat sink was

constructed via wire EDM on a 20 × 20 mm base, very similar to the boiling surface of

Fig. 3.7, with eight, 0.7 mm thick, 10 mm high fins. Figure 7.2 shows boiling data

obtained for this heat sink in saturated FC-72 at atmospheric pressure. The boiling heat

sink is shown to provide more than twice the heat dissipation capability of the unfinned

EDM aluminum surface of Figs. 4.4 and 4.5, as represented by the dashed line in Fig. 7.2.


0

20

40

60

80

100

120

140

160

0 5 10 15 20 25

∆∆∆∆T sat (K)

Hea

t Dis

sipa

tion

(W)

experimental dataunfinned surface

FEA-based prediction

Figure 7.2: Experimental boiling heat sink data with results of the FEA-based model.

The solid line in Fig. 7.2 represents heat sink performance predictions based on the FEA

method described above, using temperature dependent heat transfer coefficients extracted

from the EDM aluminum pool boiling data of Fig. 4.4. The particular heat transfer

coefficient values used are provided in Appendix G. The fin thermal conductivity

(177 W/mK) was assumed to be uniform and independent of temperature. The variation

of the thermal conductivity of aluminum over the temperature range of interest is

relatively small, and sensitivity analyses of aluminum thermal conductivity on fin heat

transfer performance yielded negligible differences.

The FEA-based prediction of boiling heat sink performance compares well with the

experimental data shown in Fig. 7.2. Discrepancies may be due to the fact that the boiling

heat sink was fabricated separately from the unfinned surface which provided the heat

transfer coefficients used in the finite element model. While both were fabricated using

Chapter 7: Design and Optimization of Boiling Heat Sinks 163 wire EDM, process parameters may have been somewhat different resulting in somewhat

different surface characteristics. Regardless, these results validate the analysis approach

as being suitable for design-level parametric studies.

In addition to the aluminum heat sink described above, the design and fabrication of

polished silicon heat sinks for experimental evaluation was pursued. The concept

included the self-heating behavior of the silicon heaters used in the pool boiling and

channel experiments. It was hoped that rectangular dies of different sizes could be

bonded together to form parallel plate heat sinks. For example, twenty-nine 0.7 mm thick

dies could be used to form a structure similar to the aluminum heat sink discussed above,

with three shorter pieces forming the base area between each longer fin piece. Aluminum

electrodes could be sputtered along the top and bottom of the back side of the heat sink to

provide electrical contact with each die. Details of the design appear in Appendix H.

Fabrication of these silicon heat sink structures was pursued in the University of

Minnesota’s Microtechnology Lab (MTL). Unfortunately, the diffusion furnace process

that was relied on to fuse the polished silicon surfaces failed to bond the dies together. It

also became apparent that even if it had, it would be difficult to maintain die alignment

and prevent the creation of additional heat transfer area and unwanted nucleation sites

along the edges of the die interfaces.

Chapter 7: Design and Optimization of Boiling Heat Sinks 164 7.2 ALUMINUM BOILING HEAT SINK PARAMETRIC STUDY

A wide variety of fin analyses have been performed to map out the parametric space

relevant to potential electronics cooling applications, employing the modeling approach

discussed in the previous section. The thickness/effusivity effects on boiling CHF,

discussed in Section 4.3 and included in the stacked die optimization of Chapter 6, are

not included in these fin analyses. As shown in Fig. 4.9, these effects are not significant

for aluminum and silicon thicknesses above 0.1 mm. Furthermore, CHF is to be expected

to occur first at the very base of the fins and on the exposed areas between fins, where the

thickness of the heat sink base will be assumed sufficient to overcome this limitation on

CHF.

Initially, large fin heights are used to maximize heat dissipation. Given the magnitude of

boiling heat transfer coefficients, fin height is not expected to be a limiting factor in the

design of these heat sinks. Fin efficiency and the effects of reduced fin height are

explored after optimum geometries are identified. The number of inter-fin spaces is

assumed to be one less than the number of fins in all cases, matching the form of the

illustration in Fig. 7.1. Only two of the following three parameters, fin spacing, fin

thickness, and number of fins, are independent for a given base width. In general, fin

thickness must be specified for the FEA model, and the number of fins must be an

integer, so fin spacing is the natural candidate for the dependent variable.

For aluminum fins with the EDM surface characterized in Chapters 4 and 5, the heat

transfer coefficient is not expected to vary with fin spacing, as shown in Fig. 5.7. The

only effect of fin spacing will be on CHF, the maximum heat flux that can be dissipated

from the fin surfaces. Thus, one set of conduction analyses over a range of fin thickness

and base temperature may be used to generate performance curves for a wide variety of

heat sink configurations. This maximum heat flux is translated into maximum heat sink

base temperature and base heat transfer coefficient using the boiling curve for the EDM

aluminum surface, Fig. 4.4.

Chapter 7: Design and Optimization of Boiling Heat Sinks 165 7.2.1 Basic Aluminum Boiling Heat Sink Results

Figure 7.3 shows a sampling of heat dissipation curves generated for 20 mm high

aluminum fins using heat transfer coefficients extracted from the EDM surface pool

boiling data of Fig. 4.4. Heat dissipation results are provided per unit fin length, L. Thus,

a 2 mm thick fin with a base superheat of 14°C is shown to dissipate 900 W/m2, or 9 W

per 10 mm of longitudinal size, L. The 20 mm fin height, H, proved to be sufficient to

maximize fin heat dissipation, as well less than 1% of the total fin heat was dissipated

from the fin tip in all but the thickest fins. As expected, the larger cross sectional area of

thicker fins yields greater heat dissipation at a given base temperature. Note that CHF for

the unconfined aluminum surface occurred at a superheat near 15°C. However, it is

expected that optimum heat sink geometries will have narrow spacings, δ, well into the

confined boiling regime and, therefore, reduced CHF and superheat compared to

unconfined pool boiling.

In addition to the curves shown in Fig. 7.3, similar results were generated for fin

thicknesses of 0.25, 0.75, and 1.5 mm. Analysis results for these seven fin thickness over

a base superheat range of 4 to 14°C (in increments of 2°C) with a fixed fin height of

20 mm were fit to a fourth degree polynomial function using the multivariate regression

capabilities of Mathcad, version 12.1. This function was created to facilitate the

exploration of the parametric space in a quick and efficient manner. Table 7.1 shows the

coefficients obtained for the fitting polynomial, which may be expressed as:

( )∑∑= =

−=′4

1

4

1satb,fin

i j

jiji TTtCq (7.3)

The fitted polynomial matched the majority of the FEA results within less than 1%. At

the minimum and maximum values of the independent parameters, some results were as

much as 4% different. This function was included in the spreadsheet used to calculate

total array heat dissipation from the FEA results for individual fins, based on Eq. (7.2).


0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20

Fin Base Temperature Rise Above Saturation (°C)

Fin

Heat

Dis

sipa

tion

Per U

nit L

engt

h (W

/m)

2 mm thick

1 mm thick

0.5 mm thick

0.1 mm thick

Figure 7.3: Boiling heat dissipation per unit fin length, L, for 20 mm high aluminum fins

with EDM surface, in saturated FC-72 at 101 kPa (1 atm).

Table 7.1: Polynomial coefficients of Eq. (7.3).

i j C i,j i j C i,j

0 0 4.1442E+01 1 3 -8.7558E+010 1 -2.1811E+01 2 0 -1.5220E+080 2 4.2410E+00 2 1 -2.4450E+070 3 -2.2800E-01 2 2 -3.5070E+050 4 4.6950E-03 3 0 1.4520E+111 0 6.6140E+04 3 1 6.6070E+091 1 1.6970E+04 4 0 -3.9690E+131 2 4.1400E+03

Chapter 7: Design and Optimization of Boiling Heat Sinks 167 Figure 7.4 shows the maximum heat sink heat dissipation calculated in this manner for

various fin thicknesses and numbers of fins, on a 20 × 20 mm base. The combination of

sixteen 0.59 mm thick fins yields the maximum heat dissipation of 148 W, nearly three

times the highest heat dissipation achievable from the unfinned based under these same

conditions, 54 W. Fortunately, the maximum is quite shallow, both in terms of fin

thickness and the number of fins. Many geometries are predicted to dissipate in excess of

140 W, or a heat flux of 350 kW/m2 (35 W/cm2) based on the heat sink base area.

0

20

40

60

80

100

120

140

160

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Fin Thickness (mm)

Tota

l Sin

k He

at D

issi

patio

n (W

)

6 fins10 fins12 fins16 fins20 fins30 fins

Figure 7.4: Maximum heat sink heat dissipation for various aluminum fin thicknesses and

numbers fins, L = W = 20 mm, EDM aluminum in saturated FC-72 at 101 kPa (1 atm).

Chapter 7: Design and Optimization of Boiling Heat Sinks 168 7.2.2 Optimum Aluminum Boiling Heat Sinks

The locus of maxima for the heat dissipation curves of Fig. 7.4 is shown in Fig. 7.5 along

with similar results for 10 and 30 mm long heat sinks, all 20 mm wide. In Fig. 7.5 total

sink heat flow is divided by heat sink base area to yield the base heat flux for comparison

purposes. As discussed in the text preceding Eq. (7.2), the CHF correlation developed for

symmetric channels, Eq. (5.2), is employed in this heat sink analysis and captures the

trend of decreasing CHF with increasing heat sink length, L (or, more precisely the aspect

ratio of the inter-fin channel, L/δ). Thus, maximum heat sink base heat flux is higher for

shorter heat sinks, though total heat dissipation increases with heat sink length and is

greater for longer heat sinks. Table 7.2 lists relevant details for optimum 8, 20, 35 and 50

fin aluminum heat sinks with 20 × 20 mm bases. These geometries are also represented

graphically in Figs. 7.5 through 7.7.

0

100

200

300

400

500

600

0 10 20 30 40 50

Number of Fins, N

Hea

t Sin

k B

ase

Hea

t Flu

x (k

W/m

2 )

L = 10 mmL = 20 mmL = 30 mmTable 7.2 Geometries

Figure 7.5: Loci of maxima of aluminum heat sink performance curves, EDM aluminum

in saturated FC-72 at 101 kPa (1 atm).

Chapter 7: Design and Optimization of Boiling Heat Sinks 169 Table 7.2: Select optimum EDM aluminum heat sink configurations (20 × 20 mm base).

8 Fins 20 Fins 35 Fins 50 FinsFin Thickness, t (mm) 1.36 0.444 0.229 0.138

Fin Spacing, δ (mm) 1.30 0.585 0.352 0.267Channel CHF Limit (kW/m2) 116 88.6 63.7 49.9

Base Temperature Rise Above Saturation (T b - T sat) 13.6 11.5 9.8 8.8Base Heat Transfer Coefficient, h b (W/m2K) 8563 7699 6474 5725

Single Fin Heat Dissipation (W/m) 699 309 168 110Total Sink Heat Flow (W) 141 146 134 124

Sink Base Heat Flux (W/m2) 352 365 335 310Unfinned Base CHF Enhancement Ratio 2.6 2.7 2.5 2.3

Fin thickness and spacing for the optimum geometries of Fig. 7.5 are shown in Figs. 7.6

and 7.7. Figure 7.8 shows that fin thickness and spacing are roughly equal in the optimum

geometries. It is important to note that had channel aspect ratio effects on CHF not been

taking into account (decreasing CHF with increasing L/δ), large numbers of very thin fins

would have shown drastically improved performance over more moderate optimized heat

sinks. Given the dependence of channel CHF on aspect ratio and the increased

performance “penalty” associated with decreased spacing in longer channels, longer

optimized heat sinks tend to have slightly wider fin spacings and slightly thinner fins.

Figure 7.9 shows the result of taking the performance data of Fig. 7.5 for heat sinks with

8 to 32 fins and dividing by CHF for the unfinned base area versus heat sink length.

Clearly, the shortest (L = 10 mm) heat sinks provide the most enhancement, as inter-fin

channel dry-out occurs at higher heat fluxes. Enhancement for all the optimum

geometries ranged from 1.5 to 3.5 times the unfinned base CHF limit.


0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 10 20 30 40 50

Number of Fins, N

Fin

Spac

ing,

δδ δδ (m

m)


Figure 7.6: Fin spacings for optimum geometries of Fig. 7.5, EDM aluminum in saturated

FC-72 at 101 kPa (1 atm).

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 10 20 30 40 50

Number of Fins, N

Fin

Thic

knes

s, t

(mm

)


Figure 7.7: Fin thicknesses for optimum geometries of Fig. 7.5, EDM aluminum in

saturated FC-72 at 101 kPa (1 atm).


0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0 1.5 2.0

Fin Thickness, t (mm)

Fin

Spac

ing,

δδ δδ (m

m)

L = 10 mmL = 20 mmL = 30 mm

Figure 7.8: Relationship between fin thickness and spacing for optimum geometries of

Fig. 7.5, EDM aluminum in saturated FC-72 at 101 kPa (1 atm).

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 10 20 30 40

Heat Sink Length, L (mm)

Qsi

nk /

Qun

finne

d ba

se

Figure 7.9: Enhancement ratios for optimum aluminum boiling heat sinks with eight to

thirty-two fins, EDM surface in saturated FC-72 at 101 kPa (1 atm).

Chapter 7: Design and Optimization of Boiling Heat Sinks 172 7.2.3 Effect of Fin Height

The relative flatness in the optima identified in the previous section suggest than any

number of heat sink configurations might satisfy the needs of a given application.

However, thinner fins will require less height to maximize performance than thicker fins.

Thus, shorter heat sinks may require less material and yield reduced fabrication cost.

Figure 7.10 shows the effect of fin height on heat dissipation for the optimum heat sink

geometries detailed in Table 7.2. Interestingly, despite the fact that thinner fins approach

their asymptotic limits at shorter heights than thick fins, absolute performance is

comparable over a wide range.

0

25

50

75

100

125

150

0 5 10 15

Fin Height, H (mm)

Tota

l Hea

t Dis

sipa

tion

(W)

8 fins20 fins35 fins50 fins

Figure 7.10: Total heat sink heat dissipation as a function of fin height for select optimum

aluminum heat sinks described in Table 7.2.

Chapter 7: Design and Optimization of Boiling Heat Sinks 173 As fin height approaches zero, heat dissipation should approach the CHF limit for the

bare surface, 54 W for these 20 × 20 mm heat sinks. However, the calculations behind the

results of Fig. 7.10 assume that the channel CHF limit, calculated from Eq. (5.2), applies

for all fin heights. Clearly, as fin height approaches zero, CHF in the increasingly shallow

inter-fin spaces should increase to match the unconfined pool boiling limit. The three-

dimensional flow effects that might appear as the influence of channel depth, H, on CHF

have not been evaluated. However, CHF is expected to start at the base of fins, and the

assumption that Eq. (5.2) applies for very short fins is at worst a conservative approach.

As fin height is increased from the unfinned (H = 0) limit, sink heat dissipation rises

sharply. For fin heights larger than roughly ten times the fin thickness, however, there is

little benefit from additional increases in fin height. Considering the data of Figs. 7.5 and

7.10, it is determined that given a base area of 20 × 20 mm and FC-72 at 101 kPa (1 atm),

optimized EDM aluminum heat sinks with twelve to twenty 4 mm high fins can be

expected to dissipate two and a half times the CHF limit of the unfinned base area,

yielding a maximum heat dissipation of 140 W.

7.2.4 Effect of Fin Thermal Conductivity

The numerical analyses of the preceding sections were repeated for thermal conductivity

values of 400 W/mK representing high conductivity metals like copper and silver and

1000 and 2000 W/mK representing high conductivity carbon-based materials, such as

pyrolytic graphite and CVD diamond. As was made very clear in Chapters 4 and 5, the

boiling curves of any unique combination of heater material and surface finish must be

characterized individually if accurate design analysis results are desired. However, in

order to focus solely on the parametric effects of varying thermal conductivity, the

following analyses assume the same boiling heat transfer coefficients obtained with the

rough EDM aluminum surface.

Chapter 7: Design and Optimization of Boiling Heat Sinks 174 In executing FEA runs with increased thermal conductivity, it was found that the 20 mm

fin height used in the previous 177 W/mK analyses was sufficient to provide maximum,

asymptotic, “high fin” heat dissipation for fins with a thermal conductivity of 400 W/mK.

However, a significantly greater fin height, 60 mm, was employed to ensure maximum

performance when k = 1000 and 2000 W/mK. Higher fins led to a direct increase in the

number of elements required to provide an accurate solution as well as a corresponding

increase in analysis run times—some as long as an hour.

Single fin heat dissipation results for the alternate thermal conductivities simply

increased by constant factors over the aluminum results, across the parameter ranges

investigated (t = 0.10–2.0 mm, ∆T = 4–14°C). Increasing fin thermal conductivity from

177 to 400 W/mK produced a uniform 50% increase in single fin heat dissipation. Fins

with thermal conductivities of 1000 and 2000 W/mK dissipated 2.4 and 3.4 times more

heat than the aluminum fins, respectively (i.e. increases of 140% and 240%). Note that

these increases in fin heat dissipation scale with the square root of thermal conductivity.

For an infinitely-high rectangular fin with uniform heat transfer coefficient and thermal

conductivity, fin heat dissipation may be expressed as (Incropera and De Witt, 1996)

( ) bfin 2 TLthktLQ ∆+= (7.4)

Therefore, the observed thermal conductivity dependence for fins of the same thickness

with the same base temperature can only hold if the average heat transfer coefficient over

the active heat dissipating area of the fin is constant. Thus, while fin temperature at a

given distance from the base increases with increasing thermal conductivity and the

applied boiling heat transfer coefficients are temperature dependent, the active fin area

increases with increasing k to maintain the same average h over that area. This

phenomenon is demonstrated explicitly in Section G.3.

If the contribution of the exposed base area of a heat sink to its total heat dissipation is

large, heat sink results will not increase as much as the single fin results with thermal

conductivity. In general, for the heat sink parameter ranges explored in this chapter, the

exposed base contribution to total heat sink heat dissipation is typically on the order of

Chapter 7: Design and Optimization of Boiling Heat Sinks 175 15%. As a result, with increased thermal conductivity, enhancement factors near those

achieved for single fins are possible. These increases in heat sink heat dissipation are

shown in Fig. 7.11, which compares the heat sink enhancement ratios of Fig. 7.9 for

optimum heat sinks with eight to thirty-two fins with the increased thermal conductivity

results of this section.

Figure 7.11 shows that heat dissipation may be greatly increased with boiling heat

sinks—as high as an order of magnitude greater than the unfinned surface. Despite the

wide range of thermal conductivity investigated, optimized geometries are quite similar.

In fact, for a given base size (L, W) and asymptotically-high (H) fins, the numbers of fins

in the optimum configurations (i.e. the peaks in the three curves of Fig. 7.5) are

unchanged. Table 7.3 compares various geometrical parameters and performance results

for optimized 20 mm wide heat sinks of various lengths, L, and thermal conductivity, k.

0

2

4

6

8

10

12

0 10 20 30 40

Heat Sink Length, L (mm)

Qsin

k /

Qun

finne

d ba

se

k = 2000 W/mKk = 1000 W/mKk = 400 W/mKk = 177 W/mK

Figure 7.11: Effect of thermal conductivity on enhancement ratios for optimized 20 mm

wide heat sinks, based on experimental EDM aluminum heat transfer coefficients.


Table 7.3: Optimization results for various 20 mm wide heat sinks.

Fin Thermal Conductivity, k (W/mK) 177 400 1000 2000 2000/5*

Optimum Number of Fins, N 28 28 28 28 36Optimum Fin Thickness, t (mm) 0.373 0.387 0.397 0.401 0.284

ratio to 177 W/mK result 1 1.04 1.06 1.08 0.76Optimum Fin Spacing, δ (mm) 0.354 0.340 0.330 0.325 0.279Fin Height at 95% of Max. Heat Flow, H (mm) 3.4 5.4 8.9 12.8 12.0

ratio to 177 W/mK result 1 1.6 2.6 3.8 3.5Base Temperature Rise Above Saturation (°C) 12.1 11.9 11.9 11.8 11.3Total Sink Heat Dissipation (W) 94 137 213 297 286Sink Base Heat Flux (kW/m2) 470 686 1063 1486 1431

ratio to 177 W/mK result 1 1.5 2.3 3.2 3.0ratio to unfinned surface CHF 3.5 5.1 7.9 11.1 10.7









L = 10 mm

L = 20 mm

L = 30 mm

*Anisotropic thermal conductivity with 2000 W/mK along the fin height and 5 W/mK

through the fin thickness

Chapter 7: Design and Optimization of Boiling Heat Sinks 177 While the highest conductivity heat sinks (k = 2000 W/mK) dissipate more than 3 times

that of comparable aluminum heat sinks, optimized fin thicknesses are only 8 to 17%

thicker. Slightly thicker fins are accompanied by slightly smaller fin spacings. In general,

this leads to a slightly lower channel CHF and, therefore, slightly lower operating base

temperatures. However, regardless of heat sink length, base temperatures for optimized

geometries are all very close to 12°C above saturation.

The only significant effect of thermal conductivity on optimum heat sink geometry

evident in Table 7.3 is the fin height required to achieve 95% of the maximum,

asymptotic, “high fin” heat dissipation. As thermal conductivity is increased, this point of

diminishing returns for increasing fin height shifts to higher fins. Fin height results for

optimum heat sinks are shown as a function of material thermal conductivity in Fig. 7.12.

In contrast to aluminum boiling fins (k = 177 W/mK) which require 3 to 5 mm of height

to achieve 95% of their maximum heat dissipation, fins with thermal conductivities

ranging from 1000 to 2000 W/mK require 10 to 20 mm, as much as four times.

0

2

4

6

8

10

12

14

16

18

20

0 500 1000 1500 2000 2500

Fin Thermal Conductivity, k (W/mK)

Fin

Hei

ght,

H (m

m)

L = 30 mm

L = 20 mm

L = 10 mm

Figure 7.12: Height required to achieve 95% of asymptotic maximum for optimum fins of

Table 7.3.

Chapter 7: Design and Optimization of Boiling Heat Sinks 178 Pyrolytic graphite is an anisotropic material with a thermal conductivity as high as

2000 W/mK in the plane of its graphene sheets but with a very low thermal conductivity,

on the order of 5 W/mK, normal to them (Incropera and Dewitt, 1996). If this material

was to be used to fabricate a plate fin heat sink as illustrated in Fig. 7.1, theoretically

speaking it would be most advantageous to orient the graphene sheets parallel to the W–H

plane, i.e. normal to the fin length, L. This arrangement would provide the highest

thermal conductivity along the fin height and thickness and align the low conductivity

direction with the length of the fin, along which no heat is assumed to flow in the 2-D

analysis. The preceding isotropic 2000 W/mK results would apply in this case.

However, given fabrication constraints, it is possible that a plate fin heat sink made of

pyrolytic graphite would have its graphene sheets oriented normal to the heat sink base

(L × W) and parallel to the plane of the longitudinal plate fins (L × H). In this orientation,

the fins would have a very high thermal conductivity along their height and length but a

very low conductivity through their thickness. This type of problem is well suited to the

FEA methodology employed in this chapter, and the ANSYS™ input file shown in

Appendix G includes the option to specify different thermal conductivities in these two

directions. In order to produce accurate solution results, it was necessary to readjust the

distribution of elements along the fin thickness and height compared to the previous

isotropic analyses. In particular, the both the overall number of elements as well as the

ratio of thickness to height elements had to be increased—especially for thicker fins.

Reducing the thermal conductivity in any direction should lead to reduced heat transfer.

Figure 7.13 shows how single fin heat dissipation is impacted by anisotropy, giving the

percent difference between analysis results for an anisotropic combination of

2000 W/mK in the L–H plane with 5 W/mK through the fin thickness and an isotropic

2000 W/mK conductivity in both directions. When these single fin results are employed

in a heat sink optimization, the maxima remain shallow, but inclusion of the low

thickness conductivity shifts optimum configurations in the direction of larger numbers

of thinner fins. These results are included in the rightmost column of Table 7.3. These

Chapter 7: Design and Optimization of Boiling Heat Sinks 179 optimum configurations have approximately 30% more fins that are approximately 30%

thinner than their isotropic counterparts. Despite 4% to 8% reductions in total heat sink

heat dissipation compared to isotropic 2000 W/mK results, anisotropic pyrolytic graphite

heat sinks are still 3 times more effective than aluminum (k = 177 W/mK) and may

dissipate 6 to 11 times the CHF limit of the unfinned base, depending on heat sink length.

-20%

-15%

-10%

-5%

0%

0.0 0.5 1.0 1.5 2.0

Fin Thickness, t (mm)

Impa

ct o

f Ani

sotr

opy

on F

in H

eat D

issi

patio

n

468101214

∆T sat

Figure 7.13: Effect of anisotropy on fin heat dissipation for pyrolytic graphite

(2000 W/mK in-plane) fins with low conductivity (5 W/mK) direction oriented parallel to

the fin thickness.

Chapter 7: Design and Optimization of Boiling Heat Sinks 180 7.3 SILICON BOILING HEAT SINK PARAMETRIC STUDY

As discussed at the beginning of this chapter, it will be important to match the thermal

expansion of the heat sink to the thermal expansion of the silicon device to minimize

thermal interface resistance. While metals, such as aluminum, have high thermal

conductivities which can provide high fin efficiencies, their CTEs are typically quite high

(e.g. aluminum = 24 ppm/°C) compared to silicon (3 ppm/°C). Unfortunately, most

materials with low CTEs tend to also come with very low thermal conductivities.

However, silicon and other silicon-based alloys and ceramics do offer metal-like thermal

conductivities. Silicon carbide has a CTE very comparable to silicon, but with a thermal

conductivity comparable to copper, on the order of 400 W/mK (Harris, 1995). Silicon

itself (k = 150 W/mK at room temperature, see Fig. 7.14) is also a logical material choice

for a heat sink that is to be attached to a silicon device.

y = 480969x-1.4172

0

50

100

150

200

250

300

0 100 200 300 400 500

Temperature (K)

Silic

on T

herm

al C

ondu

ctiv

ity (W

/mK)

Figure 7.14: Temperature-dependent silicon thermal conductivity (Incropera and De Witt,

1996).

Chapter 7: Design and Optimization of Boiling Heat Sinks 181 An ANSYS™ input file very similar to the one discussed in preceding sections was used

for modeling silicon fins. It should be noted that in this model the only significant

difference is that the temperature dependence of the thermal conductivity of silicon was

included, as it varies by 10% over the temperature range of interest, 56–80°C, as seen in

Fig. 7.14. Section G.2 provides the exact details of how this temperature dependence was

implemented in the numerical analysis.

In addition, the analysis recognizes that the heat transfer coefficients for silicon channels

are dependent on fin spacing and includes these relationships in the input file. Spacing-

dependent CHF values and heat transfer coefficients were extracted directly from Fig. 5.1

and are shown in Fig. 7.15 and listed in Table G.1. Given this spacing dependence, the

input files must be modified accordingly, and separate FEA solutions must be obtained

for fins with the same geometry but different spacings. This multiplies the number of

FEA runs that must be performed and drastically expands the complexity of a full-blown

parametric analysis, such as that presented for aluminum heat sinks in Section 7.2. Thus,

the following optimization for silicon heat sinks will leverage the results of the aluminum

study to provide starting points of performance trends to which silicon heat sinks may be

compared.

Silicon heat sink optimization starts with a given fin spacing and its associated

temperature dependent heat transfer coefficient, Fig. 7.15. As before, fins are initially

assumed to be high (20–25 mm) to maximize heat dissipation. Fin base temperature will

be set at the highest superheat values achieved during the channel experiments, in the

range of 20 to 25°C, as shown in Fig. 7.15, corresponding to the CHF limit for each

channel. Based on the aluminum results of Fig. 7.8, it might be expected that optimum fin

thickness for a given spacing will be relatively close to that spacing. Thus, the FEA

simulations are iterated around that starting point to find the optimum thickness in a

computationally-efficient manner.


0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

0 5 10 15 20 25 30

∆∆∆∆T sat (°C)

Hea

t Tra

nsfe

r Co

effic

ient

(W/m

2 K)

0.3 mm0.7 mm1.0 mm1.5 mm2.0 mm

Figure 7 15: Symmetric silicon channel heat transfer coefficients for various spacings,

based on the experimental channel boiling curves of Fig. 5.1.

7.3.1 Optimum Silicon Boiling Heat Sinks

Figure 7.16 shows results obtained through the process described in the previous section

for a 0.3 mm fin spacing and 20 mm heat sink length. Fin spacing is fixed, so the heat

dissipation of the exposed base area in the inter-fin spaces is independent of fin thickness

(in this case 13.4 W/m or 0.27 W per 20 mm long space). While fin heat dissipation

increases almost linearly with increasing thickness, fewer thick fins can fit on a given

width of heat sink base, and total heat sink heat dissipation will not increase without

bound. With fin spacing and thickness set and an integer number of fins allowed, only

certain values of heat sink width are achievable. Thus, heat sink performance is expressed

in terms of the heat flux at the base of the heat sink in Fig. 7.16, as was done in Fig. 7.5,

to facilitate comparisons between different heat sink configurations. Heat flow for a

Chapter 7: Design and Optimization of Boiling Heat Sinks 183 single fin/space pair is calculated and divided by the sum of the fin thickness and spacing

to generate this result. Contributions from the fin ends (not fin tip, but fin ends at z = 0

and L) are included as before. However, there is a subtle effect from the fact that this

calculation assumes there is the same number of fins as spaces, unlike the aluminum

sinks which had N fins and N−1 spaces, per Fig. 7.1. Fortunately, the difference is only

significant for heat sinks with a relatively small number of fins.

532

533

534

535

536

537

538

539

540

541

542

0.0 0.1 0.2 0.3 0.4 0.5

Fin Thickness (mm)

Hea

t Sin

k B

ase

Hea

t Flu

x

(kW

/m2 )

0

1

2

3

4

5

6

7

8

9

10

Hea

t Dis

sipa

tion

(W)

Heat Sink Base Heat FluxFin Heat DissipationExposed Base Dissipation

Figure 7.16: Fin thickness trends for polished silicon heat sinks with 0.3 mm fin spacing

and 20 mm sink length.

