International Journal of Multiphase Flow 59 (2014) 84–101

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International Journal of Multiphase Flow

journal homepage: www.elsevier .com/locate / i jmulflow

Review

Proposed models, ongoing experiments, and latest numericalsimulations of microchannel two-phase flow boiling

0301-9322/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijmultiphaseflow.2013.10.014

⇑ Corresponding author. Tel.: +41 021 6935981.E-mail address: john.thome@epfl.ch (J.R. Thome).

S. Szczukiewicz, M. Magnini, J.R. Thome ⇑Laboratory of Heat and Mass Transfer (LTCM), Ecole Polytechnique Fédérale de Lausanne (EPFL), EPFL-STI-IGM-LTCM, Station 9, CH-1015 Lausanne, Switzerland

a r t i c l e i n f o

Article history:Received 16 July 2013Received in revised form 28 October 2013Accepted 29 October 2013Available online 9 November 2013

Keywords:Two-phase flowMicrochannelsFlow instabilityHeat transferEvaporationNumerical simulations

a b s t r a c t

A survey of the most recent work aimed at physically characterizing local heat transfer in flow boiling inmicrochannels is presented. This includes recent experimental work, new flow boiling prediction meth-ods, and numerical simulations of microchannel slug flows with evaporation. Some significant develop-ments in the measurement techniques provide simultaneous flow visualizations and measurements of2D temperature fields of multi-microchannel evaporators. In particular, information on inlet micro-ori-fices has been gained as well as better ways to reduce such heat transfer and pressure drop data for veryhigh resolution data (10,000 pixels at rate of 60 Hz). First of all, flow patterns are seen to have a signif-icant influence on the heat transfer trends in microchannels (just like in macrochannels), and thus needto be accounted by visualization during experiments and during modeling. A clear distinction betweensteady, unsteady, well- and maldistributed flows needs to be made to avoid any confusion when present-ing and comparing the heat transfer coefficient trends. In reducing the raw data to local heat transfercoefficients, the calculated values of several terms involved in the heat transfer coefficient determinationare influenced by the data reduction procedure, especially the way to deduce the local saturation pres-sures/temperatures, and may lead to conflicting trends and errors approaching 100% in local heat transfercoefficients if done inappropriately. In addition to experiments, two-phase CFD simulations are emergingas a tenable tool to investigate the local heat transfer mechanisms, especially those details not accessibleexperimentally. In particular, a new prediction method based on numerical simulation results capturesthe heat transfer in the recirculating liquid flow between elongated bubbles. Thus, it is shown here thattargeted computations can provide valuable insights on the local flow structures and heat transfer mech-anisms, and thus be used to improve the mechanistic boiling heat transfer prediction methods.

� 2013 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852. State-of-the-art of microscale two-phase flow boiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

2.1. Microchannel flow boiling heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852.2. Infra-red camera measurements applied to microchannels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3. Numerical simulations of two-phase flow boiling in microchannels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

3.1. Numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 893.2. Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4. Discussion on the most recent experimental and numerical results of heat transfer studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

4.1. Contribution of numerical simulations to the heat transfer modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.2. Heat transfer coefficient data reduction in multi-microchannels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 934.3. Stable and unstable two-phase heat transfer coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101 85

1. Introduction

A noticeable global tendency towards miniaturization driven bythe micro-electronics industry is bringing ever greater attention tomulti-microchannel two-phase flow evaporation as the mostadvantageous cooling process, utilizing the latent heat of evapora-tion to extract the heat in an energy efficient manner. As a result ofthe enhanced thermal performance compared to other processes,better axial temperature uniformity (Agostini et al., 2008b), re-duced coolant flow rates, and thus smaller pumping powers (Agos-tini et al., 2007) are obtained. Therefore, two-phase flow coolingprovides an excellent opportunity to continue the progress relativeto Moore’s law (Moore, 1965) associated with a tremendous chal-lenge of removing the continuously increasing heat fluxes dissi-pated by modern CPUs. The large amount of experimental work,theory and prediction methods have been reviewed in the pastfew years by Thome (2004, 2006), Cheng et al. (2008), Thomeand Consolini (2010) and Baldassari and Marengo (2013). Conse-quently, the present review has a narrow scope to look at somenew emerging issues regarding experimentation and the targeteduse of numerical simulations to gain local, transient insight intothe two-phase evaporation process and improvement of its heattransfer models.