Chapter 7: Design and Optimization of Boiling Heat Sinks 184 The optimum fin thickness identified in Fig. 7.16, i.e. 0.29 mm, is very close to the fin

spacing, 0.3 mm. (Note that if the contributions from the fin ends are not included, the

optimum shifts to 0.275 mm.) Optimum thicknesses of 0.66, 0.85, 1.15, and 1.61 mm

were similarly found for spacings of 0.7, 1.0, 1.5, and 2.0 mm, respectively. Figure 7.17

shows the maximum heat sink base heat flux for each of these geometries, along with the

individual contributions from each fin and exposed inter-fin base area (W). Unlike the

20 mm long aluminum heat sinks which show a maximum in heat sink dissipation at a

channel spacing of 0.7 mm, due to the inverse dependence of the silicon channel heat

transfer coefficients on the fin spacing, the silicon heat sink performance continues to

improve down to the smallest spacing investigated, yielding 541 kW/m2 (54.1 W/cm2)—

nearly five times the CHF limit of the unfinned surface, 114 kW/m2 (11.4 W/cm2)

measured for polished silicon.

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0 2.5

Fin Spacing, δδδδ (mm)

Hea

t Sin

k B

ase

Hea

t Fl

ux (

kW/m

2 )

0

2

4

6

8

10

12

14

16

Hea

t Dis

sipa

tion

(W)

Heat Sink Base Heat Flux Fin Heat DissipationExposed Base Dissipation

Figure 7.17: Maximum base heat flux (kW/m2) for 20 mm long optimum silicon heat

sinks and individual contributions from each fin and exposed inter-fin base area (W).

Chapter 7: Design and Optimization of Boiling Heat Sinks 185 Figure 7.18 shows that silicon heat sinks with smaller fin dimensions outperform

comparable aluminum heat sinks. It might have been expected that the aluminum heat

sinks would perform better than the silicon, as the fin thermal conductivity and, more

importantly, boiling heat transfer coefficients are higher. However, the silicon surfaces

encounter their limiting heat transfer rates, i.e. CHF, at higher superheats, though the

resulting maximum heat fluxes are comparable. Furthermore, channel enhancement

maintains high heat transfer rates at temperatures relatively close to saturation. As a

result, the silicon fins are more efficient, as will be discussed below.

0

100

200

300

400

500

600

0.0 0.5 1.0 1.5 2.0

Fin Spacing, δδδδ

(mm)

Hea

t Sin

k B

ase

Hea

t Flu

x (k

W/m

2 )

AluminumSilicon

Figure 7.18: Comparison of optimum 20 mm long silicon and aluminum heat sinks.

Chapter 7: Design and Optimization of Boiling Heat Sinks 186 7.3.2 Fin Height and Fin Efficiency

Figure 7.19 shows boiling performance as a function of fin height for a 20 mm long

silicon heat sink with a fin spacing of δ = 0.3 mm and the base superheat corresponding

to CHF at that spacing (22.4°C). The top, solid curve shows a maximum heat dissipation,

541 kW/m2 (54.1 W/cm2) for asymptotically high fins. Below H = 5 mm, the thermal

performance drops steeply toward the bare surface limit (H = 0). The lower, dashed curve

represents predicted performance when large channel spacing silicon pool boiling heat

transfer coefficients are applied to the same geometry, with a base superheat of 19.1°C

corresponding to the same 45 kW/m2 (4.5 W/cm2) base heat flux. The differences

between these two curves illustrate the effect of low flux channel enhancement on heat

sink performance. The maximum heat dissipation is not only 50% higher, but the top

curve is much steeper as it approaches its asymptotic limit. The effects of flow entering

and exiting the fin array at the tips of short fins have not been evaluated. However, the

beneficial effects of confined flow may be easily preserved by shrouding the fin tips.

0

100

200

300

400

500

600

0 5 10 15 20

Fin Height, H (mm)

Hea

t Sin

k B

ase

Hea

t Flu

x (k

W/m

2 )

Channel Heat Transfer CoefficientsUnconfined Boiling Heat Transfer Coefficients

Figure 7.19: Silicon boiling heat sink performance as a function of fin height, δ = 0.3

mm, t = 0.29 mm, and L = 20 mm.

Chapter 7: Design and Optimization of Boiling Heat Sinks 187 Comparing the performance of individual aluminum and silicon fins can help separate the

effects that contribute to the improved performance of silicon over aluminum. The

variation of single fin heat dissipation with fin height is compared for 0.29 mm thick

silicon and aluminum fins in Fig. 7.20, while fin efficiency curves for the same appear in

Fig. 7.21. Assuming a 0.3 mm fin spacing and, therefore, a channel CHF limit of

45 kW/m2 (4.5 W/cm2), base superheat for each type of fin surface were set at different

values, each corresponding to a heat flux of 45 kW/m2. Fin efficiency is defined as the

ratio of actual fin heat dissipation to the heat that would be dissipated if the entire fin

were at the base temperature (Incropera and De Witt, 1996). Thus, the fin efficiencies of

Fig. 7.21 were calculated by dividing the actual fin heat dissipation values of Fig. 7.20 by

the product of the base heat flux (45 kW/m2) and fin surface area.

Even if large spacing (unconfined and unenhanced) pool boiling heat transfer coefficients

are used in the analysis (dashed silicon curve of Figs. 7.20 and 7.21), silicon fins are still

shown to be more efficient and dissipate more heat than same-sized aluminum fins due to

the larger temperature range over which they can operate during nucleate boiling. This

effect more than compensates for the lower thermal conductivity of silicon compared to

aluminum. Secondly, comparison of the solid silicon curves of Figs. 7.20 and 7.21, which

employ the channel boiling heat transfer coefficients associated with a 0.3 mm channel

spacing, to the dashed silicon curves demonstrates the unique effect of confinement-

driven enhancement of channel heat transfer coefficients.


0

50

100

150

200

250

300

350

0 5 10 15Fin Height, H (mm)

Fin

Hea

t Dis

sipa

tion

(W/m

)

Silicon, 0.3 mm channel

Silicon, unconfined

Aluminum

Figure 7.20: Single fin heat dissipation for 0.29 mm thick aluminum and silicon fins, with

base temperatures at the superheat corresponding to 45 kW/m2 for each surface.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 5 10 15Fin Height, H (mm)

Fin

Effic

ienc

y

Silicon, 0.3 mm channelSilicon, unconfinedAluminum

Figure 7.21: Comparison of aluminum and silicon fin efficiencies for 0.29 mm thick fins,

with base temperatures at the superheat corresponding to 45 kW/m2 for each.

Chapter 7: Design and Optimization of Boiling Heat Sinks 189 7.3.3 Effect of Fin Thermal Conductivity

The numerical analyses of the preceding sections were repeated to evaluate the benefits

of employing high conductivity materials such as silicon carbide (400 W/mK) and CVD

diamond (1000–2000 W/mK). As previously discussed, the boiling curves of any unique

combination of heater material and surface finish must be characterized individually.

However, in order to focus solely on the parametric effects of varying thermal

conductivity, the following analyses assume that polishing of these advanced materials

could provide surface characteristics and enhanced channel boiling heat transfer

coefficients comparable to the polished silicon data of Chapter 5.

Boiling heat transfer coefficients corresponding to a channel spacing (δ) of 0.3 mm were

employed. Initially, fin height (H) was set to 60 mm to maximize heat dissipation. This

also led to a direct increase in the number of elements required to provide an accurate

solution as well as a corresponding increase in analysis run times, compared to previous

analyses. Once the optimum thickness was identified for each thermal conductivity value,

fin height was varied to find the value at which fin heat dissipation was 95% of the high

fin maximum. While the channel CHF correlation developed in Chapter 5 was shown to

accurately predict CHF as a function of channel aspect ratio for silicon channels,

experimental heat transfer coefficients can not be expected to extrapolate directly to

longer or shorter channels (L). Thus, only 20 mm lengths are considered.

A summary of analysis results appears in Table 7.4. Increased thermal conductivity yields

a definite advantage for higher fins. As a result, fin heat dissipation increases, and

optimum fins are slightly thicker to help conduct this increased heat along the increased

fin heights. Figure 7.22 shows a graph of the enhancement ratio (compared to unfinned

base surface CHF) and fin height results of Table 7.4. Coincidentally, fin height and

enhancement ratio results are approximately equal in this set of results. These heat sinks

are shown to provide enhanced heat transfer approximately 5 to 18 times that of the

unfinned surface CHF. The enhanced low-flux heat transfer coefficients behind these

Chapter 7: Design and Optimization of Boiling Heat Sinks 190 results provide increased performance compared to the conductivity analyses of

Section 7.2.

Table 7.4: Results of the thermal conductivity parametric analysis, with δ = 0.3 mm,

L = 20 mm, and ∆T = 22.4°C.

Fin Thermal Conductivity, k (W/mK) 120* 400 1000 2000Optimum Fin Thickness, t (mm) 0.291 0.304 0.308 0.312

ratio to silicon result 1 1.04 1.06 1.07Fin Height at 95% of Max. Heat Flow, H (mm) 4.2 7.8 12.5 17.8

ratio to silicon result 1 1.86 2.98 4.24Sink Base Heat Flux (kW/m2) 515 913 1430 2013

ratio to silicon result 1 1.77 2.78 3.91ratio to unfinned surface CHF 4.5 8.0 12.5 17.7

*Temperature dependent thermal conductivity employed per Fig. 7.14.


0

5

10

15

20

0 500 1000 1500 2000

Thermal Conductivity, k (kW/m2)

Qsi

nk /

Qun

finne

d ba

se

0

5

10

15

20

Fin

Hei

ght,

H (m

m)

Enhancement Ratio

Fin Height

Figure 7.22: Effect of thermal conductivity on enhancement ratios and height required to

achieve 95% of asymptotic maximum, for 20 mm long heat sinks and experimental

polished silicon boiling heat transfer coefficients.

Chapter 7: Design and Optimization of Boiling Heat Sinks 192 7.4 BOILING HEAT SINK NOTES AND OBSERVATIONS

Optimized silicon heat sinks in FC-72 at 101 kPa (1 atm) have been shown to dissipate

over 500 kW/m2 (50 W/cm2) of base heat flux, nearly five times the CHF limit of the

unfinned base area, with low profile (< 5 mm high) plate fins. The polished surface finish

allows the heat sink to operate at a higher base temperature while remaining below CHF

and also provides low flux, confinement-driven enhancement. The higher base

temperature is still within a range acceptable for microelectronics applications and

provides a greater driving force for fin conduction. Confinement-driven enhancement

allows more heat to be dissipated at lower fin temperatures. The combination of these

effects yield higher fin efficiencies and improved heat dissipation over comparable

aluminum heat sinks.

While boiling performance needs to be evaluated individually for any unique fluid and

surface combination, results of parametric studies of thermal conductivity suggest that

target microelectronic device heat fluxes in the neighborhood of 1000 kW/m2

(100 W/cm2) could be readily dissipated with heat sinks made from silicon carbide and/or

various advanced carbon-based materials like pyrolytic graphite and CVD diamond.

While not discussed previously, in the context of the heat sink analyses, the

thermophysical properties of these alternate materials yield very high effusivities, ρcpk,

as shown in Fig. 7.23. Thus, very thin layers of these materials (tens of microns) maybe

be used as boiling surfaces without significant negative CHF effects, as discussed in

Section 4.3.


1.E+08 1.E+09 1.E+10

Aluminum

Silicon

Silicon Carbide

Silver

Copper

Pyrolytic Graphite

CVD Diamond

ρρρρ c p k

Figure 7.23: Product of density, specific heat, and thermal conductivity for various

candidate heat sink materials (Incropera and De Witt, 1996).

Results from the single phase natural convection parallel plate optimizations of Chapter 6

can be used to estimate the heat dissipation of optimum single phase liquid cooled

parallel plate heat sinks. Fin efficiency for a longitudinal rectangular plate fin with a

uniform thermal conductivity and heat transfer coefficient and convection at the tip may

be expressed as (Incropera and De Witt, 1996):

( )Hm

Hm′

′= tanhη (7.5)

where

( )Htk

htHmfin

2 += (7.6)

and

2tHH +=′ (7.7)

Chapter 7: Design and Optimization of Boiling Heat Sinks 194 Table 6.2 shows typical single phase heat transfer coefficients around 200 W/m2K and

volumetric heat dissipation on the order of 10 MW/m3 (10 W/cm3). Combining these

results with a fin efficiency calculation and the (relatively small) contribution from the

exposed base area in the inter-fin spaces yields heat sink base heat fluxes ranging 30–

50 kW/m2 (3–5 W/cm2) for 5–20 mm high fins—an order of magnitude smaller than

achievable with boiling.

As discussed in Appendix B, the literature contains a variety of examples of heat sinks

that can dissipate 2 to 3 times that of the unfinned surface with the same finish,

comparable to the EDM aluminum heat sink results of this chapter. However, throughout

the literature, reasons for selecting boiling fin spacing and other design parameter values

are based on simple qualitative arguments, if discussed at all. As demonstrated by the

significantly higher silicon heat sink results of this chapter which account for the fin

spacing dependence of boiling heat transfer rates, complex designs can only be optimized

after the basic heat transfer phenomena are understood. The simple longitudinal

rectangular heat sinks explored in this chapter can also serve as a baseline to which more

advanced boiling heat sink geometries and approaches may be compared.

195

CHAPTER

EIGHT

SUMMARY AND RECOMMENDATIONS

This chapter begins with a summary of experimental and theoretical contributions of the

present work and concludes with a discussion of recommendations for future research.

8.1 CONTRIBUTIONS

8.1.1 Experimental Contributions

Evidence of confinement-driven boiling heat transfer enhancement in vertical channels is

very well documented in the literature and much has been observed about its nature and

behavior. However, the majority of the available correlations is empirically-based and

they tend to be very restricted in their range of applicability and portability. In order to

further elucidate the effect of this type of geometrical confinement on boiling heat

transfer, an experimental study was been performed on vertical, rectangular parallel plate

channels of typical microelectronics dimensions.

Chapter 8: Summary and Recommendations 196 The experimental apparatus and data acquisition system was constructed to facilitate the

investigation of boiling heat transfer with candidate thermal management liquids. This

effort included the design and fabrication of novel self-heating silicon heaters for

accurate simulation of IC devices. Special care was taken in evaluating the experimental

uncertainties and measurement corrections necessary to provide accurate experimental

data.

Saturated and subcooled pool boiling data were obtained to characterize the unconfined

boiling behavior of various silicon and aluminum heater surfaces. Correlating constants

for the Rohsenow (1952) correlation were determined for each. In addition, an

exploration of surface roughness effects support the trends of the Cooper (1984)

correlation for pool boiling heat transfer. Polished silicon heaters showed the lowest

boiling heat transfer coefficients (2–4 kW/m2K), and highest superheats (>25°C).

Increasingly rough surfaces showed boiling curve shifts to lower temperature superheats.

The rough EDM aluminum surface provided the highest heat transfer rates (as high as

8 kW/m2K) achieving CHF at a superheat of only 15°C.

Pool boiling CHF observed for the aluminum surfaces was identical (well within the

estimated measurement uncertainty) to the prediction based on the Kutateladze-Zuber

correlation. CHF data obtained for the silicon heaters were somewhat lower than

predicted but still within accepted correlation accuracy limits. Observed CHF values were

independent of surface roughness for both aluminum and silicon heaters. Relative effects

of subcooling on CHF for polished silicon heaters showed excellent agreement with the

subcooling factor of the Arik and Bar-Cohen (2003) CHF correlation, with a maximum

absolute deviation of 3.2%.

Channel boiling experiments were conducted at atmospheric pressure for silicon (20 × 20

mm and 20 × 30 mm) and aluminum (20 × 20 mm) heaters. Channel spacing was varied

over the range 0.3–20 mm, providing channel aspect ratios (height/spacing) as high as 67,

for symmetrically and asymmetrically heated channels. Qualitative trends identified in

Chapter 8: Summary and Recommendations 197 the literature were verified, and the quantitative performance of the various surfaces and

channel configurations was obtained throughout the entire nucleate boiling regime,

including CHF. Polished and scratched silicon heater channels showed significant low

flux enhancement at small channel spacings, while polished silicon channels in highly

subcooled liquid and all aluminum heater channels showed no low flux enhancement.

At small channel spacings and high heat fluxes, deteriorated heat transfer (relative to pool

boiling) was observed, and CHF tended to decrease, particularly for channels with aspect

ratios larger than 10. The percent degradation of the CHF limit with decreasing channel

spacing was observed to be independent of heater material or surface treatment and took

the form of a roughly hyperbolic function of channel aspect ratio.

8.1.2 Theoretical Contributions

The Bar-Cohen and Schweitzer (1985) thermosyphon boiling model was corrected and

then updated to match their experimental data and better correlate the effect of channel

heat flux on the forced convection correction factor. Predictions from the new model

yielded good agreement with the two phase heat transfer data of Bar-Cohen and

Schweitzer (1985) for low flux channel boiling of water. However, when applied to the

experimental data of the current research, this model did not predict the observed trends

and levels of enhanced channel boiling. Additional low flux enhancement models

prevalent in the literature were considered. Given that the observed enhancement of

nucleate boiling performance with decreased channel spacing was found to depend on the

type of heater employed, an alternative enhancement mechanism based on vapor and

nucleation site interactions was proposed.

The Bonjour and Lallemand (1997) correlation for CHF in asymmetrically heated

channels was extended to apply to symmetric channels and was shown to provide

excellent agreement with experimental data from the current study for both symmetric

and asymmetric channels (within ± 12%).

Chapter 8: Summary and Recommendations 198

Based on the extended channel CHF correlation, a methodology for the optimization of

immersion cooled 3-D stacked dies was developed, and an equation relating the optimum

die spacing to die length, thickness, and fluid parameters (density ratio and reduced

pressure) was derived. Optimum 3-D stacked die geometries were identified, and

optimum designs were shown to be able to dissipate hundreds of megawatts per cubic

meter (1 MW/m3 = 1 W/cm3). The relative insensitivity of maximum heat dissipation to

die thickness over the range of interest was demonstrated. System pressure was shown to

have little effect on optimum geometries, but maximum heat dissipation will scale with

the pressure dependence expressed by the Kutateladze-Zuber CHF correlation.

Modifications to the governing volumetric heat dissipation optimization equation to

address localized device hot spots and other unique phenomena were also addressed.

An FEA-based approach was developed to efficiently evaluate and explore parametric

effects on boiling heat sink performance—including, perhaps for the first time, the

explicit dependence of fin spacing on boiling heat transfer coefficients and CHF. The

overall methodology, including the assumption (prevalent in the literature) that localized

boiling on extended surfaces could be predicted using heat transfer coefficients obtained

from isothermal surface boiling data was validated with comparison to boiling heat sink

data obtained in the current study. A detailed parametric study of both confinement-

enhanced and non-confinement-enhanced materials was performed, and maximum heat

dissipating geometries were identified.

For both optimum silicon and aluminum heat sink geometries, over the parameter ranges

explored (L = 10–30 mm, δ ≥ 0.3 mm, saturated FC-72 at atmospheric pressure), fin

thickness was found to be approximately equal to the fin spacing, though more so for

thinner fins. Fin heights roughly ten times the fin thickness (3–5 mm) provided near-

asymptotic maximum heat dissipation.

Chapter 8: Summary and Recommendations 199 Aluminum heat sink maxima were shown to be quite shallow, with many configurations

based on a 20 × 20 mm base area able to dissipate 2.5 to 3 times that of the unfinned base

area CHF limit. Longer heat sinks (L = 30 mm) provided somewhat less performance

enhancement, while shorter heat sinks (10 mm) were shown to dissipate in excess of 3.5

times the unfinned base area—driven by the effect of decreasing CHF limit with higher

aspect ratio fin channels.

Silicon heat sink performance continued to improve down to the smallest fin spacing

investigated (0.3 mm), to 541 kW/m2 (54.1 W/cm2)—nearly five times the CHF limit of

the unfinned polished silicon surface—and significantly outperformed the optimum

aluminum geometries. As these boiling structures are CHF-limited, the higher

temperature superheats of the silicon surfaces and confinement-driven enhancement yield

higher fin efficiencies and greater heat dissipation. Results indicate that heat dissipation

could be further maximized at fin spacings below 0.3 mm—beyond the capability of the

current investigation.

While boiling performance needs to be evaluated individually for any unique fluid and

surface combination, thermal conductivity parametric studies were performed using the

empirically-determined rough aluminum and polished silicon heat transfer coefficients.

Single fin heat dissipation was shown to scale with the square root of fin thermal

conductivity, demonstrating that the average heat transfer coefficient over the active heat

dissipating area of appropriately high fins is invariant to fin thermal conductivity. Heat

sink performance predictions suggest that target microelectronic device heat fluxes on the

order of 1000 kW/m2 (100 W/cm2) could be readily dissipated with heat sinks made from

silicon carbide and/or various advanced carbon-based materials like pyrolytic graphite

and CVD diamond.

Chapter 8: Summary and Recommendations 200 8.2 RECOMMENDATIONS FOR FUTURE WORK

Emerging 3-D packaging technologies may present the greatest near- and mid-term

thermal management challenges. Extensions of the optimization presented in Chapter 6

should include a deeper exploration of the effects of localized hot spots as well as

potential implications of candidate interconnect schemes. It is expected that while wires,

balls, bumps, or other physical implementations of the electrical interconnect might

impede two phase flow in and around stacked dies channels, they may also provide

additional bubble nucleation sites and heat transfer area.

Further possible heat sink enhancements include widening the heat sink base to extend

beyond the edges of the device. Maximum heat sink heat dissipation will initially scale

nearly linearly with increased heat sink width, depending on the heat spreading

capabilities of the base. The FEA-based numerical heat sink optimization methodology

developed in the context of this research would be a good candidate for software-based

design optimization tools. This would be particularly advantageous when analyzing high

aspect ratio fins with high thermal conductivities that require a large number of elements

and long solution run times to more efficiently identify optimum geometries. With more

detailed confined boiling heat transfer coefficient data, further extensions could include

other longitudinal fin profiles (e.g. triangular, parabolic) and other advanced fin

geometries. Experimental validation of enhanced extended surfaces will require advanced

silicon fabrication techniques, with particular attention paid to surface characteristics.

The effects of confinement-driven enhancement and the role of nucleation site parameters

must be explored further. In particular, polished silicon channels with sub-0.3 mm

spacings should be investigated experimentally. Given the importance of understanding

the nature and extent of various enhancement mechanisms, the measurement of two

phase flow parameters should accompany channel heat transfer investigations. Based on

the review of various techniques in Appendix D and experiences discussed in Section 3.4,

a non-intrusive, full-field optical technique, such as high speed photography with

Chapter 8: Summary and Recommendations 201 advanced digital processing, is recommended. This approach would exclude the study of

symmetric channels, though insights and models developed for asymmetrically heated

channels should be extendable by analysis.

Fortunately, we are at the beginning of an era when computational tools and computing

resources can adequately simulate two phase flow and heat transfer in bubble-sized

geometries. While examples in the literature are quite scarce, the process outlined in

Appendix F for implementing these types of volume of fluid (VOF) multiphase

simulations in the Fluent software should serve as a good starting point. Logical next

steps include optimization of the geometry and mesh to run efficiently on large parallel

computing systems (to reduce run times to manageable durations) and the incorporation

of mass transfer between the phases. In addition to basic heat transfer and two phase flow

evaluation in parallel plate channels, CFD simulation tools may also help answer more

subtle confinement questions and facilitate the design and optimization of more complex

boiling structures.

Finally, the entire body of research should be extended to new thermal management

fluids, some of which, like 3M’s Novec™ products, have been shown to posses CHF

limits 50–90% greater than FC-72 (Arik, 2001). These fluids have been engineered to

posses superior environmental properties, and new information regarding their material

properties and heat transfer capabilities continues to become available. The application of

additional passive enhancement techniques (e.g. fluid mixtures) to confined boiling

structures should also be explored.

202

APPENDIX

A

FLUID PROPERTIES AND BOILING CORRELATION

PARAMETERS

As suitable dielectric liquids are available in a wide range of boiling points (Tsat), the

working fluid for a given application can be selected to best suit the environmental

envelope. Table A.1 compares property data for saturated water with selected

Fluorinert™ fluids. As the table shows, the electrical characteristics of candidate fluids

that make them suitable for direct contact with electrical systems also tend to be

accompanied by relatively poor thermal properties. For a given temperature difference,

the boiling heat flux can be expected to be many times greater for water than for

Fluorinert™. The dominant factor leading to this difference in the Cooper (1984)

correlation, Eq. (4.1), is the difference in molecular weights. Cooper (1984) argues that

the Csf parameter in the Rohsenow (1959) correlation, Eq. (1.4), which depends on the

particular combination of fluid and surface properties, must include much of the

molecular weight effect. Clearly, Csf must also depend on surface roughness.

Appendix A: Fluid Properties and Pool Boiling Correlation Parameters 203

Table A.1: Saturation properties and property groupings at atmospheric pressure.

FC-72 FC-84 FC-77 WaterSaturation Temperature, T sat (°C) 56.6 82.5 101 100Thermal Conductivity, k f (W/mK) 0.0522 0.0531 0.0569 0.68Specific Heat, c p (J/kgK) 1098 1142 1171 4217Heat of Vaporization, h fg (kJ/kg) 84.5 90.8 95.7 2257Liquid Density, ρ f (kg/m3) 1620 1445 1522 987Vapor Density, ρ g (kg/m3) 13.4 14.3 15.1 0.596Dynamic Viscosity, µ f (Pa·s) 0.000454 0.000373 0.000420 0.000279Surface Tension, σ (N/m) 0.00827 0.0120 0.01300 0.0589Thermal Expansion Coefficient, β (1/K) 0.001639 0.001500 0.001380 0.000750Prandtl Number, Prf 9.55 8.03 8.64 1.73Critical Pressure, P crit (Mpa) 1.83 2.87 1.58 21.8Reduced Pressure, P r 0.0554 0.0353 0.0641 0.00465Molecular Weight, M (g/mol) 338 388 416 18

(1/K) 0.00028 0.000365 0.000313 0.735857

(kJ/m2s) 52.9 36.7 42.8 255

sp

hc

ffg Pr

( )σ

ρρµ gf

fgf

−gh

Complete saturation property data for FC-72 appear in Table A.2. Select properties were

calculated from the following equations, with the saturation temperature expressed in

degrees Celsius, while the remainder are provided in tabular form by the manufacturer

(3M, 1990).

( )15.2735443.118.589 sat ++= Tc p (A.1)

( )15.27310168.1090672.0 sat4

f +×−= − Tk (A.2)

( ) 2532.1sat

65.45115.2731042705.0

+−= Tσ (A.3)

sat00261.0740.1

00261.0T−

=β (A.4)

Appendix A: Fluid Properties and Pool Boiling Correlation Parameters 204

Table A.2: FC-72 saturation properties as a function of pressure (3M, 1990).

P T sat α β c p h fg k µ ρ f ρ g σ(kPa) (°C) (m2/s) (1/K) (J/kgK) (J/kg) (W/mK) (Pa·s) (kg/m3) (kg/m3) (N/m)8.61 0 3.31E-08 1.50E-03 1011 99182 5.88E-02 9.50E-04 1755 1.37 1.33E-0211.6 5 3.29E-08 1.51E-03 1019 98000 5.82E-02 8.74E-04 1738 1.80 1.29E-0214.6 10 3.26E-08 1.52E-03 1026 96818 5.76E-02 8.00E-04 1720 2.23 1.24E-0219.0 15 3.23E-08 1.53E-03 1034 95593 5.70E-02 7.43E-04 1706 2.86 1.20E-0223.5 20 3.20E-08 1.55E-03 1042 94369 5.64E-02 6.87E-04 1692 3.48 1.15E-0230.0 25 3.17E-08 1.56E-03 1050 93094 5.59E-02 6.44E-04 1680 4.36 1.10E-0236.6 30 3.13E-08 1.57E-03 1057 91820 5.53E-02 6.01E-04 1669 5.23 1.06E-0245.7 35 3.09E-08 1.58E-03 1065 90497 5.47E-02 5.68E-04 1659 6.41 1.02E-0254.7 40 3.06E-08 1.60E-03 1073 89174 5.41E-02 5.35E-04 1650 7.59 9.71E-0367.2 45 3.02E-08 1.61E-03 1080 87789 5.35E-02 5.09E-04 1641 9.14 9.27E-0379.5 50 2.98E-08 1.62E-03 1088 86404 5.29E-02 4.83E-04 1631 10.7 8.84E-0396.0 55 2.94E-08 1.64E-03 1096 84970 5.23E-02 4.61E-04 1623 12.7 8.41E-03101 56.6 2.93E-08 1.64E-03 1098 84511 5.22E-02 4.54E-04 1620 13.4 8.27E-03112 60 2.91E-08 1.65E-03 1104 83536 5.18E-02 4.39E-04 1614 14.8 7.99E-03134 65 2.87E-08 1.66E-03 1111 82046 5.12E-02 4.18E-04 1603 17.5 7.57E-03155 70 2.84E-08 1.68E-03 1119 80557 5.06E-02 3.98E-04 1593 20.2 7.15E-03182 75 2.81E-08 1.69E-03 1127 79024 5.00E-02 3.80E-04 1581 23.7 6.74E-03209 80 2.78E-08 1.71E-03 1135 77492 4.94E-02 3.62E-04 1569 27.2 6.33E-03243 85 2.75E-08 1.72E-03 1142 75928 4.88E-02 3.43E-04 1554 31.6 5.93E-03276 90 2.73E-08 1.73E-03 1150 74365 4.83E-02 3.25E-04 1539 36.0 5.54E-03317 95 2.71E-08 1.75E-03 1158 72783 4.77E-02 3.20E-04 1520 41.5 5.15E-03359 100 2.69E-08 1.77E-03 1165 71201 4.71E-02 3.14E-04 1501 47.0 4.77E-03409 105 2.68E-08 1.78E-03 1173 69447 4.65E-02 3.08E-04 1477 53.8 4.39E-03459 110 2.68E-08 1.80E-03 1181 67693 4.59E-02 3.03E-04 1453 60.6 4.02E-03519 115 2.68E-08 1.81E-03 1189 65994 4.53E-02 2.96E-04 1424 69.1 3.65E-03579 120 2.68E-08 1.83E-03 1196 64295 4.48E-02 2.90E-04 1394 77.5 3.30E-03650 125 2.70E-08 1.85E-03 1204 62215 4.42E-02 2.82E-04 1357 88.0 2.95E-03721 130 2.72E-08 1.86E-03 1212 60134 4.36E-02 2.74E-04 1321 98.6 2.61E-03805 135 2.76E-08 1.88E-03 1219 57642 4.30E-02 2.65E-04 1277 112 2.27E-03889 140 2.80E-08 1.90E-03 1227 55149 4.24E-02 2.56E-04 1233 126 1.95E-03987 145 2.87E-08 1.92E-03 1235 52059 4.18E-02 2.45E-04 1180 144 1.64E-031085 150 2.94E-08 1.94E-03 1243 48969 4.13E-02 2.34E-04 1128 162 1.34E-031199 155 3.05E-08 1.95E-03 1250 45048 4.07E-02 2.21E-04 1065 189 1.05E-031313 160 3.18E-08 1.97E-03 1258 41128 4.01E-02 2.08E-04 1003 215 7.79E-041446 165 3.35E-08 1.99E-03 1266 35693 3.95E-02 1.93E-04 930 259 5.25E-041579 170 3.56E-08 2.01E-03 1274 30258 3.89E-02 1.78E-04 858 303 2.94E-041733 175 4.19E-08 2.03E-03 1281 12459 3.83E-02 1.48E-04 714 485 9.67E-051825 178 4.70E-08 2.05E-03 1286 1780 3.80E-02 1.30E-04 628 594 8.44E-06

205

APPENDIX

B

REVIEW OF BOILING HEAT SINK LITERATURE

The boiling heat sink studies identified in Table 1.3 and summarized briefly in

Section 1.4 of the introductory chapter are reviewed in detail below.

B.1 KLEIN AND WESTWATER (1971)

In the earliest of boiling heat sink studies, Klein and Westwater (1971) investigated the

boiling performance of copper pin and plate fins in water and R113. The authors explored

various fin combinations to determine the effect of horizontal fin spacing on nucleate

boiling and CHF.

For single, horizontal rows of two to five 6.35 mm (0.25”) diameter pin fins in R113, the

authors observed very modest (less than 5%) improvements in nucleate boiling and CHF

over the boiling performance of a single fin for horizontal spacings from 1.6 mm to

27.4 mm. Deteriorated boiling performance was observed only when the fins were

allowed to touch (spacing = 0 mm), yielding a reduction in heat dissipation of 17%–31%

Appendix B: Review of Boiling Heat Sink Literature 206 per fin. The authors attributed this deterioration to the accumulation of vapor in the

crevices between the fins. These results were shown to be independent of fin height for

19.1 mm (0.75”) and 28.6 mm (1.125”) high fins. An array of ten fins, three staggered

horizontal rows of three, four, and three fins with a vertical spacing of 9.5 mm (0.375”),

produced somewhat different results. For a horizontal spacing of 0.8 mm (0.032”), the

peak heat dissipation for the inner fins was approximately 22% greater than that of a

single fin. The authors do not provide an explanation for this enhancement. Similar

results were obtained for water, though results for finite spacings less than 1.6 mm

(0.062”) were not presented. No significant boiling enhancement was observed, and

deteriorated performance was only obtained with fin spacings of zero.

An array of three, vertical plate fins, 6.35 mm (0.25”) thick, 28.6 mm (1.125”) high, and

38.1 mm (1.5”) long was also tested in R113. No significant effect of neighboring plates

was observed for fin spacings of 4.7 mm, 3.2 mm, and 1.6 mm (0.186”, 0.125”, and

0.062”), though the heat dissipation for the 3.2 mm spacing was marginally better than

the other cases. At a spacing of 0.8 mm (0.032”), however, heat dissipation dropped

approximately 35%, as bursts of vapor were observed exiting the array in all directions

(even downward).

From these results, Klein and Westwater (1971) recommend a minimum horizontal

spacing of 1.6 mm (0.062”) to allow boiling fins in an array to act independently of each

other. Further, the authors note that this dimension is on the order of the bubble departure

diameter of “ordinary” liquids in nucleate pool boiling. This spacing recommendation

continues to be cited quite frequently in the literature, e.g. (Kumagai et al., 1987),

(Mudawar and Anderson, 1993).

Appendix B: Review of Boiling Heat Sink Literature 207 B.2 ABUAF et al. (1985)

Abuaf et al. (1985) studied the pool boiling performance of horizontal copper and brass

heaters in degassed saturated R113 at pressures from 3.7 to 101 kPa (0.037 to 1 atm).

Two sizes of cylindrical heater blocks, with diameters of 51 and 76 mm, included 3.2 mm

high integral machined square pin fins, 1.6 mm in size with a fin spacing of 1.6 mm.

Boiling heat transfer results did not differ significantly for the two base sizes. CHF

increased by a factor of 2 to 2.5 times that of the unfinned surface, despite having a

surface area 3 times larger.

These boiling heat sinks showed the same pressure trends as unfinned surface data

reported in a previous study by Abuaf and Staub (1983). With decreasing pressure,

boiling curves shifted to higher superheats and CHF was shown to decrease in

accordance with the Kutateladze-Zuber correlation, Eq. (1.5), down to a pressure of

30 kPa. Below 30 kPa, CHF continued to decrease with decreasing pressure, though not

as rapidly as predicted by the Kutateladze-Zuber correlation.

The authors performed a theoretical analysis of their boiling fins, employing the 1-D fin

conduction equation and nonlinear heat transfer boundary conditions based on a variety

of empirical correlations. Predictions from their model compared favorably with their

101 kPa experimental data but failed to agree with subatmospheric data. The authors

attribute this lack of agreement to confinement effects, such as increased bubble

departure diameters, in the inter-fin spacings at low pressures.

B.3 PARK AND BERGLES (1986)

Park and Bergles (1986) investigated the boiling performance of several different,

vertically oriented copper heat sinks in R113. Various copper structures, nominally 4.5 ×

4.5 × 1 mm thick, were epoxied to 12.7 µm thick nichrome foil heaters. Experiments

Appendix B: Review of Boiling Heat Sink Literature 208 focused on temperature overshoot at ONB and heat transfer performance in the low heat

flux region for saturated and approximately 16°C subcooled conditions. Heat flux results,

based on the heat source area as well as total heat sink surface area, were compared for

the various heat sinks and bare foil heaters.

A solid copper block, or “plain heat sink,” 4.4 × 4.5 × 1.0 mm, provided heat transfer

performance similar to, though somewhat better than that of a bare foil heater, when

compared on the basis of total surface area. Addition of this plain heat sink to the foil

heater reduced the temperature overshoot at ONB, ∆Tsat, from 19°C to 11°C. Small

differences in the overshoot and established boiling behavior are attributed to differences

in surface material and finish.

Microhole heat sinks were formed by drilling four small holes (diameters ranging 0.34–

0.89 mm) through the height of copper blocks ranging in side dimensions 4.34–4.67 mm.

These microhole heat sinks showed enhancement over both the bare foil heater and plain

heat sink that exceeded the simple increase in heat transfer area. The authors attribute this

enhancement to bubble agitation and liquid pumping of the relatively high velocity two

phase flow (compared to the external surfaces) in the holes. Across the low heat flux

region investigated, 0.71 mm diameter holes provided the most consistent performance

enhancement.

Low-profile longitudinal rectangular plate fins, 0.64 mm high, were created by machining

1.02mm thick copper blocks ranging in side dimensions 4.47–4.70 mm. All of these plate

fin heat sinks contained 5 fins with a pitch of approximately 1 mm. Fin thickness and

spacing ranged 0.20–0.73 mm and 0.24–0.9 mm, respectively. While heat transfer

capability did not vary much with fin spacing, smaller fin spacings were somewhat better

at lower heat fluxes, while larger spacing were slightly more effective at higher heat

fluxes. The boiling performance of these plate fin arrays was shown to be similar to that

of the plain heat sink, when normalized to the total heat transfer area. The authors suggest

that this lack of additional enhancement may come from the fact that liquid and vapor

Appendix B: Review of Boiling Heat Sink Literature 209 could easily enter and exit the low-profile arrays from the front. Thus, the interfin

channels did not experience and could not benefit from the increased velocity of the two

phase flow seen in the microhole arrangement.

B.4 KUMAGAI et al. (1987)

Kumagai et al. (1987) created arrays of (approximately) longitudinal, rectangular plate

fins a the end of cylindrical copper rods, 10 mm in diameter. Arrays of 1–10 mm high

and 0.2–1.5 mm thick fins with spacings ranging 0.28–2 mm were tested in R113 in both

vertical and horizontal orientations in an attempt to optimize volumetric heat dissipation

based on the heat sink envelope. As expected, all heat sink configurations provided heat

dissipation capability greater than the bare, unfinned surface, typically 200%–300%.

Vertically oriented heat sinks showed smoother liquid and vapor flow and, as a result,

somewhat better performance than horizontally oriented arrays with which some counter

currents were observed between fins.

In a previous study (Jho et al., 1985) the authors developed an analytical methodology for

predicting and optimizing the boiling performance of longitudinal plate fin arrays.

Unfortunately, this methodology did not account for fin to fin interactions and,

consequently, the dependency of boiling heat transfer rates on fin spacing. As a result,

optimization results suggested that, “both the fin thickness and the fin spacing should be

as small as possible” (Kumagai et al., 1987). Due to the interaction of adjacent fins, their

experimental boiling heat sink results showed consistently better than expected

performance at low to mid heat fluxes and consistently poorer than expected performance

near CHF.

As a result of their parametric study, Kumagai et al. (1987) showed that the smaller fin

spacings led to improved performance at low heat fluxes, though the 0.5 mm spacing was

best near CHF. While varying the fin thickness showed little effect at low to moderate

Appendix B: Review of Boiling Heat Sink Literature 210 heat fluxes, the thinnest fins investigated (0.2 mm) provided the greatest heat dissipation

capability near CHF. In order to obtain an optimum fin height, the authors consider

experimental heat sink results for 0.2 mm thick fins with a 0.28 mm spacing. In

calculating the power dissipation per heat sink envelope volume, the fins were “assumed

to be located on the surface of a cylinder 12.5 mm in diameter” (Kumagai et al., 1987).

Of the 1, 2, 5, and 10 mm fin heights investigated, volumetric heat dissipation was

greatest, and roughly equal, for 1 and 2 mm fin heights. The shorter, 1 mm high fins

made a very sharp transition to film boiling, while the nucleate boiling curves for the

2 mm high fins continued for another 5–10°C before making the jump to film boiling,

with relatively little change in volumetric heat dissipation. The authors consider this an

advantage of the 2 mm high fins in terms of easing the jump in base temperature from

CHF to film boiling, despite the fact that the observed temperature difference, ∆TCHF-film,

was on the order of 200°C. The real advantage of the higher fins may be their behavior

approaching CHF, providing a plateau of thermal performance before the critical jump to

film boiling. Regardless, a fin height of 2 mm was chosen as the optimum. The optimum

heat sink geometry identified (2 mm high, 0.2 mm thick, 0.5 mm spacing) produced

approximately a 200% improvement in peak heat dissipation over results obtained for a

bare, unfinned surface.

B.5 ANDERSON AND MUDAWAR (1988, 1989), MUDAWAR AND

ANDERSON (1990, 1993)

In a series of papers by Anderson and Mudawar (1988, 1989) and Mudawar and

Anderson (1990, 1993), the heat transfer behavior of a wide variety of micro-enhanced

surfaces and structures in FC-72 is investigated from boiling incipience to CHF. All

enhancement techniques were applied to a vertically oriented 12.7 × 12.7 mm square

base/heater area. The authors obtained a peak heat flux (at CHF) of 200 kW/m2 for the

bare, mirror polished, unenhanced silicon surface in saturated pool boiling. Arrays of

smooth and microenhanced pin fins (3.63, 5.75, and 12.7 mm in diameter and 7.26, 11.5,

Appendix B: Review of Boiling Heat Sink Literature 211 16, and 40 mm high) were among the structures tested. Fin spacings on these arrays were

set at the expected bubble departure diameter (0.6 mm), and fin heights were limited to

conform to what the authors considered practical multichip module packaging

requirements. These boiling heat sinks provided heat fluxes from 800–1060 kW/m2

(400%–530% enhancement) in saturated conditions and nearly 1600 kW/m2 with 35°C of

subcooling. However, microenhanced pin fin arrays provided roughly twice the

performance increase obtained by applying the same microscale surface enhancements to

the base heater surface alone.

B.6 MCGILLIS et al. (1991)

McGillis et al. (1991) studied saturated pool boiling of water at low pressures from

horizontal square pin fin heat sinks. The heat sinks were machined from a 12.7 mm

square copper base. Fin spacings of 0.30, 0.41, 0.81, 1.59, and 3.58 mm were

investigated. Nominal fin thicknesses were 0.6 and 1.8 mm (± 0.2 mm), providing an

integral numbers of fins ranging from 3 to 12. Fin height was varied from zero (unfinned

surface) to as high as 10.2 mm.

The authors propose that reduced operating pressure will bring the saturation temperature

of water and, therefore, boiling surface superheats down to an acceptable range for

microelectronics cooling. Thus, system pressure was set at 4 and 9 kPa (0.04, 0.09 atm)

to produce saturation temperatures of 29.0 and 43.6°C, respectively. At these reduced

pressures, only one or two nucleation sites were active, and departing bubbles were very

large, on the order of the size of the heat sink itself. As a result, heat transfer

enhancement was maximized at the smallest fin spacing investigated where confined

superheated liquid led to faster bubble growth and departure times. Heat transfer

performance was independent of fin thickness and independent of fin height above

2.54 mm. At 9 kPa (0.09 atm) with 2.54 mm high and 1.8 mm thick fins, CHF increased

from 800 kW/m2 (80 W/cm2) for the unfinned surface to 2300 kW/m2 (230 W/cm2) with

Appendix B: Review of Boiling Heat Sink Literature 212 a fin spacing of 0.30 mm. Likewise, heat sink base superheat was reduced from 20–30°C

to around 10°C.

B.7 DULNEV et al. (1996)

Dulnev et al. (1996) experimentally and analytically explored the heat dissipation

capability of a 40 × 40 × 20 mm high pin fin heat sink. The fins were primarily of

rhombic cross-section, 5.5 mm on a side and spaced 1.6 mm apart. Due to the hexagonal-

shaped heat sink base of this array, some of the exterior fins were triangular in cross-

section. The analytical development given by Dulnev et al. (1996) seeks to maximize the

heat flux from the heat sink base area. Unfortunately, the treatment does not include the

effects of fin spacing on boiling heat transfer rates and suggests that heat flux increases

indefinitely with decreasing fin spacing. A minimum 1.6 mm fin spacing was selected

from a heat exchanger reference (Kern and Kraus, 1977). With this minimum spacing set,

the authors calculate a heat flux-maximizing rhombus side length of 5.5 mm. Finally, an

expression for an infinitely high fin is manipulated to find the height at which 95% of the

fin's heat has been dissipated, 20 mm. The authors claim “satisfactory” agreement

between their analytical model and experimental heat sink, which was able to dissipate

1200 kW/m2 through boiling of R113 at a base superheat, ∆Tsat, of 23°C, though further

results or data are not given.

B.8 GUGLIELMINI et al. (1996, 2002), MISALE et al. (1999)

Guglielmini et al. (1996) explored the effects of non-boiling waiting period, system

pressure, and geometry on arrays of straight copper pin fins of square cross section in

saturated Galden HT-55. Two fin sizes were investigated, 0.4 mm and 0.8 mm in width.

The fin height was 3 mm and the fin spacing was equal to the fin width in both cases.

Both system pressure and pre-test non-boiling waiting period effects were evident at low

Appendix B: Review of Boiling Heat Sink Literature 213 heat fluxes. However, at heat fluxes roughly half of CHF, the boiling curves merge for

the various cases. Heat transfer coefficients were generally higher and the hysteresis

effect was greatly reduced for fin arrays oriented vertically. In the vertical orientation,

rising vapor is forced to pass by more of the heat sink surface and is likely to activate

more boiling nucleation sites than in the horizontal orientation where patch boiling was

observed. These fin arrays provided increases in peak heat dissipation 2.5–3 times that of

the bare unfinned surface. Misale et al. (1999) looked at the performance of these same

heat sinks inside channels 5 mm and 3.5 mm wide. In the vertical orientation, boiling

performance was unaffected by the presence of the opposing channel wall, while

horizontal heat sinks showed significantly deteriorated performance due to vapor

trapping.

In a further follow-up study, Guglielmini et al. (2002) investigated pool boiling heat

transfer from horizontal copper square pin fin arrays immersed in saturated FC-72 at

saturation pressures of 50, 100, and 200 kPa. Four basic array configurations were

studied: 3 or 6 mm high fins, 0.4 or 1.0 mm wide, with fin spacing equal to the fin width.

Eight additional configurations were created by systematically removing rows of fins

from the base configurations. The authors achieved over 700 kW/m2 with the 6 mm fins,

compared to approximately 140 kW/m2 for an unfinned planar surface. The authors

mention potential for a great number of available nucleation sites created by the electron

discharge machining of the fin arrays. Unfortunately, no description of the surface

characteristics of the unfinned surface is given.

B.9 FANTOZZI et al. (2000)

Fantozzi et al. (2000) investigated boiling of saturated HCFC141b at atmospheric

pressure from aluminum heat sinks with 30 mm diameter, horizontally-oriented circular

bases. The heat sinks consisted of arrays of seven 2 mm thick longitudinal rectangular

plate fins spaced 2 mm apart, with fin heights of 0, 2, 5, and 10 mm. Based on traditional

Appendix B: Review of Boiling Heat Sink Literature 214 1-D fin analysis (Kern and Kraus 1972), and an assumed uniform heat transfer coefficient

of 10000 W/m2K, the authors estimated that the 10 mm fin height would maximize fin

heat dissipation, achieving (if not exceeding) 98% of the asymptotic, infinitely high fin

limit.

The authors included an additional passive enhancement technique which they call pool

boiling with controlled return (PBCR). With this technique, vapor generated at the

boiling heat sink is condensed in the experimental apparatus and collected in a special

reservoir. The condensate then flows through 0.8 mm diameter tubes under the force of

gravity, forming low velocity liquid jets directed back at the heated surface in the inter-

fin spaces. Using this technique, an 85% increase in the CHF of the unfinned surface

(H = 0) was achieved, 0.37 MW/m2 vs. 0.2 MW/m2 (37 W/cm2 vs. 20 W/cm2) with and

without PBCR, respectively.

When applied to the 10 mm high heat sink, PBCR had the effect of reducing superheats

at low and intermediate heat fluxes, but maximum achievable heat sink heat dissipation

was unaffected at 0.87 MW/m2 (87 W/cm2) based on the heat sink base area, an increase

of more than twice the CHF limit of the plain, unfinned surface with PBCR. However,

the heat sink base superheat increased to more than 2.5 times that of the unfinned surface

at CHF, 53°C vs. 20°C. With PBCR, maximum heat dissipation of the 2 and 5 mm high

heat sinks was 0.47 MW/m2 and 0.66 MW/m2 (47 W/cm2 and 66 W/cm2), respectively,

with only modest increases in base temperature compared to CHF for the unfinned

surface, less than 5°C. Results for the 2 and 5 mm high heat sinks without PBCR are not

presented, but the authors claim the PBCR enhancement is significant for these cases.

In order to explore CHF and the transition to film boiling in more detail, the authors

fabricated a special heater surface with a single 10 mm high fin. They were able to

demonstrate that CHF occurs locally where the surface temperatures exceed the superheat

observed at CHF for the plain, unfinned surface, i.e. 20°C. With elevated heat sink base

Appendix B: Review of Boiling Heat Sink Literature 215 temperatures, stable film boiling may occur at the heat sink base, with nucleate boiling

along intermediate portions of the fins and natural convection at and near the fin tips.

B.10 RAINEY AND YOU (2000), RAINEY et al. (2003)

Rainey and You (2000) combined pin fin heat sinks with a microporous coating to

explore “double enhancement” of pool boiling. Experiments were performed in saturated

FC-72 at atmospheric pressure, with the heat sink base oriented horizontally. Pin fins

were machined in 10 mm square copper bases using a high-speed steel slitting saw blade.

The 5 × 5 array consisted of 1 mm square pins with an inter-fin spacing of 1 mm.. Fin

heights of 0.25, 0.5, 1, 2, 4, and 8 mm were investigated in addition to the unfinned base

area. The “ABM” microporous coating consisted of aluminum particles with diameters

ranging from 1 to 20 µm and a Devcon brushable ceramic binder, for a total coating

thickness of approximately 50 µm.

CHF for the unfinned machined and coated base surfaces were 190 and 260 kW/m2 (19

and 26 W/cm2), respectively. With the addition of fins, CHF was comparable for both

surface finishes and scaled almost linearly with the ratio of total to base area for all heat

sinks, with the exception of uncoated heat sinks with 8 mm high fins. Deteriorated CHF

for the uncoated 8 mm fins compared to the coated 8 mm fins is attributed to the

inferiority of nucleation site characteristics leading to non-boiling areas near the fin tips.

CHF for the 8 mm high ABM coated fins was 1290 kW/m2 (129 W/cm2), nearly five

times CHF of the coated, unfinned base surface. However, the heat sink base superheat at

this operating point was 53°C (Tb = 110°C absolute).

In a follow-up study, Rainey et al. (2003) expanded the work to include pressure,

subcooling, and orientation effects. System pressures of 30, 60, 100, and 150 kPa were

investigated with subcoolings of 0, 10, 30, and 50°C, though not all combinations were

achievable, as the bulk liquid temperature was limited to a minimum of 12°C. In general,

Appendix B: Review of Boiling Heat Sink Literature 216 pressure and subcooling effects on heat sink performance were consistent with unfinned

surface behavior observed by the authors as well as evident elsewhere in the literature, as

discussed in detail in Chapter 4. Both heat sink orientations showed similar performance

through most of the nucleate boiling regime, though the horizontal orientation was found

to produced 10–20% higher CHF values. The authors attribute this observation to

presumed reduced boiling heat transfer coefficients on the downward-facing pin fin

surfaces. However, their results are contrary to the pin fin results of Guglielmini et al.

(1996) which show better performance in the vertical orientation, albeit with somewhat

narrower fin spacings.

B.11 YEH (1997)

Yeh (1997) developed an analytical methodology for optimizing longitudinal, rectangular

plate fins by maximizing total heat dissipation for a fixed total fin volume. The one-

dimensional heat conduction analysis assumed a constant fin thermal conductivity and a

uniform base temperature. Temperature-dependent heat transfer coefficients were

expressed with a power-law formulation, allowing for the approximation of a variety of

heat transfer mechanisms, including nucleate and film boiling. Unfortunately, this

formulation precludes the inclusion of fin-to-fin interactions and the resulting dependence

of heat transfer coefficient on fin spacing. The mathematical development is quite

advanced, both in derivation and presentation of the solutions.

The expected input parameters are required: working fluid, fin material, and base width,

length, and temperature. The total fin volume or, equivalently, the total fin profile area

must be given, following traditional least-material optimizations (e.g. Bar-Cohen and

Jelinek, 1985). In addition, since the development does not include the effect of fin

spacing on heat transfer rates at the fin surfaces, one more parameter, either the fin

thickness or number of fins, must be specified. The derivation and form of the solution

differ depending on which of these parameters is set a priori. The authors found that the

Appendix B: Review of Boiling Heat Sink Literature 217 aspect ratio of fins in an optimum array is larger than that of a single optimum fin.

Results were compared with experimental data from the literature for natural convection

fin arrays. It is shown that this methodology provides poor agreement with this data for

shorter, thicker fins, due to two-dimensional conduction effects.

218

APPENDIX

C

EXPERIMENTAL APPARATUS PHOTOGRAPHS AND

SCHEMATICS

The follow pages contain additional photographs and schematics of the experimental

apparatus that do not appear in the main chapters of the dissertation. The figures begin

with drawings of the experimental module. These are followed by drawings and a

photograph of the fixtures used to facilitate sputtering of aluminum electrodes on the

edges of the silicon heaters. Photographs of the experimental apparatus appear next,

including a view from the bottom taken during a boiling experiment. Finally, schematics

and photographs of the experimental boiling heat sink and apparatus used to test it, as

discussed in Chapter 7, conclude this chapter.

Dimensions are in inches unless otherwise noted, as piece parts were fabricated using

British machine tools.

Appendix C: Experimental Apparatus Photographs and Schematics 219

1.1502.800

4.450

3.160

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4.375

0.475

3.625

0.250

10-24 threadedthrough holes3.940

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o-ring groovedepth = 0.080”width = 0.145”

0.3475

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3.625

0.250

10-24 threadedthrough holes3.940

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0.3475

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Figure C.1: Front view of aluminum experimental module.


0.375

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1.9753.625

1/8”NPT threadedthrough holes(Q drill, 0.332”)

3/4”NPT threaded(29/32” drill)

0.375

0.875

1.375

0.375

5.225

1.9753.625


3/4”NPT threaded(29/32” drill)

0.375

0.875

1.375

Figure C.2: Top view of aluminum experimental module.


5.600

0.375

5.225

0.375

1.375

3.925

1.675

1.460

1/16”NPT threadedthrough holes(C drill, 0.242”)


4.140

0. 875

5.600

0.375

5.225

0.375

1.375

3.925

1.675

1.460



4.140

0. 875

Figure C.3: Bottom view of aluminum experimental module.


4.100


0.710

2.605

1.495

0.250

0.575

0.900

0.104

10-24 threaded0.750”deep

0.875

4.100


0.710

2.605

1.495

0.250

0.575

0.900

0.104

10-24 threaded0.750”deep

0.875

Figure C.4: Side view of aluminum experimental module.


0.5002.150

3.800

3.260

2.150

1.040

0.250

10-24 clearance

4.040

0.260


0.4475

3.8525

0.4475 3.8525

0.5002.150

3.800

3.260

2.150

1.040

0.250

10-24 clearance

4.040

0.260


0.4475

3.8525

0.4475 3.8525

Figure C.5: Polycarbonate window, 0.25” thick.


13362.150

2.964

2.964

2.150

4-40 clearance

1.336

2.1” D

13362.150

2.964

2.964

2.150

4-40 clearance

1.336

2.1” D

Figure C.6: Shaft-supporting polycarbonate wall, 0.25” thick.


0.4361.25

2.064

2.064

1.25

4-40 threaded

0.436

2.0” D

2.500

0.4361.25

2.064

2.064

1.25

4-40 threaded

0.436

2.0” D

2.500

Figure C.7: Polycarbonate shaft support, 2.5” deep.


Figure C.8: Silicon heater substrate and modified module wall, 0.25” thick polycarbonate.


0.335

0.7290.350

0.675

1.000

1.250

1.500

0.125

1.250

1.000

1.000

0.125

0.335

0.7290.350

0.675

1.000

1.250

1.500

0.125

1.250

1.000

1.000

0.125

Figure C.9: Aluminum module leg standoff blocks.


0.335

0.729

0.350

0.675

1.000

0.500

0.500

0.335

0.729

0.350

0.675

1.000

0.500

0.500

Figure C.10: Aluminum module legs, 12” long (not to scale).


Figure C.11: Aluminum module feet, 12” long.


1.500

1.0000.400

0.356

1.145

0.787

0.200

1.300

1.500

0.3001.000

0.358

1.143

0.787

0.200

1.300

0.590

0.590

1.500

1.0000.400

0.356

1.145

0.787

0.200

1.300

1.500

0.3001.000

0.358

1.143

0.787

0.200

1.300

0.590

0.590

Figure C.12: Aluminum fixture for 20 × 20 mm silicon heater electrode sputtering process.


1.500

1.0000.400

0.356

1.145

1.181

0.200

1.300

0.590

1.500

0.3001.000

0.358

1.143

1.181

0.2001.300

0.590

1.500

1.0000.400

0.356

1.145

1.181

0.200

1.300

0.590

1.500

0.3001.000

0.358

1.143

1.181

0.2001.300

0.590

Figure C.13: Aluminum fixture for 20 × 30 mm silicon heater electrode sputtering process.


Figure C.14: Photograph of aluminum fixture for 20 × 30 mm silicon heater electrode sputtering process.


Figure C.15: Photograph of backside of module assembly including module legs.


Figure C.16: Photograph of backside of module with 20 × 30 mm silicon heater installed.


a. b.

Figure C.17: Photographs of module interior through bottom window:

a.) unpowered heaters, large channel spacing, δ ≈ 5 mm; b.) single unconfined heater, powered.


2 mm3 mm

50 mm

20 mm

2 mm

10 mm

7 mm

Heat Sink Heater Assembly

ThermocoupleLocations

××2 mm

3 mm

50 mm

20 mm

2 mm

10 mm

7 mm

Heat Sink Heater Assembly

ThermocoupleLocations

××

Figure C.18: Experimental boiling heat sink drawing.

Figure C.19: Experimental boiling heat sink photographs.


Boiling Heat Sink

Heater Assembly

Water-Cooled Cold Plate

Liquid-Filled Enclosure

27mm

80mmCartridge Heater

Power Leads

Lexan WallThermocouple Leads

Heater Assembly

Cold Plate

Condenser Ports

Water-Cooled Condensers

Boiling Heat Sink

Heater Assembly

Water-Cooled Cold Plate

Liquid-Filled Enclosure

27mm

80mmCartridge Heater

Power Leads

Lexan WallThermocouple Leads

Heater Assembly

Cold Plate

Condenser Ports

Water-Cooled Condensers

Figure C.20: Experimental boiling heat sink apparatus.