Numerous micro-evaporators have been tested over the pastfew years. Their reported heat transfer performances, quantifiedin terms of local heat transfer coefficients, depend on the datareduction methods and assumptions each study used. Several as-pects, such as determination of the local fluid saturation tempera-ture, edge heat losses and heat spreading effects, and flow stability,need to be more carefully taken into account when comparing andmodeling heat transfer coefficient results. Obviously, only the val-ues calculated in the same manner, when merged together, willbring adequate conclusions on microchannel cooling capabilities.Moreover, the experimental techniques for measurements havesome technical limitations due to the small length and time scalesinvolved in flow boiling within microchannels. For instance, thetime response for thermocouples in point-wise temperature mea-surements is usually larger than the characteristic time of theinvestigated phenomena, whilst experiments with Micro ParticleImage Velocimetry (MicroPIV) still remain a challenging task atthese high flow velocities.

On the other hand, the recent advances on multiphase Compu-tational Fluid Dynamics (CFD) techniques, together with theincreasing processing power of computers, are making numericalsimulations an ever more powerful and reliable tool to providenew and detailed insights into the local hydrodynamics and ther-mal features of flow boiling in microchannels. The accuracy ofthe gas–liquid interface tracking and modeling of interfacial effectsis of primary importance for microscale-aimed computationalmethods, since the interface topology plays a fundamental role inflows within microdevices. Volume Of Fluid (VOF) (Hirt and Nic-hols, 1981) and Level Set (LS) (Sussman et al., 1994) methods areindeed the most widely used algorithms to model interfacial flows,due to their accuracy, robustness and easiness of implementation.In fact, the cited algorithms only add a ‘‘color function’’ equation(to identify each phase) to the single-phase flow equation set,which includes mass, momentum and energy equations, that arethen solved in a fixed computational grid. However, it is importantto remark that while numerical simulations provide an advancedtool to investigate two-phase flows which may also anticipateexperimental findings, the development of such computationalmethods requires detailed experimental measurements to validatetheir new algorithms.

The present paper is organized as follows: first the most recentexperimental findings on microscale two-phase flows are reviewed

in Section 2, then Section 3 outlines the latest advances in multi-phase numerical simulations in microchannels, next Section 4 dis-cusses their mutual contribution and related issues of datareduction, stable and unstable flow, and hydrodynamics to the heattransfer coefficient trends, and finally Section 5 summarizes themain conclusions of this work.

2. State-of-the-art of microscale two-phase flow boiling

In spite of the large number of papers published in the flowboiling domain, many aspects still need to be better explained inorder to provide a fuller understanding of local two-phase flowboiling characteristics. Such knowledge is essential to developmore reliable prediction methods that can be used for designingnew high-performance microchannel heat spreaders for micro-electronic and power electronic applications. This section presentsthe most recent experimental results in microscale two-phase flowresearch aiming to determine the contribution of geometricalparameters and other two-phase flow aspects on the heat transfercoefficient trends, which are then discussed in terms of two-phaseflow patterns and flow transitions.

2.1. Microchannel flow boiling heat transfer

Geometrical parameters, such as the hydraulic diameter and themanifold’s material and its shape, may significantly influencemicroscale two-phase flow results (Hetsroni et al., 2005). Forexample, several experimental studies reported significant heattransfer enhancement of flow boiling in small (Agostini and Bon-temps, 2005; Karayiannis et al., 2010) and narrow channels (Suet al., 2005) compared to conventional macrochannels. On theother hand, the measurement reliability decreases with decreasingtube diameter, as pointed out by Mishima and Hibiki (1996). Addi-tionally, numerous differences between micro- and macrochannelsmight be due to inaccurate dimensional measurements in themicroscale (Agostini et al., 2006), where the surface roughness ef-fect on heat transfer at low to medium vapor qualities in the slugflow regime is noticeable (Agostini et al., 2008d).