238

APPENDIX

D

THERMAL ANEMOMETRY IN TWO PHASE FLOWS

Since its introduction in the early 1950’s, thermal anemometry has been used in an

incredible number of studies to measure a wide range of fluid flow characteristics. More

commonly used in single phase flows, various researchers have also used thermal

anemometry for phase detection in two-phase flows, to measure quantities such as void

fraction, slip ratio, bubble size, and bubble frequency, as well as for the identification of

two-phase flow regimes (e.g. (Hsu et al.,1963), (Toral, 1981), (Serizawa et al., 1984),

and (Wang et al., 1987)). Hot Wire Anemometry: Principles and Signal Analysis (Bruun,

1995) is an excellent reference for information related to all aspects of thermal

anemometry. Bubbly gas/liquid flows are of general interest in a wide variety of

engineering fields (e.g. reactor design, oil transport, heat exchangers/refrigeration

systems). Analytical models of two-phase flow are most often very approximate, at best,

and are usually based on some type of empirical factor or correlation. Thus, the ability to

measure local two-phase flow parameters can be extremely useful in any two-phase flow

facility. This appendix discusses basic thermal anemometry operating principles applied

to two-phase flow, how it compares with other measurement techniques, and sources of

measurement error.

Appendix D: Thermal Anemometry in Two Phase Flows 239 D.1 BASIC PRINCIPLES

When considering a fixed control volume of a heterogeneous gas/liquid mixture, void

fraction is defined as the ratio of the volume occupied by the gas phase to the total

volume of interest (gas and liquid).

total

gas

liquidgas

gas

VV

VVV

=+

≡α (D.1)

Thus, void fraction is non-dimensional quantity, ranging from 0 to 1 (often expressed as a

percentage).

When considering a single point in space, the local void fraction is expressed as the ratio

of the amount of time the point is occupied by gas to the total time of observation.

total

gas,, τ

τα =zyx (D.2)

Thus, in this sense void fraction is inherently a time-averaged, steady-state quantity.

A hot-wire or hot-film probe can be used to detect the passing of gas and liquid phases at

a specific point in space. For a constant temperature probe, heat dissipation from the

probe will be significantly higher when in contact with the liquid phase than it will be

when it is surrounded by gas. The resulting anemometer output signal can then be

analyzed to determine the local void fraction.

Figure D.1 shows the expected anemometer response to the passage of a bubble across a

cylindrical probe when the bubble velocity is greater than that of the surrounding liquid

(e.g. buoyancy driven). A number of distinct changes in this signal can be associated with

the various stages of bubble/probe interaction.

Appendix D: Thermal Anemometry in Two Phase Flows 240

E

V

ττττ

A B

C

D

F

GH

I3

2

1

E

V

ττττ

A B

C

D

F

GH

I3

2

1

Figure D.1: Typical response of cylindrical probe signal due to passing bubble (Bruun

and Farrar, 1988).

A: Approach

As the bubble approaches the probe, liquid at the leading surface of the bubble is pushed

toward the probe at a greater velocity than the surrounding liquid. As a result, the

anemometer signal increases until point B. In some cases, the bubble velocity may be

taken as the liquid velocity corresponding to the output voltage at point B (assuming the

proper single-phase liquid calibration of the probe is performed), since it can be expected

that the liquid right at the leading surface of the bubble is moving at the bubble velocity.

B: Contact

The leading surface of the bubble comes in contact with the probe at point B and menisci

begin to form. As liquid phase convection at the probe is suppressed and the gas phase

begins to cover the surface of the probe, heat transfer from the probe is hindered, leading

to a reduction in power supplied by the anemometer and a corresponding drop in the

output signal.

C: Menisci Recede

Appendix D: Thermal Anemometry in Two Phase Flows 241 As the menisci recede toward the trailing edge of the probe, any liquid film left on the

probe will begin to evaporate, and heat loss from the probe will continue to decrease,

though not as quickly as when liquid convection was suppressed at point B.

D: Menisci Merge

At this point the two menisci begin to merge at the trailing edge of the probe.

E: Thin Liquid Film

After the menisci merge, a thin liquid film may remain, stretched between the back of the

probe and the support prongs at the probe ends. The shape of the meniscus attached to the

probe will remain virtually constant as liquid is continually evaporated from the probe

surface.

F: Breakage

In some cases, the thin liquid film between the prongs of the probe may break, giving rise

to a sharp peak at point F. However, in some cases this will not happen before the back of

the bubble arrives at the front of the probe (Bruun and Farrar, 1988).

G: Bubble Back

When the back of the bubble reaches the front of the probe, contact with the liquid phase

results in an increase in heat transfer from the probe, and the anemometer signal begins to

rise.

H: Advancing Menisci

Increased liquid cooling of the probe continues as the menisci advance. The anemometer

signal rises sharply until these menisci merge and the bubble leaves the probe.

Appendix D: Thermal Anemometry in Two Phase Flows 242 3: Bubble Detachment

Once the back side of the bubble leaves the probe surface at point 3, the anemometer

signal takes on values corresponding to liquid velocities in the bubble wake.

I: Wake Dispersal

The anemometer signal eventually drops to the undisturbed liquid value as the effects of

the bubble wake velocity dissipate.

The appropriate time duration to prescribe to this bubble event is the time between the

arrival of the front of the bubble at the front of the probe and the arrival of the back of the

bubble at the front of the probe, i.e. the time between points 1 and 2 of Fig. D.1. The

curve illustrated in Fig. D.1 corresponds to a direct hit of the probe by a bubble. Many

researches also discuss the effects and implications of partial hits, glancing hits, and

partially glancing hits—all resulting in similar output signals, though some or all

segments of the curve of Fig. D.1 may be less pronounced or sloped somewhat differently

(e.g. see Bremhorst and Gilmore (1976)). The exact shape of the anemometer signal will

vary somewhat for other probe configurations (conical hot-film, etc.) and flow

conditions, but the overall idea is the same for all. Bubble arrival and departure are

signaled by very distinct changes in the anemometer signal.

V

ττττ

liquid

gas

V

ττττ

liquid

gas

Figure D.2: Typical anemometer signal in bubbly two-phase flow (Hsu et al., 1963).

Appendix D: Thermal Anemometry in Two Phase Flows 243 Figure D.2 shows an actual anemometer output signal from a cylindrical hot-film probe

in a water/steam two-phase flow (Hsu et al., 1963). A variety of bubble events can be

identified in this figure, where the signal dips below the average, or baseline voltage. The

main task of the researcher is to analyze these types of anemometer output signals, to

identify bubble passage events and determine the fraction of time the probe spends in the

gas phase (void fraction). Successful phase identification relies on the expectation that

fluctuations in the output signal resulting from bubble-probe interaction are in some way

significantly different, and therefore distinguishable, from the fluctuations of the liquid

phase. One particular method of signal analysis will be discussed in detail in a later

section.

Thermal anemometry performed in this manner also has the capability of providing

additional information about the structure of the two-phase flow. While the bubble

residence time on the probe is so short that gas phase velocities are not readily

determinable (Farrar and Bruun, 1989), liquid phase velocities, turbulence characteristics

and the like may be obtained through single-phase probe calibration and proper

separation of the liquid and gas components of the anemometer signal. For examples of

simultaneous gas and liquid phase measurements, the reader is referred to works by

Resch et al. (1974), Jones and Zuber (1978), and Wang et al. (1987).

It is important to note that when using thermal probes in liquids, proper attention must be

paid to the relation between the probe temperature, set by the operating overheat ratio,

and the liquid saturation temperature at the system conditions. If the probe temperature is

set significantly above the liquid saturation temperature, film boiling may take place at

the probe surface, and the probe will “see” only the gas phase, regardless of the state of

the surrounding fluid. If liquid phase velocity information is desired, it may be necessary

to operate at a sufficiently low overheat ratio so that boiling does not take place on the

probe. This effect may have particularly serious implications when the surrounding liquid

is at or near saturation.

Appendix D: Thermal Anemometry in Two Phase Flows 244 Some researchers suggest a probe operating temperature corresponding to nucleate

boiling (Hsu et al., 1963). This overheat provides a compromise between probe

sensitivity and signal distortion. When liquid phase information is sought, it may be

possible to filter false bubble events triggered by nucleate boiling on the probe from the

anemometer signal in lieu of reducing the probe operating temperature.

Since hot-wire and hot-film probes come in a variety of sizes and configurations,

selection of an appropriate probe for a given system requires serious consideration and

may very well be critical to obtaining meaningful data. Several advantages and

disadvantages of hot-wire and hot-film probes are listed below (Nelson, 1984).

Advantages of hot-wires over hot-film probes:

• Size – typically 5 µm in diameter vs. 50 µm for cylindrical hot-film probes

• Higher Temperature Coefficient of Resistance

• Lower Signal-to-Noise Ratio

Advantages of hot-films probes over hot-wires:

• Less Heat Loss to Supports — quartz substrate has low thermal conductivity

• Better Frequency Response — sensitive part is distributed on surface rather than

entire cross section

• Various Configurations

• Rugged and Stable

• Resist Fouling

Appendix D: Thermal Anemometry in Two Phase Flows 245 D.2 COMPARISON WITH OTHER TECHNIQUES

A variety of experimental phase detection techniques have been employed in two-phase

flow studies. This section discusses the basic operation and advantages and disadvantages

of some of the most commonly used techniques as well as a comparison of their

applicability to measuring local void fractions in two-phase flow. For a more thorough

treatment of the subject, the reader is referred to the work by Cartellier and Achard

(1991).

D.2.1 Resistivity Probes

At the heart of a resistivity probe phase detection system is a small (typically 5-15 µm in

diameter), needle-point electrode located at the point of interest in the flow. A second,

significantly larger electrode is located elsewhere in the fluid where it is sure to remain in

contact with the liquid phase at all times. Phase identification relies on the variation in

electrical resistance between the two electrodes when the first electrode is in contact with

the different phases (i.e. the gas phase will not conduct electricity, leading to a huge

resistance between the electrodes). Clearly, this technique can only be used with

electrically conducting liquids and cannot provide information about the flow

characteristics of the liquid phase. Output signals from the resistivity probe look similar

to those from a thermal anemometer (though without the fluctuations due to velocity

variations of the liquid phase) and are analyzed in a similar fashion. For examples of

measurements made with resistivity probes, the reader is referred to works by Serizawa et

al. (1975) and Liu and Bankoff (1993).

D.2.2 Optical Probes

Optical probes rely on the back reflection of radiated light as an indication of the fluid

phase located at the probe tip. Unfortunately, optical probes do not accurately detect

bubbles smaller than the probe tip (typically a few tenths of a millimeter), and, like

Appendix D: Thermal Anemometry in Two Phase Flows 246 resistivity probes, cannot provide information about the liquid phase. Cartellier (1990)

performed interface-piercing tests with various optical probes in order to characterize

their performance. The authors note, in particular, the unsuitability of such probes in

flows with small bubbles and/or low void fractions.

Herringe and Davis (1974) performed a direct quantitative comparison of an infrared

optical probe, a single needle resistivity probe, a cylindrical hot-wire probe, and a conical

hot-film probe for local phase change detection in air/water mixtures. The single-needle

resistivity probe was able to detect the smallest bubbles, caused the smallest disturbance

in the flow, and provided the most accurate measurement of local void fraction. However,

in high void fraction flows a double-needle probe was required. The hot-wire probe was

the second-most promising probe studied as well as the author’s recommendation for use

in dielectric liquids. The authors advise that future studies explore the trade-off between

wire strength and probe response speed. The conical hot-film probe caused too much

bubble deflection and did not detect small bubbles well, leading to a significant

underestimation of the local void fraction. The infrared optical probe provided results

comparable to those of the hot-wire and double-needle resistivity probe. However, the

optical probe did not display an as well defined response speed and failed to provide a

smooth void fraction profile.

D.2.3 Laser Doppler Anemometry

As with seeding particles used in conventional single-phase laser Doppler anemometry

(LDA), the light scattering characteristics of bubbles in a two-phase flow can be

employed in the same manner to obtain bubble velocities, diameters, and frequencies as

well as void fractions. When seeding particles are included, liquid phase velocities and

flow patterns are also obtainable. Unfortunately, LDA systems are very costly and require

a large amount of time from an experienced researcher to setup the various optics and

other instruments involved. Reduction of the resulting laser scattering information

becomes doubly complicated since special equipment and procedures are needed to

Appendix D: Thermal Anemometry in Two Phase Flows 247 distinguish between seed and bubble signals. Further, a review of LDA literature

performed by Sheng and Irons (1991) showed that this technique is unsuitable for flows

containing large bubbles at moderate void fractions. The authors went on to present the

results of a combined LDA and resistivity probe technique. Inclusion of the resistivity

probe in the measurement system allowed the authors to overcome LDA shortcomings

associated with large bubble/moderate void fraction flows.

Table D.1 shows a qualitative comparison of the measurement techniques discussed in

this section as applied to two-phase flow measurements. From this table as well as the

preceding discussion it is clear that thermal anemometry is a promising option for two-

phase flow measurements, particularly in dielectric liquids.

Table D.1: Relative comparison of various two-phase flow measurement techniques.

Technique Dielectric Liquids Cost Intrusiveness Liquid

Information Setup Data Reduction

Thermal Anemometry + + – + + –Resistance Probes – + – – + –Optical Probes + + – – + –LDA + – + + – – –

Appendix D: Thermal Anemometry in Two Phase Flows 248 D.3 SOURCES OF MEASUREMENT ERROR

The use of thermal anemometry probes in two-phase flows brings a whole new range of

measurement error issues in addition to those associated with single-phase measurements.

Proper treatment of typical single-phase measurement issues, such as temperature

compensation and conduction heat loss, has been explored in a variety of studies

(Freymuth, 1979) (TSI, 2001), and will not be discussed here. Error sources unique to

two-phase measurements are discussed in detail below.

D.3.1 System Disturbance Effects and System-Sensor Interactions

As thermal anemometry, by its very nature, is an intrusive technique, one may expect

significant system disturbance and system-sensor interaction effects. Clearly, as the probe

size approaches characteristic flow dimensions (hydraulic diameter, etc.), the presence of

the probe in the flow will significantly disturb and alter bulk flow characteristics. When

this is the case, particular attention must be paid to appropriate flow constriction and

other related bias error corrections. This type of disturbance effect is common to all

intrusive probes (e.g. pitot tubes, thermocouples, enthalpy probes), and will not be

addressed in detail here.

Since the principle of thermal anemometry is based on a transfer of heat from the probe

to the surrounding fluid, one must consider the effect of this heat gain on the system.

Fortunately, in systems where the main flow velocity is in a single direction, heating of

the fluid by the probe should not affect upstream conditions. Further, in the case of two-

phase flow studies, the use of low overheat ratios will also serve to dampen this effect.

While it is often assumed that voids in a two-phase flow all move at the same, average

gas phase velocity, an actual gas-phase velocity distribution may lead to two opposing

effects. The contribution of faster bubbles or voids (moving more quickly past the probe)

will be underrepresented in the total time, τgas, the probe spends in the gas phase.

Appendix D: Thermal Anemometry in Two Phase Flows 249 However, it can likewise be expected that a disproportionately high number of faster

voids will come in contact with the probe over a finite sampling time. This effect may be

of particular concern in buoyancy-driven flows, where terminal bubble velocity is

proportional to the square of the bubble diameter (Toral, 1981). Larger bubbles will move

more quickly past the probe, leading to an underestimation of the local void fraction, but

at the same time more large bubbles pass the probe, tending toward an overestimation of

the local void fraction.

In order to overcome this potential source of error, Serizawa (1974) as reported in (Toral,

1981) recommends a sampling time of 1 to 3 minutes, sufficiently long enough to provide

adequate statistical treatment of bubble velocity and size distribution effects for time-

averaged void fraction measurements. Further, Toral (1981) observed no significant

difference in void fractions measured at a given point for observation periods of 30 s and

5 minutes.

Most importantly, when the size of bubbles is on the order of the probe size or smaller,

bubble-probe interactions should be expected to significantly bias measurement results.

Some possibilities and their potential effects are:

• Bubbles are slowed by the probe (overestimation of void fraction)

• Liquid film left on probe (underestimation of void fraction)

• Vapor film left on probe (overestimation of void fraction)

• Deformation/delayed penetration (underestimation of void fraction)

• Bubble deflection (underestimation of void fraction)

The last two effects in this list are, by far, the most significant. Supporting this conjecture

is the fact that void fraction measurements almost always underpredict the true void

fraction, regardless of the type of probe used. These effects are common to all intrusive

probe techniques.

Appendix D: Thermal Anemometry in Two Phase Flows 250 D.3.2 Calibration Errors

As has been stated, this technique relies on the user’s ability to distinguish between liquid

and gas events in the anemometer output signal. Since this is a binary-type of

measurement, specific calibration of the probe is not necessary. All that is required is that

the system and probe be set up in a way that provides relatively clear identification of

gas-phase events among a backdrop of random liquid fluctuations (sufficient overheat

ratio, etc.). Specific signal analysis techniques and the “calibration” of phase separation

criteria will be discussed in the next section.

However, due to the large inaccuracies inherent to this type of measurement, it is often

suggested that this type of void fraction measurement be backed up with information

from some other source (photographic techniques, other types of probes used in parallel,

precise control of the amount of gas delivered to a system, etc.). Alternatively, the

measurement system could be calibrated against a known flow situation. However, due to

the inherently wide differences in two-phase flows, the known “standard” would need to

represent the flow system of interest as closely as possible. Cartellier and Achard (1991)

estimate that the accuracy of any standard calibration procedure for local void fraction

measurement would be “not less than” a few percent.

D.3.3 Observational Errors

There are many potential criteria for phase discrimination in an output signal. All the

basic signal processing schemes require the definition of some critical threshold,

attenuation factor, or the like. It is the experimenter’s ability (or inability) to identify this

critical parameter that determines the basic observational bias and precision errors.

One analysis technique (Resch et al., 1974) is based on the assumption that bubble arrival

and departure are associated with two successive signal extremes which are greater than

the adjacent fluctuations of the liquid phase. Thus, one defines a peak-to-peak fluctuation

Appendix D: Thermal Anemometry in Two Phase Flows 251 threshold, l, as illustrated in Fig. D.3. Fluctuations smaller than this threshold are

attributed to the liquid phase, while fluctuations greater than the threshold are attributed

to the passing of a phase boundary.

This critical threshold must be determined experimentally, based on an observation of the

effect of its value on the resulting void fraction. Thus, the data signal must be processed

multiple times to explore this effect. Clearly, if the threshold is made too small, all signal

fluctuations will be attributed to bubble passing events, and the resulting measured void

fraction will be 1. Alternately, if the threshold used is too large, all fluctuations in the

signal will be counted as random fluctuations in the liquid phase, and the measured void

fraction will be 0. Hopefully there is some identifiably appropriate value between these

two extremes.

Fluctuation Threshold, l=

ττττ

AIR WATER AIR WATER AIR

Fluctuation Threshold, l=

ττττ

AIR WATER AIR WATER AIR Figure D.3: Illustration of fluctuation threshold for an air/water two-phase flow (Resch et

al., 1974).


1.0

0.5

0

Void

Fra

ctio

n, αα αα

Fluctuation Threshold

lmin lcr lmax

1 2

1.0

0.5

0

Void

Fra

ctio

n, αα αα

Fluctuation Threshold

lmin lcr lmax

1 2

Figure D.4: Fluctuation threshold determination (Resch et al., 1974).

Figure D.4 shows idealized void fraction vs. fluctuation threshold behavior. One can

identify two critical thresholds, one (1) corresponding to the size of the largest liquid

phase fluctuation, and a second (2) corresponding to the size of the smallest bubble-

generated fluctuation. If the difference between these critical thresholds is sufficiently

large (without overlap), a plateau should appear in the middle of the void fraction vs.

fluctuation threshold curve. This plateau represents the “true” measured void fraction.

When the difference between the largest liquid phase fluctuation and the smallest bubble-

induced fluctuation is small, the appropriate critical threshold may be identified by a

single point of inflection. If the largest liquid phase fluctuation is larger than the smallest

bubble-induced fluctuation (overlap), it may be very difficult to identify an appropriate

critical threshold. Further, the particular values of these critical thresholds can be

expected to vary with system conditions and must be evaluated on a case-by-case basis.

The user’s ability (or inability) to specify the critical fluctuation threshold determines the

signal analysis bias error/uncertainty.

D.4 UNCERTAINTY ANALYSIS


Resch et al. (1974) used a conical hot-film probe to explore bubbly two-phase flow

(air/water) in a hydraulic jump. Single point observations were made for a duration of

102.4 s. Anemometer output signals were digitized at a frequency of 2,500 cps and stored

on magnetic tape for analysis by a digital computer. Turbulence characteristics of the

liquid phase as well as two-phase flow parameters, such as void fraction, bubble size, and

waiting time, were investigated.

8

10

12

14

16

18

20

22

24

0.6 1.0 1.4 1.8 2.2 2.6 3.0

Fluctuation Threshold, l (V)

Void

Fra

ctio

n, αα αα

(%)

a. undeveloped inflow

Fr = 2.85

8

10

12

14

16

18

20

22

24

0.6 1.0 1.4 1.8 2.2 2.6 3.0


Void

Fra

ctio

n, αα αα

(%)

b. fully developed inflow

Fr = 2.85

20

22

24

26

28

30

32

34

36

0.6 1.0 1.4 1.8 2.2 2.6 3.0


Void

Fra

ctio

n, αα αα

(%)

c. undeveloped inflow

Fr = 6.00

4

5

6

7

8

9

10

11

12

0.6 1.0 1.4 1.8 2.2 2.6 3.0


Void

Fra

ctio

n, αα αα

(%)

d. fully developed inflow

Fr = 6.00

Figure D.5: Identification of critical fluctuation threshold, lcr2 (Resch et al., 1974).

D.4.1 Zeroth Order Bias and Precision Errors

Appendix D: Thermal Anemometry in Two Phase Flows 254 Figure D.5 shows actual void fraction vs. critical fluctuation threshold data obtained by

Resch et al. (1974) for four different flow conditions. It can be seen from these graphs

that the separation between liquid and phase boundary fluctuations is rarely as distinct as

the idealized case illustrated in Fig. D.4 might suggest. The appropriate critical threshold

may often be identified by a single point of inflection, the smallest peak-to-peak

fluctuation associated with air bubbles (lcr2), rather than a well-defined plateau. While the

critical threshold appears to be independent of inlet flow conditions, it does vary with the

characteristic Froude number. A numerical summary of the data presented in Fig. D.5 is

given in Table D.2.

Table D.2: Variation of void fraction with fluctuation threshold. Bold values correspond

to the critical fluctuation thresholds identified by Resch et al. (1974).

l (V) ααααa ααααb ααααc ααααd

0.8 0.1941.0 0.221 0.149 0.1021.2 0.166 0.133 0.0781.4 0.131 0.125 0.333 0.0711.6 0.118 0.118 0.300 0.0641.8 0.114 0.116 0.283 0.0622.0 0.100 0.109 0.268 0.0612.2 0.093 0.104 0.258 0.0612.4 0.086 0.243 0.0572.6 0.081 0.234 0.0572.8 0.221

From these tabulated values, we can estimate the uncertainty associated with void

fractions determined in this manner. Ideally, void fractions would be evaluated for a large

number of threshold values, particularly in the vicinity of the identified critical

thresholds. A more exact estimation of the uncertainty could then take place via a closer

examination of the void fraction trends in the data. However, since the authors only

report void fractions for the critical thresholds shown (0.2 V increments), the uncertainty

in each void fraction measurement will be associated with a fluctuation threshold range

Appendix D: Thermal Anemometry in Two Phase Flows 255 of ±0.2 V. As the difference between the measured void fractions at lcr2 and lcr2 + 0.2 V is

always larger than the difference between the measured void fractions at lcr2 and lcr2 –

0.2 V, the former is used as the void fraction uncertainty. Thus, the uncertainties in the

measured void fractions associated with this signal analysis/phase separation technique

are:

• case a: αa = 0.11 ± 0.01

• case b: αb = 0.116 ± 0.006

• case c: αc = 0.26 ± 0.02

• case d: αd = 0.061 ± 0.004

Since the measurement simply considers voltage differences in a continuous signal from

a single anemometer/voltmeter, bias errors associated with voltmeter accuracy are

negated. Further, the determination of critical threshold uncertainty includes all effects of

the resolution of the digitization process as well as other instrumentation effects.

Therefore, the uncertainties presented above include all zeroth order bias and precision

errors.

D.4.2 First Order Precision Errors

A conceptual idea of the first order precision errors associated with this technique is

difficult to develop. On one hand, an analyzed signal from a finite sampling time and the

resulting time-averaged void fraction can be thought of as a composite of a large number

of voltage signals. In this case, the first order precision uncertainty of the measured void

fraction would be included in the critical threshold uncertainty discussed in the previous

section. Unfortunately, the measurement does not consist of a simple average of actual

voltage values. Instead, void fraction determination relies on a binary type of view of the

signal, where portions of the signal are attributed to gas or liquid, and the void fraction is

the sum of the duration of “gas” events divided by the total sampling time. The duration

of these events is expected to vary in relation to the distribution of void size and velocity

particular to the flow system.


On the other hand, the void fraction obtained from the reduction of a finite-length time-

averaged signal could be viewed as a single data point. A standard deviation and

associated precision uncertainty could be obtained from a number of void fraction values

and combined with the bias uncertainties resulting from the determination of the critical

threshold. However, this approach seems to ignore the wealth of signal data behind each

single void fraction value, and the relation between void fractions obtained from the

analysis of a single long signal or a number of shorter signals analyzed independently is

unclear. It would be very interesting to analyze the same signal in both these ways to

explore the effects of the data reduction method

In the case of looking at a variety of void fraction results from a number of independent

signals, it is highly possible that differences in measured void fractions could be mainly

due to the experimenter’s ability to set the system conditions of the experiment, rather

than a conglomeration of a large number of random effects, none of which dominates.

This view suggests some type of pooling of the uncertainties associated with each void

fraction. Unfortunately, since there is no clear way to associate standard deviations with

the measured void fractions, this type of pooling is beyond the scope of the course as well

as that of this paper (if it is even at all possible). Therefore, for the purposes of this paper,

the view will be taken that the critical threshold determination uncertainties of the

previous section also include first order precision uncertainties.

Appendix D: Thermal Anemometry in Two Phase Flows 257 D.4.3 First Order Bias Corrections

Clearly, the most important and significant sources of error and uncertainty fall in the

first order bias category. The implications of these phenomena are now discussed in the

context of the Resch et al. (1974) study. The authors observed a trend of increasing local

void fractions and extent of the bubbly-flow region with increasing Froude number. This

matched their expectation based on the anticipation of an associated increase in the air-

entrainment capacity of the hydraulic jump. Unfortunately, the authors did not mention

calibrating their system with a known standard or performing parallel void fraction

verification measurements using an alternative technique.

D.4.3.1 Propagation of Errors in Void Fraction Equation

Strictly speaking, the actual quantity determined by the signal analysis technique is the

total time the probe spends surrounded by gas, τgas, the sum of the duration of all

identified gas events. The errors associated with this sum have already been addressed in

the uncertainty associated with the identification of the critical fluctuation threshold.

However, in order to obtain void fractions, this sum is divided by the total sampling time,

τtotal.

total

gas,, τ

τα =zyx (D.3)

A rigorous treatment of first order bias errors must include the addition of the uncertainty

in the total sampling time and the propagation of this uncertainty in the reduction

equation above.

The uncertainty in the total sampling time is related to the resolution of the digitized

signal. However, it is clear that the resolution errors (1/2 LSD, maybe 1 LSD considering

start and end times) related to the 2,500 cps digitization frequency are extremely small

compared to the overall sampling time of 102.4 s. Further, it should be understood that

Appendix D: Thermal Anemometry in Two Phase Flows 258 the determination of the time of duration of each individual bubble event also suffers

from this same time resolution uncertainty, and the uncertainty associated with τgas will

overwhelmingly dominate an error propagation relation based on the void fraction

reduction equation above. Thus, any uncertainty in the total sampling time will contribute

in a completely insignificant way to the uncertainty in calculated void fraction.

D.4.3.2 Void Velocity Distribution Effect

As stated earlier, Serizawa (1974) recommends a observation period of 1-3 minutes to

eliminate potential errors resulting from the statistical distribution of bubble size and

velocity. The sampling time of 102.4 s employed in the current study is expected to

eliminate uncertainties associated with this effect.

D.4.3.3 Liquid and/or Vapor Film Left on Probe

Toral (1981) developed the following equation for approximating the residence time of a

liquid film left on the surface of a hot probe after passing through the water/air phase

boundary.

( )satL

LGL2

fLevap

4.221

Tkhd

∆=

ρσυµτ (D.4)

This equation is based on a time-dependent heat balance of the film evaporation process.

The grouping under the squared power represents the thickness of the liquid film as

approximated by Toral (1981) for cylindrical probes. Other expressions or estimations of

the liquid film thickness could be used in its place for other probe configurations. This

time of film evaporation can then be compared with the duration of a single bubble event

to approximate the extent of this effect in the overall void fraction calculation. Typical

evaporation times calculated from the equation above are on the order of microseconds.

Compared to the time a typical bubble might spend on the probe (a 1 mm bubble

traveling at 1 m/s would spend 1 ms), this effect is often quite insignificant.


Further consideration of these effects is even less concerning with a reexamination of

Fig. D.1. As was mentioned in the discussion of this illustration, the time associated with

a bubble event should be taken as the interval between points 1 and 2 as marked on

Fig. D.1. This time interval covers the initial signal drop which includes any liquid film

evaporation but does not cover the probe re-wet process from point 2 to point 3 which

would be affected by vapor left on the probe. Thus, it is concluded that proper application

of the peak-to-peak threshold signal separation technique will eliminate these errors.

D.4.3.4 Bubble Deformation and Deflection

According to Wang et al. (1987), Wang et al. (1984) developed a void fraction correction

method based on γ-ray densitometer readings for a conical hot-film probe in vertical up-

flows. Their correction was based on the parameter grouping We × Db/Dp, where We is

the bubble Weber number and Db and Dp are the diameters of the bubble and probe,

respectively. While such a correction seems very promising, the authors note that this

correction method would need for be recalibrated for different flow situations

(specifically down flows). The study being analyzed at the present time (Resch et al.,

1974) involved horizontal, forced two-phase flow. So, at best, the Wang et al. (1984)

corrections to take into account bubble deformation and deflection might provide a

starting point for the development of a void fraction correction or error estimation

relation, but they would not be directly applicable.

Toral (1981) tested the accuracy of hot-wire void fraction measurements in ethanol/air

two-phase flows. Bubbles were injected at the bottom of a long vertical tube and allowed

to rise due to buoyancy forces. The flow section pressure drop was measured and related

to the volumetric void fraction. These measurements suggest that the hot-wire technique

employed underestimated void fractions by a maximum deviation of 17% in the bubbly

flow regime. The author attributed this discrepancy primarily to bubble deformation and

deflection effects.


Void fraction errors and uncertainty related to bubble deflection and deformation effects

in the Resch et al. (1974) can be expected to be somewhat less significant than that

observed in the Toral (1981) and similar studies. Bubble diameters encountered by Resch

et al. (1974) were typically 5-10mm (large). Further, in this forced-flow situation, these

bubbles are carried by the liquid flow and, therefore, should exhibit less of a probability

of being deflected by the probe. Recognizing that this effect has a solely negative effect

on void fraction measurements, measured values will be reduced by 8%, and an

uncertainty of ± 8% will be assumed to account for bubble deformation and deflection

effects in the Resch et al. (1974) measurements. This constitutes the first order bias error

estimate.

D.4.4 Total First Order Uncertainty Estimates

Thus, the root-sum-squares combination of the zeroth and first order uncertainties

evaluated in the preceding sections yields the following total uncertainties for void

fractions measured by Resch et al. (1974):

αa = 0.11 ± 0.02

αb = 0.12 ± 0.02

αc = 0.26 ± 0.04

αd = 0.06 ± 0.01

These uncertainties range 16-20%.

Appendix D: Thermal Anemometry in Two Phase Flows 261 D.5 SUMMARY AND CONCLUDING REMARKS

Thermal anemometry is a promising technique for exploring the structure of two-phase

flows, particularly when dealing with dielectric liquids with which resistance probes will

not work. While a wide variety of two-phase thermal anemometry studies have been

published over the past few decades, very few address the sources of measurement error

inherent to this very intrusive technique.

Bubble deflection and deformation by the probe are the most significant and most

difficult to quantify sources of error. The large magnitude of these errors suggests that

void fraction measurements based on thermal anemometry should be tested against

results from a separate, less intrusive technique, providing an overall calibration of the

technique. Future studies of this measurement technique need to address the complex

effects of bubble/probe interaction, focusing on a correction to take into account bubble

deformation and deflection.

262

APPENDIX

E

DATA ACQUISITION SOFTWARE

The C program written to run the data acquisition system is listed in Section E.1 below.

The code was compiled with the following command that invokes the GNU C compiler,

gcc:

gcc -o daq daq.c -lm -lcurses /usr/local/lib/gpib/cib.o

Here the name of source file is “daq.c”, and “daq” is the resulting executable. The

National Instruments C language interface file “cib.o” contains the necessary IEEE-

488 GPIB drivers, while the Curses terminal control library for Linux provides text-based

user interface commands. The following keyboard commands (defined in the data

acquisition program using the Curses library) facilitate real-time control over the

experimental process:

M manual symmetric power control

A automatic symmetric power control

C cut power to both heaters

1 cut power to heater 1

2 cut power to heater 2

Appendix E: Data Acquisition Software 263 s switch output file comment to denote steady state

t switch output file comment to denote transient

Q terminate the program

Most of these commands deal with control of the heater power supplies. The voltage

output of the main heater was always manually controlled to insure steady-state

conditions were achieved before advancing to the next power setting. Keyboard

commands could be used to quickly cut power as well as switch between manual and

automatic operation of the secondary heater during symmetric heating experiments. In

addition, pressing the “s” and “t” keys during data acquisition would switch between

writing “s” and “t” to the last column of the output file to mark steady-state and

transient operation, respectively. This feature simply allowed for more efficient data

analysis and reduction.

The data acquisition program starts by getting the current local time from the system and

creating the output data file. The name of the output data file is generated automatically

based on the current date and time. The filename format is “chyydddhhmmss.txt”.

The first two characters are set in the program to denote the type of experiments being

performed (“ch” = channel, “pb” = pool boiling). The second two characters specify the

current year. The next three characters represent the day of the year (1-366). The next six

characters provide the hour (1-24), minute, and second. For example, the channel

experiment initiated at 3:28PM on Sunday, June 1, 2003 has an associated output file

named “ch03152152847.txt”. The “.txt” filename extension denotes the plain

text format of the file itself. This naming convention not only provides a unique name for

each file, it also facilitates quick chronological sorting of data files.

After creating the output file, the program launches the Gnuplot plotting program to

provide real-time graphical displays of the output file. Examples of these graphs are

shown in Figs. 3.11 & 3.12. Then the program begins the main program loop. The current

time is obtained before scanning through the thermocouple readings and converting raw

Appendix E: Data Acquisition Software 264 thermocouple voltages to temperatures. Raw thermocouple voltages are added to the ice

bath reference voltage, multiplied by 1000 to convert volts to millivolts, and then

converted to temperatures via a 6th order polynomial, fit to a high degree of accuracy to

thermocouple manufacturer-supplied conversion tables. Conversion polynomial

coefficients are specified in the “a[]” array variable when declared at the beginning of

the program.

After thermocouple temperatures are calculated, the power supply and shunt resistor

voltages are read, and the heater power calculations are performed in accordance with

Eqs. (3.1) & (3.2). All raw measurements and derived quantities are then written to the

output file. The heater temperatures are checked to make sure they have not exceeded

100°C. If they have, heater power is cut automatically, but data acquisition continues.

Finally, the graphical displays are updated, and the program checks to see if the quit

command has been issued before returning to the beginning of the main program loop.

E.1 DATA ACQUISITION PROGRAM LISTING /*------------------------------------------------------------------Channel Boiling DAQ

variable descriptions at end------------------------------------------------------------------*/

#include <sys/timeb.h>#include <ugpib.h>#include <stdio.h>#include <stdlib.h>#include <ctype.h>#include <time.h>#include <math.h>#include <string.h>#include <unistd.h>#include <fcntl.h>

#define OFF 0#define ON 1#define True 1#define False 1

Appendix E: Data Acquisition Software 265

#define round(x) ((x)>=0?ceil(x):floor(x))

int ac1=0;int pwr,pw2,dm2,scanner,side;void set_blocking( int fd, int on );int initgpib(int *pwr, int *pw2, int *dm2, int *scanner, int *side);int cleargpib(int *pwr, int *pw2, int *dm2, int *scanner, int *side);

main()int loop,n,n2;int nice=1; /* ice bath TC channel */int nstart=1;int nend=13;int cstart=2;int cend=4;int ps;

int sec,tzero,hour,hzero;

double vtarget,prevr,prev2;double shslope=1.00505,shinter=0.0000395;double psslope=1.019106,psinter=-0.022219;double s2slope=0.999579,s2inter=0.0000246;double p2slope=1.018680,p2inter=-0.0163;double Vshm, V1m;double Vs2m, V2m;double rawv[35],temp[35];double Vpwr,Ipwr,I1,V1,P1,R1;double Vpw2,Ipw2,I2,V2,P2,R2;double Vsh,Rsh1=0.010;double Vs2,Rsh2=0.025;double Tfilm=100;double adj; /* adjusted TC voltage */double Pdimp,Idimp,Rdimp;double PPBGA,IPBGA,RPBGA;double POmold,IOmold,ROmold;double a[] = 0.000000000000000,2.620208113593E+1,

-1.121178905539E+0,2.332784592913E-1,-4.817225742252E-2,5.488174377845E-3,-2.468729712803E-4 ;

char ti,it,stead='t';char buffer[256],datafile[20];char wr_buffer[50],rd_buffer[63],rd_pwr_buff[30];

FILE *output,*fp,*f2;

time_t curtime;struct tm *loctime;

/* START PROGRAM */initgpib(&pwr, &pw2, &dm2, &scanner, &side); /*initialize instruments*/

Appendix E: Data Acquisition Software 266 set_blocking( 0, OFF ); /*preventsgetcharfrompausingprogramexecution*/

/* Get Start Time */curtime = time(NULL); /* Get start time. */loctime = localtime(&curtime); /*Convert to local time representation*/printf("%s", asctime(loctime)); /* Print start time on screen. */strftime (buffer, 256, "%y%j%H%M%S", loctime); /* Format start time. */sprintf(datafile, "ch%s.txt", buffer); /* Create data filename. *//*Print data filename to screen: year/dayofyear/hours/minutes/seconds*/printf("Data File = %s\n", datafile);/* start counting seconds */strftime (buffer, 256, "%H\n", loctime);hzero = atoi(buffer); /* hour of start time */sec = hzero*60*60;strftime (buffer, 256, "%M\n", loctime);sec = sec + atoi(buffer)*60;strftime (buffer, 256, "%S\n", loctime);sec = sec + atoi(buffer); /* second of the day */tzero = sec;

/* output file */

output = fopen(datafile, "w");fprintf(output, "#filename = %s\n", datafile);fprintf(output, "#start time = %s", asctime(loctime));fprintf(output,"# time");for( n=nstart ; n<=nend ; n++ )fprintf(output," %12d",n);fprintf(output," 20");for( n=nstart ; n<=nend ; n++ )fprintf(output," %12d",n);fprintf(output," 20");fprintf(output," Ipwr Vpwr");fprintf(output," Ipw2 Vpw2");fprintf(output," Vsh V1");fprintf(output," Vs2 V2");fprintf(output," Vshm V1m");fprintf(output," Vs2m V2m");fprintf(output," I1 P1 R1");fprintf(output," I2 P2 R2");fprintf(output,"\n");fclose(output);

/*Open Gnuplot*/

fp = popen("gnuplot -noraise -geometry 600x450+536+0","w");fprintf(fp,"set key outside\n");fprintf(fp,"set yrange [0:120]\n");fprintf(fp,"set title \"%s\"\n",datafile);fprintf(fp,"set xlabel \"Time [s]\"\n");

Appendix E: Data Acquisition Software 267 fprintf(fp,"set ylabel \"Temperature [C]\"\n");

f2 = popen("gnuplot -noraise -geometry 490x450+32+0","w");fprintf(f2,"set key outside\n");fprintf(f2,"set yrange [0:80]\n");fprintf(f2,"set title \"%s\"\n",datafile);fprintf(f2,"set xlabel \"Time [s]\"\n");fprintf(f2,"set ylabel \"Electricity\"\n");

ti = getchar();for (loop = 0; loop > -1; loop++)

fflush(stdin);

/*** Mark Time ***/

curtime = time (NULL); /* Get the current time. */loctime = localtime (&curtime); /* Convert it to local timerepresentation. */strftime (buffer, 256, "%H\n", loctime);hour = atoi(buffer);if(hour < hzero) hour = hour + 24; /* for runs past midnight :) */sec = hour*60*60;strftime (buffer, 256, "%M\n", loctime);sec = sec + atoi(buffer)*60;strftime (buffer, 256, "%S\n", loctime);sec = sec + atoi(buffer);

/***Temperature Loop***/

for( n=nstart ; n<=nend ; n++ )

sprintf(wr_buffer, ":ROUTe:CLOSE (@%d )", n);ibwrt(side,wr_buffer,strlen(wr_buffer));sprintf(wr_buffer,":read?");ibwrt(side,wr_buffer,strlen(wr_buffer));ibrd(side,rd_buffer,63);rd_buffer[ibcnt-1]='\0';

rawv[n]=atof(rd_buffer);

/* convert TC voltages to temperatures */adj = (rawv[n]+rawv[nice])*1.0e03;temp[n] =a[0]+adj*(a[1]+adj*(a[2]+adj*(a[3]+adj*(a[4]+adj*(a[5]+adj*a[6])))));if (temp[n] < 0.0) temp[n] = 0.0;if (temp[n] > 999.9) temp[n] = 999.9;

/*** check differential TC in isothermal block ***/n = 20;sprintf(wr_buffer, ":ROUTe:CLOSE (@%d )", n);

Appendix E: Data Acquisition Software 268 ibwrt(side,wr_buffer,strlen(wr_buffer));sprintf(wr_buffer,":read?");ibwrt(side,wr_buffer,strlen(wr_buffer));ibrd(side,rd_buffer,63);rd_buffer[ibcnt-1]='\0';rawv[n]=atof(rd_buffer);adj = fabs((rawv[n])*1.0e03);temp[n] =a[0]+adj*(a[1]+adj*(a[2]+adj*(a[3]+adj*(a[4]+adj*(a[5]+adj*a[6])))));

/* Read Voltage and Current from hp 6643A and 6032A power supplies */

ibwrt(pw2,"measure:voltage?",16);ibrd(pw2,rd_pwr_buff,30);rd_pwr_buff[ibcnt-1]='\0';Vpw2=atof(rd_pwr_buff);

ibwrt(pw2,"measure:current?",16);ibrd(pw2,rd_pwr_buff,30);rd_pwr_buff[ibcnt-1]='\0';Ipw2=atof(rd_pwr_buff);

/*ibwrt(pw2,"VOUT?",5);ibrd(pw2,rd_pwr_buff,20);rd_pwr_buff[ibcnt-2]='\0';Vpw2=atof(strchr(rd_pwr_buff,'T')+1);

ibwrt(pw2,"IOUT?",5);ibrd(pw2,rd_pwr_buff,20);rd_pwr_buff[ibcnt-2]='\0';Ipw2=atof(strchr(rd_pwr_buff,'T')+1);*/

ibwrt(pwr,"VOUT?",5);ibrd(pwr,rd_pwr_buff,20);rd_pwr_buff[ibcnt-2]='\0';Vpwr=atof(strchr(rd_pwr_buff,'T')+1);

ibwrt(pwr,"IOUT?",5);ibrd(pwr,rd_pwr_buff,20);rd_pwr_buff[ibcnt-2]='\0';Ipwr=atof(strchr(rd_pwr_buff,'T')+1);

/*** Power Measurements - Keithley 196 System DMM ***/n=7;sprintf(wr_buffer,"C%dXB%dX",n,n);ibwrt(scanner,wr_buffer,strlen(wr_buffer));sprintf(wr_buffer,":read?");ibwrt(dm2,"F0XR0X",6);ibrd(dm2,rd_buffer,63);rd_buffer[ibcnt-2]='\0';Vs2=fabs(atof(memmove(rd_buffer,&rd_buffer[4],13)));sprintf(wr_buffer,"N%dXB%dX",n,n);ibwrt(scanner,wr_buffer,strlen(wr_buffer));

Appendix E: Data Acquisition Software 269 Vs2m = s2slope*Vs2 + s2inter;

n=8;sprintf(wr_buffer,"C%dXB%dX",n,n);ibwrt(scanner,wr_buffer,strlen(wr_buffer));sprintf(wr_buffer,":read?");ibwrt(dm2,"F0XR0X",6);ibrd(dm2,rd_buffer,63);rd_buffer[ibcnt-2]='\0';V2=atof(memmove(rd_buffer,&rd_buffer[4],13));sprintf(wr_buffer,"N%dXB%dX",n,n);ibwrt(scanner,wr_buffer,strlen(wr_buffer));V2m = p2slope*V2 + p2inter;

I2 = Vs2m/Rsh2;P2 = I2*V2m;R2 = V2m/I2;if (Vpw2 < 0.001) R2 = 0.0;

n=9;sprintf(wr_buffer,"C%dXB%dX",n,n);ibwrt(scanner,wr_buffer,strlen(wr_buffer));sprintf(wr_buffer,":read?");ibwrt(dm2,"F0XR0X",6);ibrd(dm2,rd_buffer,63);rd_buffer[ibcnt-2]='\0';Vsh=fabs(atof(memmove(rd_buffer,&rd_buffer[4],13)));sprintf(wr_buffer,"N%dXB%dX",n,n);ibwrt(scanner,wr_buffer,strlen(wr_buffer));Vshm = shslope*Vsh + shinter;

n=10;sprintf(wr_buffer,"C%dXB%dX",n,n);ibwrt(scanner,wr_buffer,strlen(wr_buffer));sprintf(wr_buffer,":read?");ibwrt(dm2,"F0XR0X",6);ibrd(dm2,rd_buffer,63);rd_buffer[ibcnt-2]='\0';V1=atof(memmove(rd_buffer,&rd_buffer[4],13));sprintf(wr_buffer,"N%dXB%dX",n,n);ibwrt(scanner,wr_buffer,strlen(wr_buffer));V1m = psslope*V1 + psinter;

I1 = Vshm/Rsh1;P1 = I1*V1m;R1 = V1m/I1;if (Vpwr < 0.001) R1 = 0.0;

/* auto adjust c1 power */printf("%5.2f V ",(sqrt(((prev2+R2)/2)*(rint(P2/2.5)*2.5))*Vpw2/V2m));printf("%4.1f W ",rint(P2/2.5)*2.5);vtarget = sqrt(((prevr+R1)/2)*(rint(P2/2.5)*2.5))*Vpwr/V1m;sprintf(wr_buffer,"VSET %5.2f",vtarget);printf("%s ",wr_buffer);

Appendix E: Data Acquisition Software 270 if (ac1 == 1) ibwrt(pwr,wr_buffer,strlen(wr_buffer));printf("A");printf("\n");prevr = R1;prev2 = R2;

/*** OUTPUT ***/

output = fopen(datafile, "a");fprintf(output, "%-5d %5d",loop,sec-tzero);for( n=nstart ; n<=nend ; n++ )fprintf(output, " %12.5E",rawv[n]);fprintf(output, " %12.5E",rawv[20]);for( n=nstart ; n<=nend ; n++ )fprintf(output, " %12.5E",temp[n]);fprintf(output, " %12.5E",temp[20]);fprintf(output, " %12.5E %12.5E %12.5E %12.5E",Ipwr,Vpwr,Ipw2,Vpw2);fprintf(output, " %12.5E %12.5E %12.5E %12.5E",Vsh,V1,Vs2,V2);fprintf(output, " %12.5E %12.5E %12.5E %12.5E",Vshm,V1m,Vs2m,V2m);fprintf(output, " %12.5E %12.5E %12.5E",I1,P1,R1);fprintf(output, " %12.5E %12.5E %12.5E",I2,P2,R2);fprintf(output, " %c\n",stead);fclose(output);

printf(" # time");for( n=nstart+1 ; n<=nend ; n++ )printf("%5d ",n);printf(" 20");printf(" Ipwr Vpwr V1m I1");printf(" Ipw2 Vpw2 V2m I2");printf(" R1 R2");printf(" P1 P2");printf("\n");printf("%5d %5d",loop,sec-tzero);for( n=nstart+1 ; n<=nend ; n++ )printf(" %5.1f",temp[n]);printf(" %5.2f",temp[20]);printf(" %5.2f %5.2f",Ipwr,Vpwr);printf(" %5.2f %5.3f",V1m,I1);printf(" %5.2f %5.2f",Ipw2,Vpw2);printf(" %5.2f %5.3f",V2m,I2);printf(" %5.2f %5.2f",R1,R2);printf(" %5.2f %5.2f",P1,P2);printf(" %c\n",stead);


/*** Check Temperatures for Film Boiling ***/if (temp[4] > Tfilm) printf("Chip Temperature 4 Limit, Power Cut!!!\n");ibclr(pwr); ibwrt(pwr,"ISET 3.33",9); ac1 = 0;

if (temp[3] > Tfilm) printf("Chip Temperature 3 Limit, Power Cut!!!\n");ibclr(pw2); ibwrt(pw2,"*rst",4); ibwrt(pw2,"output 1",8);ac1 = 0;

if (temp[13] > Tfilm) if (temp[13] > Tfilm) if (temp[13] > Tfilm)printf("Chip 2 Temperature Limit, Power Cut!!!\n");ibclr(pw2); ibwrt(pw2,"*rst",4); ibwrt(pw2,"output 1",8);ibwrt(pw2,"ISET 3.33",9); ac1 = 0;

/* plot datafile */ps = 2+nend+1+1+1;if(loop>=2)if(loop==2)fprintf(fp,"plot ");fprintf(fp,"\"%s\" using 2:%d title\"02 Chip 1\" with points,

",datafile,ps);fprintf(fp,"\"%s\" using 2:%d title\"03 Chip 2\" with points,

",datafile,ps+1);fprintf(fp,"\"%s\" using 2:%d title\"04 Chip 3\" with points,

",datafile,ps+2);fprintf(fp,"\"%s\" using 2:%d title\"05 Bulk Far\" with points,

",datafile,ps+3);fprintf(fp,"\"%s\" using 2:%d title\"06 Bulk Above\" with points,

",datafile,ps+4);fprintf(fp,"\"%s\" using 2:%d title\"07 Bulk Below\" with points,

",datafile,ps+5);fprintf(fp,"\"%s\" using 2:%d title\"08 Bulk Near\" with points,

",datafile,ps+6);fprintf(fp,"\"%s\" using 2:%d title\"09 H2O IN\" with points,

",datafile,ps+7);fprintf(fp,"\"%s\" using 2:%d title\"10 H2O OUT\" with points,

",datafile,ps+8);fprintf(fp,"\"%s\" using 2:%d title\"11 Shunt\" with points,

",datafile,ps+9);fprintf(fp,"\"%s\" using 2:%d title\"12 Ambient\" with points,

",datafile,ps+10);fprintf(fp,"\"%s\" using 2:%d title\"13 Chip2\" with points

",datafile,ps+11);fprintf(fp,"\n");

ps = 2+nend+nend+2+1;fprintf(f2,"plot ");

Appendix E: Data Acquisition Software 272 fprintf(f2,"\"%s\" using 2:%d title\"Ipwr\" with points,

",datafile,ps);fprintf(f2,"\"%s\" using 2:%d title\"Vpwr\" with points,

",datafile,ps+1);fprintf(f2,"\"%s\" using 2:%d title\"Ipw2\" with points,

",datafile,ps+2);fprintf(f2,"\"%s\" using 2:%d title\"Vpw2\" with points,

",datafile,ps+3);fprintf(f2,"\"%s\" using 2:%d title\"V1m\" with points,

",datafile,ps+9);fprintf(f2,"\"%s\" using 2:%d title\"V2m\" with points,

",datafile,ps+11);fprintf(f2,"\"%s\" using 2:%d title\"I1\" with points,

",datafile,ps+12);fprintf(f2,"\"%s\" using 2:%d title\"P1\" with points,

",datafile,ps+13);fprintf(f2,"\"%s\" using 2:%d title\"R1\" with points,

",datafile,ps+14);fprintf(f2,"\"%s\" using 2:%d title\"I2\" with points,

",datafile,ps+15);fprintf(f2,"\"%s\" using 2:%d title\"P2\" with points,

",datafile,ps+16);fprintf(f2,"\"%s\" using 2:%d title\"R2\" with points

",datafile,ps+17);fprintf(f2,"\n");

elsefprintf(fp,"replot\n");fprintf(f2,"replot\n");

fflush(fp);fflush(f2);

/* CHECK FOR QUIT COMMAND */

/*it = getchar();while ( it != ti )if (it == 'Q') loop = -2;it = getchar();

*/

switch(getchar()) case 'Q':

loop = -2;case 'M': /* manual c1 power control */

ac1 = 0;break;

case 'A': /* automatic c1 follows c2 power */ac1 = 1;break;


case 'C': /* cut power to both chips */ac1 = 0;break;

case '1': /* cut power to chip 1 */ac1 = 0;sprintf(wr_buffer,"VSET 0.00");ibwrt(pwr,wr_buffer,strlen(wr_buffer));break;

case '2': /* cut power to chip 2 */ac1 = 0;sprintf(wr_buffer,"VSET 0.00");ibwrt(pw2,wr_buffer,strlen(wr_buffer));break;

case 's': /* mark steady state */stead = 's';break;

case 't': /* mark transient */stead = 't';break;

/*** End of Program ***/fflush(stdin);cleargpib(&pwr, &pw2, &dm2, &scanner, &side);

curtime = time (NULL); /* Get the program end time. */loctime = localtime (&curtime); /* Convert it to local timerepresentation. */printf("End Time = %s", asctime(loctime)); /*Print end time on screen*/printf("Data File = %s\n", datafile); /* Print filenames */

fclose(fp);fclose(f2);

return 0;

/*************************** SUBROUTINES ***************************/

/* sets hardware to listen mode on IEEE 488 */int initgpib(int *pwr, int *pw2, int *dm2, int *scanner, int *side)

*pwr=ibfind("dev4"); /* hp 6032A power supply */ibclr(*pwr);ibwrt(*pwr,"ISET 3.33",9); /* set current max to 2/3 shunt rating */

*pw2=ibfind("dev5"); /* hp 6643A power supply */ibclr(*pw2);ibwrt(*pw2,"*rst",4);ibwrt(*pw2,"output 1",8);


*dm2=ibfind("dev7"); /* keithley 196 system DMM */ibclr(*dm2);

*scanner=ibfind("dev8"); /* keithley 705 scanner */ibclr(*scanner);

*side=ibfind("dev2"); /* keithley 2000 DMM */ibclr(*side);ibwrt(*side,":conf:volt:dc",13);ibwrt(*side,":syst:kcl off",13);

return(0);

/* clears devices on IEEE 488 */int cleargpib(int *pwr, int *pw2, int *dm2, int *scanner, int *side)

ibclr(*pwr);ibclr(*pw2);ibwrt(*pw2,"*rst",4);ibclr(*dm2);ibclr(*scanner);ibclr(*side);return(0);

/* prevents getchar from blocking program execution */void set_blocking( int fd, int on )

static int blockf, nonblockf;static int first = True;int flags;

if ( first ) first = False;if (( flags = fcntl( fd, F_GETFL, 0 ) ) == -1 )

printf( "fcntl(F_GETFL) failed\n");blockf = flags & ~O_NDELAY;nonblockf = flags | O_NDELAY;

if ( on )

if ( fcntl( fd, F_SETFL, blockf ) == -1 ) printf( "fcntl(F_SETFL) failed\n");

else

if ( fcntl( fd, F_SETFL, nonblockf ) == -1 ) printf( "fcntl(F_SETFL) failed\n");

Appendix E: Data Acquisition Software 275 /*------------------------------------------------------------------*//* *//* Program Variables *//* *//* n = channel number *//* it = character variable for program loop control *//* ti = character variable for program loop control *//* loop = main program loop increment *//* *//* curtime = current time (unformatted) *//* buffer[] = character array for date/time codes *//* *//* filename[] = char array for data file name *//* output = output file pointer *//* *//* scanner = reference to the Keithley 706 scanner *//* scan2 = reference to the Keithley 705 scanner *//* wr_buffer[x] = buffer "write" character string *//* rd_buffer[x] = buffer "read" character string *//* *//* rawv[x] = measured raw voltage array from isothermal block *//* a[] = coefs for T type thermocouple VtoT conversion *//* temp[x] = calculated temperature array *//* *//* Defined Parameters *//* *//* OFF = 0 *//* ON = 1 *//* True = 1 *//* False = 1 *//* *//* Subroutines *//* *//* set_blocking = prevents getchar from pausing program *//* initgpib = sets hardware to listen mode on IEEE 488 *//* cleargpib = clears devices on IEEE 488 *//* *//*------------------------------------------------------------------*/

276

APPENDIX

F

CFD SIMULATION OF TWO PHASE CHANNEL FLOW

As discussed in Section 5.4.1, computational fluid dynamic (CFD) techniques show

increasing promise for the simulation of two phase flow and heat transfer in confined

geometries. The text of this chapter discusses a process created in the context of the

current research to execute multiphase simulations of buoyancy-driven saturated boiling

in narrow vertical channels using the commercially-available Fluent software. The

volume of fluid (VOF) method employed tracks the phase interface and volume fraction

of each fluid in each cell of a fixed Eulerian mesh (Harlow and Welch, 1965) (Hirt and

Nichols, 1981). Suitable applications include the simulation of large bubbles in a liquid

space where the bubbles do not merely follow the flow of the liquid phase but have a

significant effect on it (Fluent, 2005). Such simulations are necessarily transient by

nature.

While high degrees of accuracy are unreasonable to expect at this time, these numerical

simulations provide a vehicle for quantifying the order of magnitude of various effects

and exploring relevant trends. The dependence of channel mass flux on vapor generation

as well as thin film evaporation, transient conduction, and convective enhancement

Appendix F: CFD Simulation of Two Phase Channel Flow 277 mechanisms may all be investigated in this manner. If evidence can not be provided to

support the explanation of experimentally-observed confinement effects with these

potential mechanisms, it may be reasonably inferred that vapor and nucleation site

interaction effects, proposed in Section 5.4.3 and beyond the scope of these numerical

simulations, are significant and warrant further study.

Since the focus of this study is the effect of confinement on two phase flow and channel

heat transfer, and given that macroscale numerical modeling of the nucleate boiling

process on real surfaces is beyond the state-of-the-art, direct numerical simulation of

bubble nucleation and growth is not attempted. Bubble generation will instead be

approximated by a small vapor inlet located in the heated wall. A transient vapor mass

flow rate, based on the boiling parameters discussed in Section F.1, will approximate

bubble growth. Details of the implementation of the CFD model and solution settings in

the Fluent software are provided in Section F.2. Results generated for 2-D computational

domains are discussed in Section F.3, while issues related to the transition to three

dimensions and recommendations for future work are covered in Section F.4.

F.1 SIMULATION PARAMETERS

Key nucleate boiling parameters include bubble growth time (τg), bubble departure

diameter (Db), bubble frequency (f), and nucleation site density (N/A). Given this

information, an equivalent vapor mass flow inlet may be created in the CFD model. In

general, accurate prediction of these parameters is extremely difficult, and available

correlations are often limited in their applicability. Furthermore, statistical distributions

of nucleation site and bubble characteristics are rarely considered. However, for the

purposes of exploring the order of magnitude of two phase channel flow and heat transfer

effects, it is proposed that approximate bubble parameters will suffice. The following

calculations are based on the FC-72 fluid properties provided in Appendix A with

additional vapor properties (µg = 181 kPa·s, cp,g = 500 J/kgK, and kg = 0.02 W/mK) taken

Appendix F: CFD Simulation of Two Phase Channel Flow 278 from (Khalij et al., 2006). The boiling surface is assumed to be polished silicon, and an

asymmetrically heated channel will be simulated for simplicity.

F.1.1 Bubble Correlations

Tong et al. (1990) explored the suitability of a variety of bubble correlations for highly-

wetting liquids, including FC-72. They determined that the Cole and Rohsenow (1969)

departure diameter model fit available experimental data best:

( )gf

wb ρρg

ED−

= σ (F.1)

where

( )245aJ000465.0 ′⋅=E (F.2)

and

fgg

satfaJhTcp

ρρ

=′ (F.3)

with the saturation temperature is specified in absolute degrees. Tong et al. (1990)

modified the Cole and Rohsenow (1969) to include the wall temperature dependence of

departure diameter by evaluating the surface tension in Eq. (F.1) at the wall temperature.

Also following Tong et al. (1990), the bubble departure frequency is evaluated using the

Malenkov (1968) correlation:

+

=⋅

′′qhU

UDf

fggb11-1

bb

ρπ

(F.4)

where

( )

( ) ( )gfbgf

gfbb

22 ρρ

σρρ

ρρ+

++

−=

DgD

U (F.5)

Appendix F: CFD Simulation of Two Phase Channel Flow 279 Further, it is assumed that the bubble growth time, τg, is one-quarter of the overall bubble

departure period (1/f), with the waiting time, τw, equal to the remainder (Sateesh et al.,

2005) (Van Stralen et al., 1975).

Benjamin and Balakrishnan (1997) nucleation site density correlation is employed,

following Chai et al. (2000).

4.0

3sat63.1

fPr8.218Θ

∆=ϕ

TAN (F.6)

where the surface-liquid interaction parameter is given as

( )( )

f

h

kckc

p

p

ρρ

ϕ = (F.7)

and the dimensionless roughness parameter is

2

aa 4.05.45.14

+−=Θσσ

PRPR (F.8)

In Eq. (F.8), Ra is the centerline average surface roughness, assumed equal to 1 µm

following the discussion of Section 4.2, and P is the system pressure (101 kPa). This

nucleation site density correlation was validated using a large set of experimental data

from a variety of sources and covers the following parameter ranges:

1422mN 1059

mN 1013

C25∆C5µm 17.1µm 02.0

937.45Pr7.1

3-3-

a

<<

×<<×

°<<°<<<<<<

Θ.

σ

TRϕ

While values for the current system of interest are well within range for most of these

parameters, the Prandtl number for FC-72, 9.6, is high. In addition, its surface tension,

8.3×10-3 N/m is somewhat low. In fact, is it the low surface tension that also drives the

roughness parameter, Θ, out of range to a calculated value of 19. It is unclear exactly

Appendix F: CFD Simulation of Two Phase Channel Flow 280 what the impact of these deviations might be, though nucleation site density curves were

shown to flatten out at higher surface roughness (Benjamin and Balakrishnan, 1997).

Therefore, extrapolation outside the upper limit of Θ (and lower limit of σ) is expected to

be less problematic than extrapolation on the lower end. Thus, Eq. (F.8) is expected to

produce at least representative predictions of nucleation site density and will be used in

the absence of more accurate data/correlations.

F.1.2 Bubble Parameter Estimates

Total boiling heat flux is often assumed to consist of additive contributions from the

latent heat carried away from the wall by departing bubbles, the sensible heat washed

away from the wall in the bubble wake, and convection in the non-boiling inter-bubble

surface areas (Tong et al., 1990). Theoretical nucleate boiling correlations based on this

construct often include a parameter which represents the relative area of influence of

bubble nucleation sites. This area parameter not only facilitates calculation of convective

heat transfer in the inter-bubble spaces but also helps define the amount of liquid

captured in the bubble wake. The sensible heat transferred in the bubble wake is often

evaluated by an analysis of transient conduction from the wall to the fresh bulk liquid that

takes the place of the departing bubble and wake liquid during the bubble waiting period,

τw.

Taking the view that a variety of mechanisms may transfer different amounts of heat for a

given boiling surface temperature, confinement-driven boiling enhancement/degradation

is shown as a function of wall superheat in Fig. F.1, based on the asymmetric channel

boiling curves of Fig. 5.2. Here the difference between the channel heat flux and

unconfined pool boiling heat flux at a given wall superheat is expressed as a percentage

of the unconfined pool boiling heat flux at that superheat, i.e.

( ) ( )( )∞→∆′′

∞→∆′′−∆′′δ

δδ,

,,sat

satsat

TqTqTq (F.9)

Appendix F: CFD Simulation of Two Phase Channel Flow 281

-50%

0%

50%

100%

150%

200%

250%

300%

350%

400%

450%

500%

0 5 10 15 20 25 30

∆∆∆∆T sat (°C)

Hea

t Flu

x En

hanc

emen

t/Deg

rada

tion 0.3 mm spacing

0.7 mm spacing1.5 mm spacing1.6 mm spacing

Figure F.1: Ratio of difference between channel and unconfined heat fluxes to

unconfined heat flux at a given wall superheat, Eq. (F.9), for the asymmetric channel data

of Fig. 5.2.

It is clear from Fig. F.1 that significant low flux enhancement occurs at wall superheats

ranging from 5°C to 15°C. Thus, in the numerical channel boiling simulations, the

boiling surface defined with a constant temperature (Dirichlet) boundary condition. By

changing the channel geometry, enhancement (if any) of the various heat transfer

mechanisms may then be evaluated relative to unconfined pool boiling performance.

Table F.1 shows boiling parameter calculation results for saturated FC-72 at atmospheric

pressure (101 kPa) based on the correlations presented in Section F.1.1, as a function of

wall superheat. Boiling heat flux was calculated using the polynomial curve fit of the

polished silicon unconfined pool boiling curve discussed in Chapter 4. The latent heat

Appendix F: CFD Simulation of Two Phase Channel Flow 282 Table F.1: Boiling parameter predictions for saturated FC-72 at atmospheric pressure

(101 kPa) based on Eqs. (F.1)–(F.8).

∆∆∆∆T sat

(°C)

Boiling Heat Flux (kW/m2)

Latent Heat Contribution

Bubble Departure Diameter

(mm)

Bubble Frequency

(Hz)

Bubble Period (ms)

Bubble Growth Time (ms)

Nucleation Site

Density (m-2)

5.0 3.1 3% 0.811 51.4 19.5 4.9 64286.0 3.7 5% 0.806 51.9 19.3 4.8 111087.0 4.8 6% 0.802 52.7 19.0 4.7 176398.0 6.4 7% 0.797 53.6 18.7 4.7 263319.0 8.5 7% 0.793 54.7 18.3 4.6 3749010.0 11.0 8% 0.789 56.0 17.9 4.5 5142711.0 13.7 8% 0.784 57.4 17.4 4.4 6844912.0 16.6 9% 0.780 58.8 17.0 4.3 8886612.3 17.7 9% 0.778 59.3 16.9 4.2 9635413.0 19.8 10% 0.775 60.4 16.6 4.1 11298514.0 23.1 10% 0.771 62.1 16.1 4.0 14111515.0 26.7 11% 0.766 63.8 15.7 3.9 173566

contribution to the total boiling heat flux was calculating as the time-averaged vapor

volume generation rate multiplied by the product of the vapor density and latent heat.

FluxHeat Boiling Total

234

onContributiHeat Latent Fractionalfgg

2b hf

AND ρπ

= (F.10)

The values shown in Table F.1 appear to be congruent, in at least an order-of-magnitude

sense, with experimentally-observed measurements reported in the literature for FC-72

and similar highly-wetting organic fluids, e.g. (Bonjour et al., 2000) (El-Genk and

Bostanci, 2003) (Pioro et al., 2004) (Kim et al., 2006).

As mentioned previously, 2-D models were pursued to develop and demonstrate the

numerical simulation process. In order to preserve as much similarity as possible between

the 2-D models and 3-D experiments, it was deemed important to maintain the same

bubble departure diameter to appropriately capture channel spacing effects while also

Appendix F: CFD Simulation of Two Phase Channel Flow 283 generating the same volume of vapor in the channel to provide an equivalent buoyancy

force to generate an equivalent channel mass flow rate. Thus, the point on the pool

boiling curve corresponding to the generation of a total vapor volume (number of bubbles

times the bubble departure volume) equivalent to the volume of a single 2-D (cylindrical)

bubble of the same diameter was chosen as the operating point for the simulations. This

point may be expressed mathematically as

2

b3

b

2234

=

DHHLAND ππ (F.10)

or, equivalently

23

b =LAND (F.11)

For the data of Table F.1, this operating point occurs at a wall superheat of 12.3°C. In

other words, at a wall superheat of 12.3°C, the unconfined pool boiling heat flux is

17.7 kW/m2 (1.77 W/cm2), and the predicted bubble departure diameter is 0.778 mm. The

predicted nucleation site density is 96354 1/m2, or approximately 58 nucleation sites on a

20 × 30 mm (L × H) heater. The volume of a single 0.778 mm diameter sphere is

2.47×10-10 m3, while the volume of 58 such bubbles is 1.43×10-8 m3. This total vapor

volume is equivalent to the volume of a single, 30 mm deep cylinder with a diameter of

0.778 mm. Note that both volumes are simple linear functions of the channel depth, H,

and this dimension factors out of the comparison, as in Eq. (F.11). Thus, a simulated 2-D,

0.778 mm diameter bubble with a unit depth (as defined by the unit system employed in

the CFD analysis) will represent a vapor volume equivalent to the 12.3°C operating point.

Given the bubble parameters in Table F.1 corresponding to a boiling surface superheat of

12.3°C, the mass flow rate for the vapor inlet representing the nucleation site may be

calculated. The average vapor mass generation rate over the bubble growth time is

g

g2

b

2 τρ

π HD

m

=D (F.12)

As discussed in the following section, the vapor inlet representing the nucleation site in

the CFD model was taken to be 0.1 mm in size. This dimension is not representative of

Appendix F: CFD Simulation of Two Phase Channel Flow 284 expected nucleation sites but instead represents a compromise between computation

resources and bubble behavior—i.e. 0.1 mm is large enough to maintain a reasonable

number of computational cells, while it is, at the same time, sufficiently smaller than the

bubble departure diameter. Combining this with Eq. (F.12) yields an expression for the

average vapor mass flux over the bubble growth time.

g

g2

b

2 τρ

πs

DG

= (F.13)

where s is the size of the vapor inlet, 0.1 mm, and the channel depth once factors out of

the problem. For the chosen operating point, Eq. (F.13) evaluates to 15.18 kg/m2s.

Unfortunately, getting disparate departure diameter, bubble frequency, and bubble growth

correlations to intersect at a single point is near impossible (Dhir, 2006). For a spherical

bubble growing in an infinite superheated pool, growth is initially inertia controlled, and

bubble radius tends to increase linearly with time. Later, when bubble growth is limited

by heat transfer rates, radius tends to increase as the square root of time (Carey, 1992).

For bubble growth near a heated wall, however, consider the Mikic and Rohsenow (1969)

bubble growth correlation

( )

−+

∆−

−= ∞

ττ

ττ

πτπα

τ ww

sat

w 1132

TTTJa

r f (F.14)

where

fgg

satfJah

Tc p

ρρ ∆

= (F.15)

Figure F.2 shows a graph of Eq. (F.14) and how the bubble growth rate is roughly

proportional to time to the one-third power. As a result, bubble volume is roughly linear,

and the constant value calculated in the previous paragraph may be used. This is also

consistent with the findings of Thorncroft et al. (1998) who observed that bubble

diameter increased proportionally to time raised to an exponent varying between 1/3 and

1/2 (Maity and Dhir, 2001).


0

0.1

0.2

0.3

0.4

0 0.005 0.01 0.015 0.02

Time (s)

Bub

ble

Rad

ius

(mm

)

0.00E+00

5.00E-11

1.00E-10

1.50E-10

2.00E-10

2.50E-10

3.00E-10

Bub

ble

Volu

me

(m3 )

Bubble RadiusBubble Volumeslope = 1.39E-8

Figure F.2: Bubble growth rate predicted by Mikic and Rohsenow (1969) correlation.

F.2 CFD MODELING PROCESS

Fluent software, version 6.2.16, was used to develop the following simulation process.

The approach, assumptions, and implementation will be described in detailed terms.

Anyone familiar with the basic workings of the software and able to access the Fluent

documentation should be able to recreate this process successfully. Furthermore, the

general methodology should be applicable to any CFD software with comparable

capabilities. For a thorough discussion of two phase CFD techniques and their

implementation in a variety of commercially-available software packages, see

(Muehlbauer, 2004).

Software menu names and commands will be shown in ALL CAPS. While dimensions

may be discussed in units of millimeters, it is important to maintain a consistent system

Appendix F: CFD Simulation of Two Phase Channel Flow 286 of units when using the GAMBIT and FLUENT software. Thus, input values should be

specified in meters. Temperatures will be specified in degrees Kelvin.

F.2.1 Model Geometry and Computational Grid

The geometry of interest, shown in Fig. F.3, corresponding to the experimental boiling

channels of Chapter 5 is 20 mm long (in the flow direction) and has a variable channel

spacing. For the purposes of the simulations, the computational domain has been

extended 10 mm above and below the channel exit and inlet. These regions have been

made wider than the channel itself, to approximate the experimental configuration. The

channel spacing, δ, was initially set equal to 5 mm to represent unconfined pool boiling.

The 2-D model geometry was created and meshed using the Gambit software (ver. 2.2)

provided with Fluent. The first step in defining the geometry is to define the grid and

vertices at the corners of the geometry. The x-axis is taken to be the horizontal axis, while

the y-axis is vertical, parallel to the gravity vector. As only the fluid area is included in

the computational domain, the origin of the coordinate system is located at the left end of

the bottom inlet. For the initial analysis representing unconfined pool boiling, a channel

spacing of 5 mm was chosen for simplicity (experimentally, unconfined behavior was

observed for δ ≥ 2 mm). Thus, a 3×8 array of grid points spaced 5 mm apart was defined

to assist in the creation of the fluid area (TOOLS; COORDINATE SYSTEM; DISPLAY

GRID). As the default view scales the graphics window to 1 m, in order to view the

newly-created grid points, the user will need to right-click and drag down to zoom in.

Grid points are not considered geometry, so using the FIT TO WINDOW command will

not zoom in on the grid points.

In addition to the 5 mm grid, additional grid points must be created to define the vapor

inlet representing the bubble nucleation site. As discussed earlier in this chapter, a vapor

inlet size of 0.1 mm was determined to be satisfactory. The nucleation site is centered

along the vertical length of the channel to represent an average location. Thus, x


δ g

L = 20 mm

5 mm

15 mm

Tin = Tsat

= insulated/non-conducting

Heater Surface

10 mm

10 mmδ g

L = 20 mm

5 mm

15 mm

Tin = Tsat

= insulated/non-conducting

Heater Surface

10 mm

10 mm

Figure F.3: CFD model geometry.

coordinate values of 5 and 10 mm and y values of 19.95 and 20.05 mm were used to

generate additional grid points. Vertices can then be drawn (CTRL-RIGHT-CLICK) at

grid points (GEOMETRY; VERTEX; CREATE VERTEX), and lines which define the

final geometry can be traced out (SHIFT-LEFT-CLICK) between vertices

(GEOMETRY; EDGE; CREATE EDGE).

Faces which define the fluid zone(s) are defined by specifying (SHIT-LEFT-CLICK) a

continuous loop of lines (GEOMETRY; FACE; FORM FACE). In order to facilitate

meshing around the vapor inlet, three fluid zones are defined. The computational domain

is effectively divided into two halves by a third face defined by the four nucleation site

grid points mentioned above. This geometry is shown in the screen-shot of Fig. F.4, with

the vertices and edges in cyan and the faces shaded in yellow. The center face is so thin

that it may appear as a single line. Grid point visibility was deselected for this view

(TOOLS; COORDINATE SYSTEM; DISPLAY GRID).

Appendix F: CFD Simulation of Two Phase Channel Flow 288 The larger top and bottom faces are meshed using a uniform 0.1 mm interval size

(MESH; FACE; MESH FACES). Specifying QUAD elements of type SUBMAP

produces a uniform mesh of square cells. The center face at the vapor inlet will maintain

this same 0.1 mm cell size in the x direction, however a size of 0.02 mm will be used in

the y direction to produce five cells along the vapor inlet. In order to implement this cell

size, the left and right edges of the center face are meshed separately (MESH; EDGE;

MESH EDGES). The GRADING option should be disabled to produce a uniform mesh

spacing. The center face mesh may then be meshed as before (MESH; FACE; MESH

FACES), with the spacing option deselected. Results of these operations are shown in

Figure F.5.

Figure F.4: GAMBIT screen-shot of model geometry showing vertices, edges, and faces.


Figure F.5: GAMBIT screen-shot showing mesh details in vicinity of vapor inlet.

Once the mesh has been created, boundary and fluid zones types may be specified. All

unspecified faces will be type FLUID by default and grouped together, so there is no

need to specify them unless a particular zone name is desired (ZONES; SPECIFY

CONTINUUM TYPES). The edges corresponding to the domain inlet and outlet should

be named separately and set to boundary types PRESSURE_INLET and

PRESSURE_OUTLET, respectively, using the Specify Boundary Types panel (ZONES;

SPECIFY BOUNDARY TYPES). Before running the transient, two phase VOF

simulation, a preliminary steady-state, single phase, natural convection simulation will be

run to establish the flow field, providing initial conditions to the subsequent transient

simulation. Thus, the edge defining the vapor inlet will initially be designated as type

WALL for the preliminary steady-state simulation and then changed to

MASS_FLOW_INLET for the VOF simulations. Boundary and zone types may be

Appendix F: CFD Simulation of Two Phase Channel Flow 290 changed later in FLUENT, however, defining them as separate entities in GAMBIT is

necessary. All unspecified edges will be type WALL by default and grouped into a single

boundary entity. Thus, the two edges which represent the top and bottom portions of the

heated surface must also be specified separately and given type WALL. Defining the two

halves of the heated surface as separate boundaries may facilitate individual post-

processing later.

With the zones defined, the mesh is complete. Saving the GAMBIT file is recommended

for later use, however, the mesh must be exported in a format that FLUENT can read

(FILE; EXPORT; MESH). In this case, the “Export 2-D(X-Y) Mesh” option must be

selected in the Export Mesh File window. GAMBIT also creates a text-based journal file

which contains a log of the commands used during the GAMBIT session. The journal file

representing the steps outlined above is included in Section F.5.1 for completeness.

F.2.2 Initial Single Phase Simulation

As mentioned in the previous section, a preliminary steady-state single phase simulation

will provide the initial conditions for the transient VOF simulation. With the geometry

defined, the mesh may now be brought into the 2-D double-precision version of FLUENT

(FILE; READ; CASE). Fluent will display the number of nodes (40855), cells (40200),

and faces in each zone. Autosave settings determine how often solution data is saved

(FILE; WRITE; AUTOSAVE). For a steady-state solution, the number of iterations is

specified. In this case, a large number, such as 100, will suffice.

The DEFINE; MODELS submenu contains a variety of settings. The vast majority of the

defaults are appropriate for the steady-state simulation. Default solver options are listed

in Section F.5.2 for completeness. The laminar viscous model (DEFINE; MODELS;

VISCOUS MODEL) is employed, given the results of Section 6.1 that suggest the natural

convection flow in this case is laminar. The only non-default MODELS option is the

Appendix F: CFD Simulation of Two Phase Channel Flow 291 toggle switch for the energy equation. The energy equation option must be checked to

include heat transfer in the simulation (DEFINE; MODELS; ENERGY).

As discussed in Section F.1, for the purposes of these simulations, FC-72 properties from

Appendix A are supplemented with additional vapor properties (µg = 181 kPa·s,

cp,g = 500 J/kgK, and kg = 0.02 W/mK) taken from (Khalij et al., 2006). Material

properties must be defined for each phase (DEFINE; MATERIALS). Note that material

properties for the vapor phase are not required for the initial steady-state solution but may

be input at any time for later use. While the vapor phase may be given a constant density,

the Boussinesq approximation is used for the liquid phase (Thermal Expansion

Coefficient, β = 0.00164 1/K). Since the computational domain includes only fluid, it is

not necessary to define any solid material properties.

Operating conditions are specified next (DEFINE; OPERATING CONDITIONS).

Default operating pressure and location (101325 Pa, origin) are appropriate, but gravity

must be turned on. A gravitational acceleration of -9.807 m/s2 can then be specified in the

y direction. Further, the operating temperature must be provided for the Boussinesq

model. The saturation temperature of the liquid should be specified in degrees Kelvin,

329.75 K.

Boundary conditions need to be specified at the inlet, outlet, and heater surfaces

(DEFINE; BOUNDARY CONDITIONS). The static head contribution to the pressure

field is handled automatically in the background by FLUENT. Thus, for the inlet and

outlet, pressure conditions should be set to zero by default. However, the temperature

needs to be changed to the liquid saturation temperature, 329.75 K. A constant

temperature of 342.1 K, corresponding to the 12.3°C temperature rise of the surface

above saturation, must be specified on each heater wall individually. For the purposes of

the steady-state initial solution, this includes the vapor inlet which is initially set to type

WALL. All of the other walls will be adiabatic by default. In addition, the correct

Appendix F: CFD Simulation of Two Phase Channel Flow 292 working fluid (liquid FC-72), as named during material properties specification, needs to

be selected for the fluid zone.

The SOLVE menu contains commands for solution control, monitoring, and execution.

The Solution Controls window (SOLVE; CONTROLS; SOLUTION) contains settings

critical to providing adequate convergence of the iterative solution. Under “Pressure-

Velocity Coupling,” the PISO option should be selected, though “Skewness-Neighbor

Coupling” may be unselected. The PRESTO! option should be selected for pressure

discretization. All other default options (including under-relaxation factors) will suffice.

All of these solution control options are listed in Section F.5.2 for completeness.

The entire fluid domain may be set initially at the saturation temperature of the liquid,

329.75 K (SOLVE; INITIALIZE; INITIALIZE). Other pressure and velocity initial

conditions may remain the default value of zero. Given the coupling between the energy

and momentum equations, a large number of iterations is required, and a convergence

criteria of 1×10-6 is recommended for all residuals (SOLVE; MONITORS; RESIDUAL).

Various output quantities of interest (inlet and outlet mass flow rates, wall heat fluxes)

may be output at each solution iteration (SOLVE; MONITORS; SURFACE). The

solution may then be pursued for a fixed number of iterations (SOLVE; ITERATE) or

until all residuals drop below 1×10-6, which ever occurs first.

The simulation described above met the convergence criteria after 2545 iterations, which

took less than forty-five minutes to run on a 3 GHz Pentium-based PC. Solution residuals

are shown in the graph of Fig. F.6, while Figs. F.7 and F.8 contain contour plots of

temperature and velocity, respectively. In the final solution, the mass flow rate through

the channel is 0.0169 kg/s, and the average heater heat flux is 2.60 kW/m2. As the

boundary layer is thinner near the channel inlet, the bottom half of the heater dissipates

60% of the total heat, while the top half dissipates 40%. The average natural convection

heat transfer coefficient is 211 W/m2K—within 3% of predictions based on the

correlations discussed in Section 6.1 and results shown in Fig. 6.9.


Figure F.6: Scaled solution residuals for initial steady-state single phase solution.

Figure F.7: Temperature results for initial steady-state single phase solution.


Figure F.8: Velocity results for initial steady-state single phase solution.

F.2.3 Transient VOF Simulation

The model developed for the steady-state initial conditions may be used as the basis for

the VOF model. However, some settings and conditions will need to be changed. To start,

the case (model) and data (solution) files from the steady-state analysis should be opened

into FLUENT (2-D, double precision version). The autosave settings (FILE; WRITE;

AUTOSAVE) may be changed. For a transient solution, the specified save frequency is

the number of time steps. A time step of 0.1 ms will be used, and 100 bubble generation

cycles may be required to establish steady behavior. Thus, saving the solution every 10

time steps (every 1 ms) would generate 2000 case and data files. Each pair of files may

be 20 MB in size, for a total of 40 GB by the end of the simulation. These types of

considerations should be evaluated before setting the AUTOSAVE frequency.

Fortunately, all intermediate steps do not need to be preserved long-term, and the binary

Appendix F: CFD Simulation of Two Phase Channel Flow 295 files may be typically compressed close to 50% using standard operating system file

compression utilities.

The solver settings must be changed to reflect the transient, multiphase nature of the

simulation. The Unsteady option should be selected in the solver window (DEFINE;

MODELS; SOLVER). “Non-Iterative Time Advancement” and “Frozen Flux Formation”

should not be checked. The Volume of Fluid model is specified in the Multiphase Model

window (DEFINE; MODELS; MULTIPHASE). The default number of phases, 2, is

appropriate, though “Geo-Reconstruct,” “Solve VOF Every Iteration,” and “Implicit

Body Force” options should be checked.

Given the high vapor velocity during bubble growth, the k-ε turbulence model is

employed (DEFINE; MODELS; VISCOUS). The following options should all be

selected: Realizable, Enhanced Wall Treatment, Pressure Gradient Effects, Thermal

Effects. The default model constants (shown in Section F.5.3) are used.

If vapor material properties were not defined during the setup phase of the steady-state

solution, they should be specified next. The liquid phase should be identified as the

primary phase, with the vapor phase as the secondary phase (DEFINE; PHASES).

Surface tension is specified in the Phases Interaction window. A constant value of

0.008273 N/m is used. The Wall Adhesion option should also be selected in this window.

In addition to the operating conditions specified during setup of the steady-state

simulation, an operating density must be specified (DEFINE; OPERATING

CONDITIONS). It is critical here that the density of the liquid phase (1620 kg/m3) at the

liquid inlet temperature (saturation, 329.75 K) be specified. The FLUENT documentation

simply states that the density of the least dense phase should be used as the operating

density (FLUENT, 2005). This is only appropriate when the gas phase is the primary

phase and the liquid is held in a channel or some other type of container. If the vapor

density is specified as the operating density for this buoyancy-driven channel simulation,

Appendix F: CFD Simulation of Two Phase Channel Flow 296 the liquid will simply fall through the channel, traveling from top to bottom, under the

force of gravity.

Before boundary conditions are adjusted, the transient profile which defines the vapor

mass flow rate at the nucleation site must be defined and loaded into the software. As

discussed in Section F.1.2, the bubble growth time is 4.2 ms, over which a constant vapor

mass flux of 15.18 kg/m2s will be assumed. The remainder of the 16.9 ms bubble

departure period, 12.7 ms represents the waiting time, τw. In order to get the bubble to

detach properly from the wall, it was determined necessary to produce a very short slug

of liquid from the inlet representing the nucleation site at the end of the bubble growth

time. Thus, a liquid mass flux decreasing of 100 kg/s over the first 0.1 ms time step

immediately following bubble growth is also specified. The resulting liquid volume will

be less than a hundredth of a millimeter thick and simply serves to rewet the surface after

bubble growth and allows the bubble to detach from the wall. It is suspected that if the

nucleate site was modeled as a very small inlet, more closely representing actual

nucleation site geometries, the availability of surrounding liquid and growth force of the

bubble would be sufficient to detach the bubble from the wall and rewet the nucleation

site.

The transient vapor and liquid mass flux profiles specified to create this behavior are

shown graphically in Fig. F.9. The points which define this curve are included in a simple

text file which is then read into FLUENT. A listing of the mass flux profile input file

based on Fig. F.9 is included in Section F.5.3 for completeness. The first line of the file

specifies the profile name, that the profile is transient, the number of points, and an

option to indicate if the profile is periodic (1) or not (0). Subsequent lines list values for

each variable (time, vapor mass flux, liquid mass flux) at each step in the profile. When

the profile input file is read into FLUENT (DEFINE; PROFILES), the profile name and

variable fields will be displayed. These profiles are now available for use in boundary

condition specifications.


0

20

40

60

80

100

120

0.000 0.005 0.010 0.015

Time (s)

Vapo

r Mas

s Fl

ow R

ate

(kg/

s)vaporliquid

Figure F.9: Nucleation site mass flux profiles.

With the addition of a second phase, boundary condition specifications require a number

of modifications from those used for the initial steady-state simulation. Each of the wall

zones (including the adiabatic boundaries) now require a specification of the contact

angle between the phases (DEFINE; BOUNDARY CONDITIONS; PHASE MIXTURE).

The FLUENT documentation (FLUENT, 2005) describes how contact angle is defined as

the angle between the wall and the tangent to the phase interface at the wall, as measured

inside the “first” phase. However, the “first” phase is not necessarily the primary phase

specified in the DEFINE; PHASES window. The “first” phase for specification of the

contact angle is defined as the first phase listed in the WALL window under the

MOMENTUM tab (DEFINE; BOUNDARY CONDITIONS; PHASE MIXTURE). In

this case, the “first” phase is the vapor phase, and a contact angle approaching 180°

should be specified for highly-wetting liquids; 179° is assumed for the purposes of these

Appendix F: CFD Simulation of Two Phase Channel Flow 298 simulations. If the contact angle is defined incorrectly, the bubble will not detach from

the wall and instead spread along it as it slowly moves up under buoyancy forces.

The nucleation site zone which was previously given type WALL must now be changed

to MASS-FLOW-INLET (DEFINE; BOUNDARY CONDITIONS; MIXTURE). The

saturation temperature (329.75 K) should be specified for this inlet. The “Direction

Specification Method” may be set to “Normal to Boundary” for convenience. Pressure

and turbulence conditions are set to zero. In addition to these mixture properties, the

individual phase mass flux profiles must be specified. The “Mass Flow Specification

Method” should be set to “Mass Flux,” and the variable names defined in the profile

input file representing each phase may then be specified.

Remaining boundary conditions concern the channel inlet and outlet. Each of these

boundary zone requires mixture and individual specifications (DEFINE; BOUNDARY

CONDITIONS). For the mixture specifications, temperature was set at the saturation

temperature (329.75 K) during setup of the steady-state simulation. All pressure and

turbulence conditions should be set to zero. The volume fraction of the secondary phase

must also be specified at these boundaries. The default value of zero is appropriate. The

volume fraction of the primary phase is calculated automatically as the difference

between unity the specified volume fraction of the secondary phase.

None of the solution control settings need to be changed from the previous simulation.

Additional defaults related to turbulence modeling will not be changed either (SOLVE;

CONTROLS; SOLUTION). These settings are listed in Section F.5.3 for completeness.

The steady-state solution data file which will provide initial conditions for the VOF

simulation needs to be read into FLUENT (FILE; READ; DATA). Additional initial

conditions because of the additional phase and turbulence settings must be added

(SOLVE; INITIALIZE; PATCH). Turbulent Kinetic Energy and Turbulent Dissipation

Rate should be set to zero for the mixture phase throughout the fluid zone. The only patch

Appendix F: CFD Simulation of Two Phase Channel Flow 299 vapor phase option is Volume Fraction, which should be set to zero, as the domain is

exclusively filled with liquid initially.

Solution monitors and residual convergence criteria may be set as before. However, it

may be desirable to switch to reporting monitored quantities at every Time Step rather

than at every Iteration (SOLVE; MONITORS; SURFACE). The Iterate window

(SOLVE; ITERATE) now contains options for Time Step Size, Number of Time Steps,

and Max Iterations Per Time Step. As mentioned previously, a fixed 0.1 ms time step is

used. The number of time steps specified is relatively inconsequential, as the solution

process may be stopped and restarted at any time. It was determined via trial and error

that setting the maximum number of iterations per time step at 40 is sufficient. Residuals

may not drop below 1×10-6 for each iteration of these VOF solutions, but they do tend to

level off within 40 iterations. In addition, monitored quantities, such as heat fluxes and

mass flow rates, may be observed to level off well within 40 iterations.

F.3 VOF SIMULATION RESULTS AND DISCUSSION

Figure F.10 shows solution residuals for the first 86 ms of simulation time, corresponding

to the first 5 bubble generation cycles. The numbering of iterations continues from the

steady state solution used for the initial conditions, and the start of the transient runs is

quite obvious, shortly after 2500 iterations in this case. As discussed in the previous

section, convergence is achieved during some of the time steps well within forty

iterations, while others level off but do not converge. Approximately 2 hours of solution

time were required for each bubble period (16.9 ms of simulated time), running on a

3 GHz Pentium-based PC. The simulation was allowed to run for nearly 80 bubble cycles

until steady conditions were achieved, as will be discussed below. Thus, the entire VOF

simulation took on the order of a week to solve.


Figure F.10: Scaled solution residuals for the first 5 bubble generation cycles of the 5 mm

channel simulation.

The progression of phase contours from the start of the transient simulation through

seven bubble generations is shown in Fig. F.11 in 4 ms time steps. Recalling that the

bubble growth time is 4.2 ms, the first image in the series represents nearly the entire

growth of the first bubble. Every four images almost covers a bubble period. Recall from

Fig. F.8 that liquid velocities are initially on the order of 1 m/s in the vicinity of the

nucleation site. Thus, by the time the second bubble has been generated, around 20 ms,

the first bubble has moved roughly 0.2 mm in the vertical direction. This distance is small

compared to the size of the bubbles, and, as a result, the two bubbles merge. The third

bubble is generated from 33.8 to 38.0 ms. While the fourth bubble is being generated

around 52 ms, the third is merging with the first two. By this time, the buoyancy of the

vapor has begun to accelerate the rising of the bubbles, and the leading coalesced bubble

has traveled significantly more than 0.050 s times 0.01 m/s, or 0.5 mm. The images

corresponding to t = 68, 88, and 104 ms include the growth of the fifth, sixth, and seventh


t = 4 ms t = 8 ms t = 12 ms t = 16 ms t = 20 ms t = 24 ms t = 28 ms




Figure F.11: Phase contour plots at 4 ms time steps from the beginning of the VOF

simulation through the first seven bubble generations, δ = 5 mm.

Appendix F: CFD Simulation of Two Phase Channel Flow 302 bubbles, respectively. Given the constant bubble generation rate, the fact that the fourth

bubble does not merge with the leading coalesced bubble until the seventh bubble

generation period also demonstrates the acceleration of the flow in the channel.

The progression of monitored inlet and outlet mass flow rates is shown in Fig. F.12. Mass

flow into the computational domain is taken to be positive. At the end of the steady state

single phase simulation, the inlet and outlet mass flow rates were equal to 0.017 kg/s.

However, during bubble growth the force of the expanding vapor volume creates a short

increase in the outlet mass flow rate and a corresponding decrease in the inlet mass flow

rate. During the first six bubble cycles, the inlet mass flow rate even goes negative,

signifying a net outflow due to vapor bubble expansion. Between bubble events, the inlet

and outlet mass flow rates exceed the initial condition of 0.017 kg/s during the first

bubble waiting time due to the increase in buoyancy in the channel.

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Simulated Time (s)

Mas

s Fl

ow R

ate

(kg/

s)

InletOutlet

Figure F.12: Inlet and outlet mass flow rates as a function of time, δ = 5 mm.


Figure F.13: Contour plots of 5 mm channel liquid phase volume fraction at various

simulation times.

Appendix F: CFD Simulation of Two Phase Channel Flow 304 The mass flow rate through the channel increases quickly as bubbles are generated and

fill the channel as shown in Fig. F.13. The fifth and sixth bubbles eventually reach and

merge with the leading coalesced bubble before it reaches the outlet at a time t = 0.24 s.

As the large leading bubble exits the computational domain, the outlet mass flow rate

experiences a transient peak, going positive for approximately 7 ms, as the outlet flow

experiences a brief net inflow (backflow). After the exit of the coalesced leading bubble,

and due to the large (two orders of magnitude) difference in the densities of the liquid and

vapor phases, the outlet mass flow rate decreases in magnitude somewhat for each

subsequent exiting bubble, as seen in Fig. F.12.

Once the leading bubble exits the channel, flow and heat transfer are relatively steady,

though with some periodic character. The bubble flow path near the outlet continued to

shift until reaching the final pattern shown in the bottom right corner of Fig. F.13 at

t = 1.0 s. The simulation was continued until t = 1.34 s, to ensure asymptotic heat

dissipation was achieved, as shown in Fig. F.14.

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Simulated Time (s)

Hea

t Flu

x (W

/m2 )

Top HalfBottom Half

Figure F.14: Heater top and bottom heat flux as a function of time, δ = 5 mm.

Appendix F: CFD Simulation of Two Phase Channel Flow 305 Heat flux from the top and bottom halves of the heated surface also experience transient

fluctuations due to bubble growth and motion. Time-averaged versions of the mass flow

and heat flux curves of Figs. F.12 and F.14 appear in Figs. F.15 and F.16, respectively.

Here values are averaged over two bubble periods. At the end of the simulation, the inlet

and outlet mass flow rates are equal to 0.28 kg/s, differing by less than 2%, primarily due

to the vapor and liquid entering the domain at the nucleation site. The nucleation site

mass flow rate is 0.43 g/s averaged over the bubble period.

Heat fluxes from the top and bottom halves of the heater were 9.96 and 4.86 kW/m2,

respectively, at the end of the simulation, as shown in Fig. F.16. These heat fluxes

represent a significant increase compared to the corresponding single phase natural

convection results of 2.09 and 3.12 kW/m2, respectively. Unlike during single phase

natural convection, when the bottom half dissipates more heat because the boundary layer

is thinner, the motion of bubbles along the top half of the heater promotes fluid mixing

and yields twice the heat dissipation from the top as the bottom.

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Simulated Time (s)

Mas

s Fl

ow R

ate

(kg/

s)

InletOutlet

Figure F.15: Time-averaged inlet and outlet mass flow rates, δ = 5 mm.


0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Simulated Time (s)

Hea

t Flu

x (W

/m2 )

Top HalfBottom Half

Figure F.16: Time-averaged heater top and bottom heat fluxes, δ = 5 mm.

The disruption of the thermal boundary layer due to passing bubbles is shown clearly in

the color contour plot of Fig. F.17. Local heat flux values along the heater surface are

shown in Fig. F.18, along with an image showing the corresponding bubble locations.

Clearly the periodic disturbances caused by bubble motion significantly increases heat

transfer. The single phase heat flux profile is also included for comparison. While not

directly affected by localized bubble motions and fluid mixing, heat transfer on the lower

half of the heater surface is enhanced due to the increased flow rate in the channel. As the

channel mass flux was increased by an order of magnitude, corresponding liquid

velocities were also an order of magnitude higher than those observed in the single phase

natural convection solution. Figure F.19 shows fluid velocity contours at the end of the

VOF simulation.


Figure F.17: Temperature contour plot at end of 5 mm channel VOF simulation.

0

5

10

15

20

0 5 10 15Local Surface Heat Flux (kW/m2)

Dis

tanc

e A

long

Hea

ter (

mm

)

VOF Solution 1.34 s

Single Phase

Figure F.18: Surface heat flux profiles for 5 mm channel single phase natural convection

solution and VOF simulation results at t = 1.34 s.


Figure F.19: Velocity contour plot at end of VOF simulation, δ = 5 mm.

As shown in Table F.1, the experimental boiling heat flux measured at this wall superheat

was 17.7 kW/m2, and only 1.6 kW/m2 of that total would be attributed to the latent heat

contribution from bubbles of this size. The results of this section suggest that 7.4 kW/m2

is attributable to enhanced natural convection resulting from increased liquid flow rates

past the surface and bubble-induced mixing and disruption of the thermal boundary layer.

It is, as of yet, undetermined what mechanisms are responsible for the remaining

8.7 kW/m2. Evaporation of superheated liquid between the heated surface and passing

bubbles should be evaluated. As discussed previously in this chapter, the custom user-

defined functions that would incorporate mass transfer between the phases have not yet

been developed. However, it should also be noted that from the outset these simulations

were based on potentially inaccurate bubble correlations, with the purpose of exploring

the order of magnitude of various effects. In particular, the nucleation site density

correlation may not predict the behavior of this particular experimental boiling surface

very well. Further, the simulations described thus far have been two-dimensional. It is

Appendix F: CFD Simulation of Two Phase Channel Flow 309 reasonable to expect that multiple discrete bubbles would have a combined area of

influence larger than a 2-D “cylinder,” simply due to the larger bubble area to volume

ratio.

The simulations discussed thus far were repeated for smaller channel spacings of 0.7 and

0.3 mm. In the case of the 0.3 mm channel, a slightly different meshing approach was

taken to provide six 0.05 mm wide fluid elements across the channel. Cell size remained

0.1 mm in the y-direction, except at the nucleation site, as before. Narrow channel VOF

simulations reached steady conditions significantly sooner than the 5 mm channel and

were terminated after 0.60 s of simulated time. Table F.2 contains a summary and

comparison of results from the single and two phase simulations with these three channel

spacings. Numerical single phase heat transfer results are lower than but within 5% of

predictions based on the correlations of Section 6.1 when the same liquid properties are

used. Elenbaas numbers at these channel spacings are included in Table F.2. An

examination of the Nusselt number curves of Fig. 6.2 quickly shows that, in terms of

single phase convective cooling, the 5.0 and 0.7 mm channels behave as unconfined

isolated plates, while the 0.3 mm channel is approaching fully developed conditions.

Table F.2: Summary and comparison of simulation results.

5 0.7 0.3 5 0.7 0.3

0.0169 0.0079 0.0021 0.28 0.10 0.026

3.4 11 7.0 56 143 87top 2.09 1.72 0.32 9.96 9.63 6.99

bottom 3.12 3.40 2.47 4.86 8.45 8.38average 2.60 2.56 1.39 7.41 9.04 7.69

211 207 113 600 732 622

216 215 118

7.5×105 288 9.7

Two PhaseSingle Phase

Heat Flux (kW/m2)

Elenbaas Number

Prediction via Eq. (6.15) (W/m2K)

Channel Mass Flow Rate (kg/s)

Average Heat Transfer Coefficient (W/m2K)

Channel Spacing, δ (mm)

Channel Mass Flux (kg/m2s)


Figure F.20: Comparison of temperature results from single phase numerical simulations.

The results provided in Table F.2 include channel mass flux in addition to the channel

mass flow rate. While the total mass flow rate is greatest for the 5 mm channel, mass flux

based on the channel cross-sectional area and, therefore, fluid velocities are greatest for

the 0.7 mm channel. Temperature contours from the single phase simulations are

compared in Fig. F.20. While the liquid flow in the 5 mm channel is clearly unconfined,

the thermal boundary layer in the 0.7 mm channel interacts somewhat with the opposing

unheated wall. Thus, while heat transfer from the bottom half of the heater increases 9%

due to the increased mass flux, heat transfer from the top half of the heater is reduced by

18% because of the thermal boundary layer interaction/sensible heat rise of the liquid,

and the net result is a difference of less than 2% in total heat transfer between these two

cases. In the 0.3 mm channel, however, not only is the channel mass flux reduced, but the

fluid also reaches the heater temperature before the channel exit. This produces

significantly deteriorated total heat transfer compared to the wider channels (nearly half).

Appendix F: CFD Simulation of Two Phase Channel Flow 311 This behavior is evident in the data of Table F.2, where it is shown that 89% of the total

heat is dissipated from the bottom half of the heater.

Figure F.21 shows sample liquid phase volume fraction contour plots from the two phase

0.7 mm and 0.3 mm channel simulations. With the exception of the narrower channels

and flattened bubbles, these simulations proceed in a manner very similar to the 5 mm

channel. Large leading coalesced bubbles are formed as the channel flow is established.

Eventually velocities are high enough that individual bubbles flow up the channel and out

of the computational domain without coalescing. With bubble diameter on the order of

0.7 mm, all bubbles are flattened in the 0.3 mm channel. With only six computational

cells across the channel width, this coarse simulation can not simulate a thin liquid film

between the wall and vapor phase.

In contrast to the single phase simulations which predict decreasing heat transfer with

decreasing channel spacing, the two phase simulation results show maximum heat

transfer at a spacing of 0.7 mm. Heat flux results for the 0.3 mm channel are very

comparable to the 0.7 mm channel along the bottom half of the heater, as shown in both

Table F.2 and Fig. F.22. However, along the top half of the heater there exist large low-

flux regions where flattened bubbles cover the heater surface. These vapor-covered

regions are clearly larger in the narrower channel where bubbles are significantly

flattened, leading to significantly reduced heat transfer from the top half of the heater in

the 0.3 mm channel. This behavior is also evident in the temperature contour plots of

Fig. 23.


Figure F.21: Contour plots of narrow channel liquid phase volume fraction at various

simulation times.


0

5

10

15

20

0 5 10 15 20 25Local Surface Heat Flux (kW/m2)

Dis

tanc

e A

long

Hea

ter (

mm

)0.3 mm0.7 mm

single phase

two phase

Figure F.22: Surface heat flux profiles from narrow channel simulation results.

Figure F.23: Comparison of temperature results from two phase numerical simulations.

Appendix F: CFD Simulation of Two Phase Channel Flow 314 F.4 NEXT STEPS

It is hoped that the effort described in this chapter provides a good foundation for further

research in this area. The logical step for continuing development of the model is to

incorporate mass transfer between the phases, so that thin film evaporation from the

heated wall to confined bubbles may be included. As there is no option for vapor

evaporation and condensation built into the FLUENT software, a custom user-defined

function (UDF) will need to be created for this purpose.

As it is currently unknown whether or not the current solutions are mesh independent,

mesh refinement studies should be performed. Of course, the impact of the size of the

vapor inlet representing the nucleation site should be evaluated. Once thin film

evaporation is incorporated into the simulation, mesh density at the wall and its effect on

the software’s ability to resolve the phase interface and accurately predict the liquid film

thickness will be important. In addition, and partially related, the impact of various

turbulence models and options is yet to be determined. Many of the turbulence models

have special considerations for mesh density and how calculations near the wall are

performed.

The 5 mm channel simulations show bubbles rising very close to the heated surface. This

behavior is contrary to the characteristic pattern observed by Bonjour and Lallemand

(2001) of bubbles rising in a column approximately 2–2.5 bubble diameters away from

the surface at low and moderate heat fluxes. In order to represent this behavior and

improve the accuracy of the unconfined simulations, it may be necessary to modify the

vapor inlet representing the nucleation site to provide a bubble detachment force

sufficient to propel bubbles away from the surface.

The simulation process outlined in this chapter was extended to a three-dimensional

computational domain. The only substantial difference was that a different operating

point on the boiling curve was chosen. A lower wall superheat was chosen to reduce the

Appendix F: CFD Simulation of Two Phase Channel Flow 315 nucleation site density so that it could be reasonably assumed that a single bubble could

act independently of other bubbles while traveling up a narrow strip of channel. Thus, the

model would need only include a single vapor inlet and a narrow strip of channel, with

symmetry boundary conditions on its min- and max-z faces. Unfortunately, the added

dimension greatly multiplied the solution run time. Based on preliminary 3-D

simulations, it was estimated that a full transient VOF simulation could take many

months to complete. While some refinement of the mesh and solution controls might

subtly increase computational performance, they could not provide an order-of-

magnitude improvement. It may be possible to optimize the model to run effectively and

efficiently on a large parallel supercomputer system, though this type of resource was not

available to the current effort.

Clearly, the ultimate goal of this line of research would be to model an entire heater

surface, in 3-D, with a variety of randomly-placed nucleation sites. Perhaps such a

simulation could be based on a carefully-constructed experiment, where individual sites

are located, and bubble parameters (departure diameter, growth time, frequency, etc.) are

measured, e.g. (Judd and Chopra, 1993). Unfortunately, it will be some time before that

sort of computing power is available. In the meantime, development of the required

simulation processes and phenomenological models is a worthwhile pursuit and may still

provide insight on buoyancy-drive two phase flow and boiling heat transfer in confined

geometries.


F.5 FILE AND COMMAND LISTINGS F.5.1 GAMBIT Journal File / Journal File for GAMBIT 2.2.30, Database 2.2.14, ntx86 BH04110220/ Identifier "default_id3528"/ File opened for write.undo begingroupcoordinate modify "c_sys.1" xyplane xaxis add 0 AND 0.005 AND 0.01 AND 0.015 \snap nolines

coordinate modify "c_sys.1" xyplane yaxis add 0 AND 0.005 AND 0.01 AND 0.015 AND \0.02 AND 0.025 AND 0.03 AND 0.035 AND 0.04 snap nolines

window modify coordinates "c_sys.1" xyplane gridundo endgroupundo begingroupcoordinate modify "c_sys.1" xyplane xaxis add 0.005 AND 0.01 snap nolinescoordinate modify "c_sys.1" xyplane yaxis add 0.01995 AND 0.02005 snap \nolines

window modify coordinates "c_sys.1" xyplane gridundo endgroupvertex create coordinates 0.015 0 0vertex create coordinates 0.015 0.01 0vertex create coordinates 0.01 0.01 0vertex create coordinates 0.005 0.01 0vertex create coordinates 0 0.01 0vertex create coordinates 0 0 0vertex create coordinates 0.015 0.04 0vertex create coordinates 0 0.04 0vertex create coordinates 0 0.03 0vertex create coordinates 0.005 0.03 0vertex create coordinates 0.01 0.03 0vertex create coordinates 0.015 0.03 0vertex create coordinates 0.01 0.01995 0vertex create coordinates 0.01 0.02005 0


vertex create coordinates 0.005 0.02005 0vertex create coordinates 0.005 0.01995 0edge create straight "vertex.3" "vertex.2" "vertex.1" "vertex.6" "vertex.5" \"vertex.4"

edge create straight "vertex.3" "vertex.13" "vertex.14" "vertex.15" \"vertex.16"

edge create straight "vertex.16" "vertex.4"edge create straight "vertex.16" "vertex.13"edge create straight "vertex.14" "vertex.11"edge create straight "vertex.10" "vertex.15"edge create straight "vertex.11" "vertex.12" "vertex.7" "vertex.8" "vertex.9" \"vertex.10"

face create wireframe "edge.13" "edge.18" "edge.17" "edge.16" "edge.15" \"edge.14" "edge.12" "edge.8" real

face create wireframe "edge.3" "edge.2" "edge.1" "edge.6" "edge.4" "edge.5" \"edge.10" "edge.11" real

face create wireframe "edge.7" "edge.8" "edge.9" "edge.11" realsaveface mesh "face.1" "face.2" submap size 0.0001undo begingroupedge delete "edge.9" "edge.7" keepsettings onlymeshedge picklink "edge.7" "edge.9"edge mesh "edge.9" "edge.7" size 2e-05undo endgroupface mesh "face.3" submapsavephysics create "KJLG_inlet" btype "PRESSURE_INLET" edge "edge.3"physics create "KJLG_outlet" btype "PRESSURE_OUTLET" edge "edge.16"physics create "KJLG_site" btype "WALL" edge "edge.9"physics create "KJLG_heatertop" btype "WALL" edge "edge.13"physics create "KJLG_heaterbottom" btype "WALL" edge "edge.10"saveexport fluent5 "5mm_meshfile.msh" nozval/ File closed, 6.36 cpu second(s), 18767736 maximum memory.


F.5.2 Steady-State Simulation FLUENT Options

DEFINE; MODELS; SOLVER (all defaults)

Solver = Segregated

Space = 2D

Velocity Formulation = Absolute

Gradient Option = Cell-Based

Formulation = Implicit

Time = Steady

Porous Formulation = Superficial Velocity

DEFINE; OPERATING CONDITIONS

Operating Pressure = 101325 Pa

Reference Pressure Location = 0, 0

Gravity = selected

Gravitational Acceleration X = 0 m/s2

Gravitational Acceleration Y = -9.807 m/s2

Operating Temperature = 329.75 K

Specified Operating Density = not selected

SOLVE; SOLUTION; CONTROLS

Pressure-Velocity Coupling = PISO

Skewness Correction = 1

Neighbor Correction = 1

Skewness-Neighbor Coupling = not selected

Under-Relaxation Factors

Pressure = 0.3

Density = 1

Body Forces = 1


Momentum = 0.7

Energy = 1

Discretization

Pressure = PRESTO!

Momentum = First Order Upwind

Energy = First Order Upwind

F.5.3 VOF Simulation FLUENT Options

DEFINE; MODELS; SOLVER

Solver = Segregated

Space = 2D

Velocity Formulation = Absolute

Gradient Option = Cell-Based

Formulation = Implicit

Time = Unsteady

Transient Controls = not selected

Unsteady Formulation = 1st-Order Implicit

Porous Formulation = Superficial Velocity

DEFINE; MODELS; MULTIPHASE

Model = Volume of Fluid

Number of Phases = 2

VOF Scheme = Geo-Reconstruct

Courant Number = 0.25

Solve VOF Every Iteration = selected

Open Channel Flow = not selected

Body Force Formulation = Implicit Body Force (selected)


DEFINE; MODELS; VISCOUS

Model = k-epsilon (2 eqn)

k-epsilon Model = Realizable

Near-Wall Treatment = Enhanced Wall Treatment

Enhanced Wall Treatment Options = both Pressure and Temperature selected

Model Constants (all defaults)

C2-Epsilon = 1.9

TKE Prandtl Number = 1

TDR Prandtl Number = 1.2

Energy Prandtl Number = 0.85

Wall Prandtl Number = 0.85

DEFINE; OPERATING CONDITIONS

Operating Pressure = 101325 Pa

Reference Pressure Location = 0, 0

Gravity = selected

Gravitational Acceleration X = 0 m/s2

Gravitational Acceleration Y = -9.807 m/s2

Operating Temperature = 329.75 K

Specified Operating Density = selected

Operating Density = 1620 kg/m3

Mass flux profile input file: ((KJLG_site transient 6 1)

(time 0.00 0.00419 0.0042 0.00429 0.0043 0.0169)

(vaporflux 15.18 15.18 0.0 0.0 0.000 0.000)

(liquidflux 0.00 0.00 100.0 100.0 0.000 0.000)

)

SOLVE; SOLUTION; CONTROLS


Pressure-Velocity Coupling = PISO

Skewness Correction = 1

Neighbor Correction = 1

Skewness-Neighbor Coupling = not selected

Under-Relaxation Factors

Pressure = 0.3

Density = 1

Body Forces = 1

Momentum = 0.7

Turbulence Kinetic Energy = 0.8

Turbulence Dissipation Rate = 0.8

Turbulent Viscosity = 1

Energy = 1

Discretization

Pressure = PRESTO!

Momentum = First Order Upwind

Turbulence Kinetic Energy = First Order Upwind

Turbulence Dissipation Rate = First Order Upwind

Energy = First Order Upwind

322

APPENDIX

G

BOILING FIN ANALYSIS BATCH FILE

The ANSYS™ batch file shown in the next section was used to determine the heat

dissipation of boiling longitudinal rectangular fins, as discussed in Chapter 7. Analyses

were performed using ANSYS™ versions 8.0 and 10.0, producing identical results

without modification of the batch file. Input quantities (fin geometry, thermal

conductivity, and base superheat) are specified in the command line used to launch the

software. For example: ansys80 -p ane3fl -b -high 0.010 -thick 0.0007 -dtsat 14 -i batch.dat –o output.txt

will launch version 8.0 of ANSYS™, specifying product variable ane3fl for the ANSYS

Multiphysics product license. The “-b” option instructs the software to operate in batch

mode. Input quantities are specified next. The full fin thickness is specified, though only

half of the symmetrical fin is actually modeled. Finally, the names of the input batch file

and an output file used by the software are given. This output file is not a results file.

Rather, the output file specified in the command line will contain the various commands

used, error messages from the software, and details of how the iterative solution is

progressing. It can prove quite useful when debugging a batch file or trying to explain

unexpected results.

Appendix G: Boiling Fin Analysis Batch File 323 Operating system-level batch files may be used to automatically launch a series of

analyses and efficiently explore a wide parametric space. For example, on UNIX using

the TCSH shell, the following executable file will sequentially run 120 different analyses,

one for each unique combination of the specified input parameter values.

#!/bin/tcsh

module load ansys

foreach k ( 177 )

foreach dt ( 14 12 10 8 6 4 )

foreach t ( 0.0020 0.0010 0.0005 0.0001 )

foreach h ( 0.020 0.015 0.010 0.005 0.001 )

ansys100 –p ansysrf –b –fincond $k –dtsat $dt –thick $t –high $h < batch.dat > output.txt

end

end

end

end

In this example version 10.0 of the ANSYS University Advanced product (ansysrf) is

employed. Further, use of “<” and “>” in place of “-i” and “-o” is preferred in UNIX.

Regardless of the method employed to setup and run the analyses, results are written to a

plain text file with the filename specified in the 5th line from the bottom, “data.txt” in

this case (filename and extension are specified separately). This output file will contain

values for the following input and output parameters:

• fincond – input fin thermal conductivity, W/mK

• high – input fin height, m

• thick – input fin thickness, m

• dtsat – input base temperature rise above saturation, °C

• qbase – heat flow into the half of the fin base per unit length, W/m

• qside – heat flow out of one side of the fin per unit length, W/m

• qtip – heat flow out of half of the fin tip per unit length, W/m

Appendix G: Boiling Fin Analysis Batch File 324 Individual base, side, and tip heat flows are calculated for the corresponding sides of the

half-symmetry finite-element model. Thus, the total fin heat dissipation may be

caluculated as qbase + qside + qtip, with units of watts per unit fin length, as the model

is 2-D. Heat balance and an accurate solution is achieved when qbase – (qside + qtip)

≈ 0. Depending on the fin dimensions and thermal conductivity, the number of elements

along the fin height (hiel) and half thickness (thel) may need to be modified to provide

an accurate solution. The batch file shown in Section G.1 includes an equation that bases

the number of height elements on the height of the fin. This relationship produced

acceptable results for many of the analyses performed for Chapter 7. However, it will not

be appropriate for all fins and, in particular, requires significant modification when a

highly anisotropic fin thermal conductivity is specified.

With minor modifications, the batch file may be read into ANSYS™ interactive mode as

an input file to allow more detailed viewing and analysis of solution results. Figure G.1

shows an annotated color contour plot of the solution based on input parameters

corresponding to the experimental boiling heat sink discussed in Section 7.1, with a base

temperature 14°C above saturation. Numerical output corresponding to this solution is: 177 1.E-02 7.E-04 14 264.008964 260.660323 2.07825938 X.

Note that heat balance is achieved within 0.5%.

Appendix G: Boiling Fin Analysis Batch File 325

Figure G.1: Contour plot of fin temperatures resulting from the ANSYS™ batch file shown in Section G.1 with input parameters

corresponding to the experimental boiling heat sink discussed in Section 7.1 and a base temperature 14°C above saturation.

fin base symmetry plane fin tip

∆Tsat (°C)


G.1 ALUMINUM FIN BATCH FILE /batch !if to be read into interactive session, remove this line

/units,si

! Parameter values passed from command line:

! fincond = fin thermal conductivity

! thick = fin thickness

! high = fin height

! dtsat = fin base superheat

hiel = 1200*high/0.020 !number of element divisions along fin height

thel = 100 !number of element divisions along 1/2 thicknesses

fincondx=fincond

fincondy=fincond !modify if material is anisotropic

tsat = 0 !bulk temp. used in heat transfer coeff. specification below

!* enter preprocessor

/PREP7

!* select element type

ET,1,PLANE55

!* select material property temperature based on element surface temp

KEYOPT,1,1,1

KEYOPT,1,3,0

KEYOPT,1,4,0

KEYOPT,1,8,0

KEYOPT,1,9,0

!* material properties

UIMP,1,KXX, , , fincondx,

UIMP,1,KYY, , , fincondy,

!*

MPTEMP,1,0

MPTEMP,2,4.82

MPTEMP,3,7.42

MPTEMP,4,9.31

MPTEMP,5,11.73

MPTEMP,6,12.61

MPTEMP,7,13.49


MPTEMP,8,14.45

MPTEMP,9,14.91

MPDATA,HF,1,1,200

MPDATA,HF,1,2,2139

MPDATA,HF,1,3,4535

MPDATA,HF,1,4,6126

MPDATA,HF,1,5,7855

MPDATA,HF,1,6,8283

MPDATA,HF,1,7,8558

MPDATA,HF,1,8,8574

MPDATA,HF,1,9,8508

!* create area

RECTNG,0,high,0,thick/2,

FLST,5,2,4,ORDE,2

FITEM,5,2

FITEM,5,4

CM,_Y,LINE

LSEL, , , ,P51X

!*

CM,_Y1,LINE

CMSEL,,_Y

LESIZE,_Y1, , ,thel,1,

CMDEL,_Y

CMDEL,_Y1

!*

FLST,5,2,4,ORDE,2

FITEM,5,1

FITEM,5,3

CM,_Y,LINE

LSEL, , , ,P51X

!*

CM,_Y1,LINE

CMSEL,,_Y

LESIZE,_Y1, , ,hiel,1,

CMDEL,_Y

CMDEL,_Y1


!*

MSHKEY,0

CM,_Y,AREA

ASEL, , , , 1

CM,_Y1,AREA

CHKMSH,'AREA'

CMSEL,S,_Y

!*

AMESH,_Y1

!* exit preprocessor and enter solver

FINISH

/SOLU

!* find corner node numbers

!* sw node

NSEL,S,LOC,X,0

NSEL,R,LOC,Y,0

*get,swnode,node,0,num,min

ALLSEL,ALL

!* se node

LSEL,S, , , 2

NSLL,S,1

NSEL,R,LOC,Y,0

*get,senode,node,0,num,min

ALLSEL,ALL

!* ne node

LSEL,S, , , 2

NSLL,S,1

NSEL,R,LOC,Y,thick/2

*get,nenode,node,0,num,min

ALLSEL,ALL

!* nw node

NSEL,S,LOC,Y,thick/2

NSEL,R,LOC,X,0

*get,nwnode,node,0,num,min

ALLSEL,ALL

!


!* pick base nodes

NSEL,S,LOC,X,0

D,ALL,TEMP,dtsat,

!select all

ALLSEL,ALL

!* apply convection on lines 2&3 and transfer to nodes/elements

FLST,2,2,4,ORDE,2

FITEM,2,2

FITEM,2,-3

SFL,P51X,CONV,-1, ,tsat, ,

sbctran

!* solve

/STAT,SOLU

SOLVE

!* exit solver, enter postprocessing

FINISH

/POST1

!* average base flux

!select base nodes

LSEL,S, , , 4

NSLL,S,1

FLST,5,2,1,ORDE,2

FITEM,5,swnode

FITEM,5,nwnode

NSEL,U, , ,P51X

!get node data

*get,numnodes,node,0,count

*get,lownode,node,0,num,min

curnode=lownode

tfsum=0

*do,i,1,numnodes

*get,curtf,node,curnode,tf,X

tfsum=tfsum+curtf

*get,nextnode,node,curnode,nxth

curnode=nextnode

*enddo


ALLSEL,ALL

!get corner node data

*get,swtfx,node,swnode,tf,X

*get,nwtfx,node,nwnode,tf,X

!* calculate base flux

tfsum=tfsum+(swtfx+nwtfx)/2

tfavg=tfsum/(numnodes+1)

qbase=tfavg*thick/2

!*

!* average tip flux

!select tip nodes

LSEL,S, , , 2

NSLL,S,1

FLST,5,2,1,ORDE,2

FITEM,5,senode

FITEM,5,nenode

NSEL,U, , ,P51X



curnode=lownode

tfsum=0

*do,i,1,numnodes

*get,curtf,node,curnode,tf,X

tfsum=tfsum+curtf


curnode=nextnode

*enddo

ALLSEL,ALL

*get,setfx,node,senode,tf,X

*get,netfx,node,nenode,tf,X

tfsum=tfsum+(setfx+netfx)/2


qtip=tfavg*thick/2

!*

!* average side flux

!select side nodes


LSEL,S, , , 3

NSLL,S,1

FLST,5,2,1,ORDE,2

FITEM,5,nwnode

FITEM,5,nenode

NSEL,U, , ,P51X



curnode=lownode

tfsum=0

*do,i,1,numnodes

*get,curtf,node,curnode,tf,Y

tfsum=tfsum+curtf


curnode=nextnode

*enddo

ALLSEL,ALL

*get,netfy,node,nenode,tf,Y

*get,nwtfy,node,nwnode,tf,Y

tfsum=tfsum+(netfy+nwtfy)/2


qside=tfavg*high

!* output results to file

/output,data,txt,,APPEND

*MSG,INFO,fincond,high,thick,dtsat,qbase,qside,qtip

%G %G %G %G %G %G %G X

/output

FINISH

/EXIT,NOSAVE

/eof


G.2 SILICON FIN BATCH FILE MODIFICATIONS

The batch file used for modeling silicon fins was very similar to the one shown above in

Section G.1. The only significant difference is that the material thermal conductivity is

expressed as a function of temperature, in an input table very similar to that used to

specify the temperature dependent heat transfer coefficient. Thermal conductivity was

calculated for each temperature point used in the specification of the heat transfer

coefficient using the curve fit equation shown in Fig. 7.14.

Thus, instead of the following command from the aluminum input file which specifies

constant fin thermal conductivities along the fin height and thickness:UIMP,1,KXX, , , fincondx,

UIMP,1,KYY, , , fincondy,

the following commands were used to express thermal conductivity as a function of the

difference between the material temperature and the saturation temperature. Note that if

the thermal conductivity in the y-direction is not specified explicitly (as in this example),

the material is assumed to be isotropic, and the values specified for KXX are used in all

directions.

!* material properties

!* spacing = 0.3 mm

MPTEMP,1,0.00

MPTEMP,2,3.77

MPTEMP,3,4.35

MPTEMP,4,4.79

MPTEMP,5,5.41

MPTEMP,6,6.36

MPTEMP,7,8.13

MPTEMP,8,11.80

MPTEMP,9,15.95

MPTEMP,10,19.89

MPTEMP,11,22.36


MPDATA,HF,1,1,0.0

MPDATA,HF,1,2,2026.7








MPDATA,HF,1,10,2174.3

MPDATA,HF,1,11,2001.8

MPDATA,KXX,1,1,129.8











As the silicon heat transfer coefficients are different for each fin spacing, the input file

must be modified accordingly. Heat transfer coefficients were extracted directly from

Fig. 5.1 and are shown in Table G.1.


Table G.1: Temperature (°C) dependent boiling heat transfer coefficients (W/m2) for

silicon channels, based on the data of Fig. 5.1.

∆T sat h ∆T sat h ∆T sat h ∆T sat h ∆T sat h0.00 0.0 0.00 0.0 0.00 0.0 0 0.0 0 0.08.59 888.6 8.00 958.5 7.08 1072.8 3.84 2010.1 3.77 2026.7

11.94 1371.9 10.84 1499.7 9.56 1713.5 7.29 2257.6 4.35 2775.116.73 2034.9 13.24 1919.5 11.72 2173.8 8.69 2907.0 4.79 3442.219.08 2345.8 15.82 2149.9 14.02 2420.0 11.49 2962.8 5.41 3897.120.35 2547.0 17.89 2405.7 16.58 2606.1 14.93 2875.9 6.36 3957.621.61 2827.6 19.48 2660.3 18.80 2775.0 18.29 2804.6 8.13 3620.022.31 3065.4 20.57 2970.5 20.37 3004.0 20.65 2903.3 11.80 2907.623.07 3410.3 21.24 3300.5 21.43 3266.6 23.39 2924.2 15.95 2388.323.39 3549.4 21.79 3610.0 22.18 3556.9 19.89 2174.323.75 3674.0 22.27 3916.9 22.82 3638.3 22.36 2001.824.12 3776.3 22.75 4238.3 23.33 3751.824.72 3901.4 23.39 4492.9 23.93 3805.925.74 4082.0

δ ≥ 2.0 mm δ = 0.7 mm δ = 0.3 mmδ = 1.0 mmδ = 1.5 mm

G.3 AVERAGE BOILING FIN HEAT TRANSFER COEFFICIENT

As discussed in Section 7.2.4, results of the thermal conductivity parametric study

suggest that the average heat transfer coefficient over the active heat dissipating area of a

fin is invariable to fin thermal conductivity. While fin temperature at a given location

increases with increasing thermal conductivity and the applied boiling heat transfer

coefficients are temperature dependent, the active fin area increases with increasing

conductivity to maintain the same average heat transfer coefficient. As a result, single fin

heat dissipation results in the asymptotically “high fin” limit for a given thickness and

base temperature simply scale with the square root of thermal conductivity, following

Eq. (7.4). A small set of additional FEA runs were executed to explicitly demonstrate

this behavior.

Single fin heat dissipation results were generated for 0.4 mm thick fins with a base

temperature 12°C above saturation, employing the temperature-dependent EDM


aluminum surface boiling heat transfer coefficients. Initially, large fin heights were used

to identify the maximum “high fin” asymptotic limits for each thermal conductivity

value. The analysis was then iterated to find the fin height for each which provides 95%

of the maximum. Table G.2 shows the effects of increased fin thermal conductivity on fin

heat dissipation and fin height required to achieve 95% of the maximum “high fin”

asymptotic limit.

Table G.2: Single fin analysis results for 0.4 mm thick fins with a base temperature 12°C

above saturation, based on EDM aluminum surface boiling heat transfer coefficients.

Fin Thermal Conductivity

(W/mK)

Maximum Heat Dissipation per Unit Fin Length (W/m)

95% of Maximum Heat Dissipation per

Unit Fin Length (W/m)

Fin Height at 95% of Maximum Heat Dissipation (mm)

177 317 301 3.7400 478 454 5.61000 758 720 9.02000 1072 1019 12.8

Figure G.2 shows that the fin heat dissipation results of Table G.2 do indeed scale with

the square root of fin thermal conductivity. The exponential curve shown in Fig. G.2 was

obtained using Microsoft Excel curve fitting features. In fact, the fin height required to

achieve 95% of these maximum values also scales with the square root of fin thermal

conductivity. This follows the logic that if the maximum heat dissipation scales with the

square root of thermal conductivity, and the average heat transfer coefficient over the

active heat dissipating fin area is constant, the active heat dissipating fin area must also

scale with the square root of fin thermal conductivity. There is a minute discrepancy in

the fin height/thermal conductivity relationship due to the fact that the fin tip is active in

the FEA model. A slightly more accurate correlation may be achieved by considering the

effective fin height correction of Eq. (7.7) to include the tip area, as shown in Fig. G.3.


y = 23.58x0.50

0

200

400

600

800

1000

1200

0 500 1000 1500 2000 2500

Thermal Conductivity (W/mK)

Sing

le F

in H

eat D

issi

patio

n (W

/m)

Figure G.2: Variation of single fin heat dissipation with thermal conductivity for

asymptotically-high, 0.4 mm thick fins, with a 12°C base superheat, assuming EDM

aluminum boiling heat transfer coefficients.

y = 0.29x0.50

0

2

4

6

8

10

12

14

0 500 1000 1500 2000 2500


Effe

ctiv

e Fi

n H

eigh

t, H

+t/2

(mm

)

Figure G.3: Effective fin height to achieve 95% of maximum, for fins of Table G.2.


Figure G.4 contains surface temperature profiles from the numerical solution for the fins

of Table G.2. While fin temperature at a given location increases with increasing thermal

conductivity, the shape of the temperature profile along the fin height is unchanged. This

can be seen more clearly when the distance along the fin height is normalized by the

“95%” fin height for each, as it is in Fig. G.5 where the individual thermal conductivity

curves are shown to collapse to a single temperature profile. As a result, not only are the

average heat transfer coefficients for these fins the same, heat transfer coefficient profiles

are also identical when based on normalized fin height.

0

2

4

6

8

10

12

0 2 4 6 8 10 12 14

Distance Along Fin Height (mm)

∆∆ ∆∆T

sat (

°C)


Figure G.4: Surface temperature profiles for the fins of Table G.2.


0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0

Fractional Distance Along Fin Height

∆∆ ∆∆T

sat (

°C)



along fin height.

Analyses similar to those above were also performed for 0.3 mm thick fins with a 22°C

base superheat, assuming boiling heat transfer coefficients for polished silicon channels

with a spacing of 0.3 mm. A constant (temperature-independent) thermal conductivity of

120 W/mK was assumed for the baseline silicon case. Figure G.6 shows the square root

dependency of heat dissipation on thermal conductivity. Table G.3 also shows the effect

of increased fin thermal conductivity on maximum fin heat dissipation as well as the fin

height required to achieve 50% of the maximum “high fin” asymptotic limit. The 50%

height was used instead of 95% to illustrate the fact that as long as the same fraction of

the maximum heat dissipation is maintained, the square root dependency still holds, as

shown in Fig. G.7.


y = 27.22x0.50

0

200

400

600

800

1000

1200

1400

0 500 1000 1500 2000 2500


Sing

le F

in H

eat D

issi

patio

n (W

/m)

Figure G.6: Variation of maximum single fin heat dissipation with thermal conductivity

for asymptotically-high, 0.3 mm thick fins, with a 22°C base superheat, assuming 0.3 mm

polished silicon channel heat transfer coefficients.

Table G.3: Single fin analysis results for 0.3 mm thick fins with a base temperature 22°C

above saturation, based on 0.3 mm polished silicon channel heat transfer coefficients.

Fin Thermal Conductivity

(W/mK)

Maximum Heat Dissipation per Unit Fin Length (W/m)

50% of Maximum Heat Dissipation per

Unit Fin Length (W/m)

Fin Height at 50% of Maximum Heat Dissipation (mm)

120 299 150 1.6400 547 273 3.11000 865 432 4.92000 1223 612 7.0


y = 0.16x0.50

0

1

2

3

4

5

6

7

8

0 500 1000 1500 2000 2500


Effe

ctiv

e Fi

n H

eigh

t, H

+t/2

(mm

)

Figure G.7: Effective fin height required to achieve 50% of maximum, for the fins of

Table G.3.

Fin temperature profile results corresponding to the fins of Table G.3 appear in Figs. G.8

and G.9. As before, while fin temperature at a given absolute distance from the base

increases with increasing thermal conductivity, the shape of the temperature profiles are

identical when based on normalized fin height.


02468

10121416182022

0 1 2 3 4 5 6 7 8

Distance Along Fin Height (mm)

∆∆ ∆∆T

sat (

°C)


Figure G.8: Surface temperature profiles for the fins of Table G.3.

02468

10121416182022

0.0 0.2 0.4 0.6 0.8 1.0

Fractional Distance Along Fin Height

∆∆ ∆∆T

sat (

°C)



along fin height.


Thus, single fin heat dissipation and fin height results for a given fin thickness and base

superheat may be extrapolated to other fin thermal conductivities by exploiting the square

root dependence demonstrated here. The reader is warned that this relationship may not

hold if:

• the fin thermal conductivity is very low and temperature gradients through its

thickness are significant

• the fin is very short so that heat dissipation from the tip is relatively large

• the fin thermal conductivity is temperature dependent or anisotropic

Most importantly, these analyses have focused on the isolated parametric effects of

thermal conductivity and have not considered other ramifications of changing the fin

material. Boiling heat transfer coefficients will be different for different materials, and

channel boiling curves for any unique combination of fluid, heater material, and surface

finish should be characterized individually.

343

APPENDIX

H

EXPERIMENTAL SILICON HEAT SINK DESIGN

As shown in Chapter 7, boiling heat sinks and the associated high performance levels

achieved will require a large power input in an experimental evaluation. Heat was

delivered to the experimental aluminum heat sink discussed in Section 7.1 via a bulky

cartridge heater assembly. Alternatively, there would be many advantages to fabricating

an experimental heat sink out of silicon.

Self-heating, single parallel-plate channels and plate fin heat sinks could be fabricated out

of silicon wafer with an appropriately selected dopant concentration/electrical resistivity.

Appropriately cut pieces of double-side polished test grade silicon wafer could be fused

together to providing heat sink geometry and dimensions within the range of interest.

Figure H.1 shows an illustration of a proposed silicon heat sink. The structure is

composed of twenty-nine 0.7 mm thick pieces of double-side polished silicon wafer. This

arrangement, 0.7 mm thick fins with a 2.1 mm spacing (three 0.7 mm thick wafers

between each single-wafer fin), is very similar to the experimental boiling heat sink

discussed in Section 7.1. Electrodes would be sputtered on the back side of the heat sink

to provide electrical contact with the back edge of each wafer, eliminating the need for

good electrical contact between wafer surfaces.

Appendix H: Experimental Silicon Heat Sink Design 344 The overall electrical resistance of the heat sink structure, Fig. H.1, could be tailored to

match the capacities of available computer-controlled power supplies, and the heat sink

could provide its own Joule heating. The compactness of the self-heating heat sink would

provide great benefits in the design of the experimental apparatus and eliminate various

complexities associated with attaching a heating element to the heat sink base. Further,

the consistent use of silicon cut from the same batch of wafers would provide similarity

of boiling surface characteristics.

Figure H.1: Illustration of proposed silicon heat sink design.

Appendix H: Experimental Silicon Heat Sink Design 345 Finite element analysis was pursued to quantify the combined thermal-electrical

performance of a self-heating heat sink. Figure H.2 shows the geometry of interest, a

single boiling fin with its associated heat sink base. In addition to the wafer-thickness-

dictated fin thickness and spacing, the fin is 20 mm long and 5 mm high. Similar to the

boiling fin analyses discussed in Chapter 7, a temperature-dependent boiling heat transfer

coefficient was applied to the fin surfaces as well as the exposed base area. The electrode

width was varied to provide the most uniform heat delivery to the fin base and exposed

heat sink base areas.

Figure H.2: Model geometry for finite element analysis of single silicon heat sink fin.

Appendix H: Experimental Silicon Heat Sink Design 346

Figure H.3: Electrical results: a) voltage distribution, and b) current density.

Figure H.3 shows voltage and current density distributions in the fin from the FEA

solution. A voltage difference of 12 V was applied between the 3 mm wide electrodes. A

silicon electrical resistivity of 0.01 Ωm was assumed. The voltage distribution is regular

and, as expected, symmetric. The current density is also as expected—greatest near the

electrodes and decreasing through the thickness of the base and into the fin.


Figure H.4: Electrical results: Joule heating distribution.

Despite the fact that the entire structure is electrically resistive due to a uniform dopant

concentration/electrical resistivity of the silicon, it is expected that the majority of the

heat will be generated in the vicinity of the electrodes where the current density is

greatest. Figure H.4 shows the distribution of Joule heating. The scale of the contours is

logarithmic, showing that, indeed, the majority of the heat is generated near the

electrodes. A more detailed analysis of the results show that 98% of the heat generated in

the entire structure is generated in the heat sink base, with 87% being generated in the

first 6 mm of the 10 mm thick bases. Less than 2% of the heat is generated in the fin

itself.


Figure H.5: Temperature results, quarter symmetry model of heat sink.

Numerical models with 2, 3, and 4 mm wide electrodes were studied, and it was

determined that 3 mm wide electrodes provided the most uniform heat delivery to the fin

base and exposed heat sink base area for this geometry. Numerical models of the

complete heat sink (quarter symmetry) were then constructed to verify these results.

Figure H.5 shows temperature results for the quarter symmetry model of the heat sink

with geometry and properties corresponding to the single fin analysis of the previous

figures (0.7 mm fin thickness, 2.1 mm spacing, 5 mm fin height, 20 mm length, 10 × 20 ×

20.3 mm base, 3 mm wide electrodes, silicon k = 140 W/mK, ρ = 0.01 Ωm, 12 V). Based

on these results, it was determined that this heat sink has an overall electrical resistance

of 1.36 Ω, generating 106 W of heat with an applied voltage of 12 V. Furthermore, the

base design was deemed sufficient to the fin bases, despite the uneven Joule heating near

the electrodes.

Appendix H: Experimental Silicon Heat Sink Design 349 Ultimately, the behavior and performance of a silicon boiling heat sink of this sort will be

determined by the quality of electrical contact between the electrodes and wafers and

thermal contact between the wafers themselves. Good contact between the sputtered

electrodes and the edges of each wafer is necessary to ensure uniform heating in the

structure. Strong thermal contact between the wafers is required to deliver the heat

generated in the base of the heat sink between the fins into the fins for removal by the

boiling liquid. If it is determined that acceptable thermal contact cannot be achieved

between wafers, a single, thicker (3×) piece of silicon could be used in each inter-fin

space. Alternately, the fins could be made from silicon with a lower resistivity than the

inter-fin “spacers,” so that the fraction of heat expected to be dissipated by the fin would

be generated in the base part of the fin wafer, with less heat generated in the silicon

between fins. With this arrangement, less heat would need to be transferred across the

wafer interfaces to provide the desired heat delivery.

Fabrication of this type of silicon heat sink structure was pursued in the University of

Minnesota’s Microtechnology Lab (MTL). Unfortunately, the oxidation/diffusion furnace

process that was relied on to fuse the polished silicon surfaces failed to bond the dice

together, even after a variety of aggressive cleaning processes. Further, it also became

apparent that even if it had, it would be difficult to maintain die alignment and prevent

the creation of additional heat transfer area and unwanted nucleation sites along the dice

edges. Figure H.6 shows a photograph of some dice after a fusing attempt.

The design above was performed before the channel boiling experiments of Chapter 5

and, therefore, before the boiling heat sink design analyses of Chapter 7. The geometry

explored above is not optimum by far, and the approach may or may not be feasible for

sinks consisting of a larger number of thinner fins spaced much more closely together (≈

0.3 mm). However, the analyses of Chapter 7 do support the desire to test a silicon heat

sink with highly polished surfaces.


Figure H.6: Photograph of dies after attempted fusing.

351

APPENDIX

I

BOILING CURVE DATA TABLES

The channel boiling curve data displayed graphically in Chapter 5 are presented here in

tabular form.

Table I.1: Boiling curve data of Fig. 5.1 for symmetric 20 × 30 mm polished silicon

heater channels.

∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)3.8 7.63 7.3 16.4 7.1 7.60 8.0 7.664.4 12.1 8.7 25.2 9.6 16.4 10.8 16.34.8 16.5 11.5 34.0 11.7 25.5 13.2 25.45.4 21.1 14.9 42.9 14.0 33.9 15.8 34.06.4 25.2 18.3 51.3 16.6 43.2 17.9 43.08.1 29.4 20.7 60.0 18.8 52.2 19.5 51.811.8 34.3 23.4 68.4 20.4 61.2 20.6 61.115.9 38.1 21.4 70.0 21.2 70.119.9 43.2 22.2 78.9 21.8 78.722.4 44.8 22.8 83.0 22.3 87.2

23.3 87.5 22.8 96.423.9 91.1 23.4 105

1.0 mm spacing 1.5 mm spacing0.3 mm spacing 0.7 mm spacing

Appendix I: Boiling Curve Data Tables 352 Table I.2: Boiling curve data of Fig. 5.2 for asymmetric 20 × 30 mm polished silicon

heater channels.

∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)4.8 7.38 6.4 7.56 8.7 7.63 8.2 7.615.5 16.3 8.0 16.2 10.7 16.4 11.2 17.66.6 25.5 9.5 25.4 13.5 25.3 13.7 25.68.5 34.7 12.0 34.1 16.0 34.1 16.0 35.313.1 43.5 14.6 42.9 18.4 43.0 17.9 43.414.9 45.7 17.5 51.6 20.1 51.9 19.4 52.416.1 47.3 20.2 60.4 21.3 61.1 20.3 61.317.9 49.2 22.1 68.7 22.1 70.0 21.3 70.420.4 52.2 22.9 73.0 22.8 78.7 22.2 79.422.8 54.3 23.3 76.2 23.3 87.7 22.7 87.324.8 56.1 24.2 78.1 23.8 96.6 23.2 96.027.1 58.4 25.0 79.4 24.3 104 23.7 104

1.5 mm spacing 1.6 mm spacing0.3 mm spacing 0.7 mm spacing


heater channels.

∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)1.5 10.4 4.7 10.23.0 16.4 8.8 22.74.1 22.6 12.2 35.06.5 28.6 16.5 47.29.1 35.3

0.3 mm spacing 0.6 mm spacing

Appendix I: Boiling Curve Data Tables 353 Table I.4: Boiling curve data of Fig. 5.4 for asymmetric 20 × 20 mm scratched silicon

heater channels.

∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)4.3 5.12 0.6 4.83 2.4 5.23 4.2 4.928.6 11.0 1.7 11.6 4.2 11.6 7.4 11.111.5 17.2 2.3 16.4 5.4 16.8 9.8 17.113.2 24.2 3.3 22.6 6.9 22.9 12.3 23.313.9 30.3 4.4 27.5 8.5 28.7 13.8 29.314.3 36.8 5.7 35.0 10.1 34.9 14.9 35.414.3 36.9 8.0 41.0 16.3 57.7 15.5 48.014.9 49.9 15.3 46.6 23.8 73.1 16.0 60.215.0 49.4 16.6 73.115.6 62.8 16.8 77.416.1 76.1 17.3 87.616.5 87.3 18.0 10117.3 10218.2 115

large spacing limit 0.3 mm spacing 0.7 mm spacing 1.0 mm spacing

Table I.5: 30°C subcooled boiling curve data of Fig. 5.6 for asymmetric polished silicon

heater channels.

∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)-4.6 10.5 -6.1 5.81 -5.3 11.23.2 22.7 -0.7 10.7 0.4 17.17.3 34.8 2.2 22.9 4.4 23.59.9 47.2 3.5 28.7 7.2 29.413.1 59.6 5.3 34.7 10.4 35.716.0 72.2 9.5 41.2 11.2 48.118.3 85.4 13.4 43.9 11.8 60.319.7 94.4 14.4 90.822.3 111 15.8 10224.1 121 17.7 11626.4 134 19.1 12627.3 139 21.6 14128.4 146 23.0 15130.5 157 24.2 158

large spacing limit 0.3 mm spacing 0.7 mm spacing

Appendix I: Boiling Curve Data Tables 354

Table I.6: Boiling curve data of Fig. 5.7 for asymmetric aluminum heater channels.

∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)4.8 10.3 4.9 10.8 7.2 24.36.3 21.4 6.4 23.1 7.8 31.27.4 33.6 7.4 33.5 8.2 35.88.4 44.9 8.7 49.1 8.8 42.79.3 57.0 9.8 62.4 9.4 50.310.2 68.7 10.6 74.2 10.1 59.211.0 80.6 11.5 86.4 11.2 68.811.7 92.1 12.3 97.6 12.1 75.712.6 104 13.2 104 13.6 82.113.5 115 16.1 117 17.4 92.114.9 12716.9 134

∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)6.8 9.56 6.2 9.769.3 21.2 9.2 21.311.5 33.0 11.0 32.912.8 44.5 12.5 44.613.9 56.4 15.5 68.015.1 68.1 20.7 91.416.2 80.0 26.4 10317.5 91.718.9 10320.8 11523.1 12724.7 13226.9 138

∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)∆T sat

(°C)q "

(kW/m2)11.9 20.9 12.1 20.9 10.8 21.113.8 32.9 14.6 32.6 13.8 32.715.4 44.5 17.8 56.1 16.0 44.516.7 56.0 19.5 67.8 18.1 55.917.9 67.8 21.6 79.6 20.7 67.620.7 91.3 24.6 91.5 28.3 79.823.9 115 29.2 103 35.8 85.826.2 127 39.6 11529.8 139

EDM

600 grit0.4 mm spacing0.7 mm spacinglarge spacing limit

400 grit

large spacing limit 1.0 mm spacing 0.5 mm spacing

0.5 mm spacinglarge spacing limit

Appendix I: Boiling Curve Data Tables 355

Table I.7: Channel CHF data of Fig. 5.8.

Spacing (mm)

Aspect Ratio (L /δ )

q "CHF

(kW/m2)CHF Ratio

18.8 1.1 113 0.9818.8 1.1 111 0.9718.8 1.1 108 0.943.0 6.7 109 0.953.0 6.7 107 0.932.0 10.0 110 0.962.0 10.0 106 0.931.6 12.5 107 0.931.5 13.3 106 0.931.5 13.3 104 0.910.7 28.6 83.7 0.730.7 28.6 80.9 0.710.3 66.7 60.8 0.530.3 66.7 60.6 0.53

Polished Si, Asymmetric Heating, 2x3

Spacing (mm)


q "CHF

(kW/m2)CHF Ratio

18.8 1.1 122 1.0618.8 1.1 117 1.031.0 20.0 103 0.900.6 31.2 104 0.910.6 31.2 96.3 0.840.3 66.7 42.3 0.37

18.8 1.1 115 1.011.0 20.0 101 0.890.7 28.6 76.9 0.670.3 66.7 49.4 0.43

CHF Ratio

Polished Si, Asymmetric Heating, 2x2

Scratched Si, Asymmetric Heating, 2x2

Spacing (mm)


q "CHF

(kW/m2)

Spacing (mm)


q "CHF

(kW/m2)CHF Ratio

18.8 1.1 133 1.018.8 1.1 133 1.01.0 20.0 117 0.91.0 20.0 104 0.80.5 40.0 104 0.80.5 40.0 97.2 0.7

18.8 1.1 138 1.018.8 1.1 138 1.00.5 40.0 103 0.80.5 40.0 91.5 0.7

18.8 1.1 139 1.018.8 1.1 139 1.00.7 30.3 115 0.80.7 30.3 103 0.80.4 52.6 85.9 0.60.4 52.6 79.8 0.6

EDM Al, Asymmetric Heating, 2x2

400 grit Al, Asymmetric Heating, 2x2

600 grit Al, Asymmetric Heating, 2x2

Spacing (mm)

Modified Aspect Ratio

√2(L /δ )

q "CHF

(kW/m2)CHF Ratio

18.8 1.1 115 1.003.0 9.4 106 0.923.0 9.4 103 0.902.0 14.1 108 0.951.5 18.9 108 0.941.5 18.9 107 0.931.5 18.9 106 0.921.2 22.8 99.9 0.871.0 28.3 90.1 0.790.7 42.9 73.7 0.640.7 42.9 71.6 0.630.5 56.6 63.1 0.550.3 94.3 46.6 0.410.3 94.3 46.6 0.410.3 94.3 45.5 0.40

Polished Si, Symmetric Heating, 2x3

356

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