In particular, Agostini et al. (2003) showed that the flow boilingheat transfer coefficient of R134a increased by a factor of �1.74when decreasing the hydraulic diameter from 2.01 to 0.77 mm.The increase of heat transfer coefficient at low values of vaporquality with decreasing channel diameter is associated with thedecrease in the initial film thickness between the elongated bub-bles and the channel wall, as explained by Dupont and Thome(2005) based on the three-zone model of Thome et al. (2004). Forexample, Fig. 1 illustrates the local (width-averaged) heat transfercoefficient trend versus local vapor quality from inlet to outlet for atest section with 67 channels of 100 � 100 lm2 cross-section(Szczukiewicz et al., 2012b, 2013b), which were measured with avery fine resolution by means of a high-speed IR camera (for moredetails, refer to the following section). In the isolated bubble (IB)regime, in which bubbles might be smaller than the channel diam-eter or elongated, the heat transfer coefficient increases, and afterthe local maximum, it starts to decrease in the coalescing bubble(CB) regime. Then, when annular flow (AF) is formed, the heattransfer coefficient climbs considerably again, dramatically illus-trating the importance of flow patterns on the heat transfer pro-cess. In the IB regime, heat transfer increases without formationof dry patches at the end of the elongated bubbles, while in theCB regime, the heat transfer coefficient decreases due to the onsetof cyclical dryout as the vapor quality increases, which was ob-served visually by Borhani et al. (2010). The minimum coincideswith the churn flow regime (see the corresponding snapshot in

Fig. 1. Heat transfer coefficient trend for flow boiling of R236fa in a silicon multi-microchannel evaporator with orifices at the inlet of each channel restricting theflow by 50% (creating some flashed vapor to seed the evaporation process) at thechannel mass flux Gch ¼ 2299 kg m�2 s�1 and the base heat flux qb ¼ 48:6 W cm�2

(Szczukiewicz et al., 2012b, 2013b). Flow visualization images were recorded byRevellin (2005) in a sight glass at the exit of a single stainless steel tube of 0.79 mmdiameter.

86 S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101

Fig. 1). Afterwards, the heat transfer coefficient rises in the AF re-gime, when all the bubbles have coalesced and the liquid hasformed an annular ring with a continuous vapor core in the middleof the channel. It is an effect of convective boiling across the thin-ning liquid film. Therefore, the trend of the heat transfer coefficientstrongly depends on the flow pattern and the flow transitions be-tween them. These transitions are preliminary controlled by therate of bubble coalescence and they are commonly defined bythe vapor quality x, e.g. Agostini et al. (2008a), Revellin et al.(2008) and Ong and Thome (2011a).

It is worthwhile mentioning that the three-zone model ofThome et al. (2004) predicts the heat transfer coefficient to de-crease in the CB regime but to increase in the IB regime (two zoneswithout the third dryout intermittent zone). Recently, Costa-Patryand Thome (2012, 2013) have presented a new flow pattern-basedprediction method for heat transfer coefficient in microchannels.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18800

1000

1200

1400

1600

1800

2000

2200

x [−]

Gch

[kg

m−2

s−1

]

17.4 W cm−2

20.8 W cm−2

25.1 W cm−2

28.5 W cm−2

32.6 W cm−2

36.3 W cm−2

40.2 W cm−2

44.1 W cm−2

48.1 W cm−2

Fig. 2. Vapor quality at the minimum heat transfer coefficient calculated based onEq. (1) for the two-phase flow of R1234ze(E) in the test section with the inletrestrictions of expansion ratio ein;rest ¼ Wch

Win;rest¼ 2 and the base heat flux varying from

17.4 to 48:1 W cm�2. The graph was prepared using the experimental data ofSzczukiewicz (2012) considering only stable flows, namely the single-phase flowfollowed by two-phase flow without backflow and the flashing two-phase flowwithout backflow operating regimes.

The three-zone model of Thome et al. (2004) and the Cioncoliniand Thome (2011) annular flow model for convective boiling werejoined together, applying a new heat flux-dependent transitionfrom the coalescing elongated bubble regime to the annular flowregime:

xCB�AF ¼ 425qvql

� �0:1 Bo1:1

Co0:5 ð1Þ

where Bo ¼ q=ðGhlvÞ is the boiling number and Co ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffir= gDqD2

h

� �r

is the confinement number, with hlv being the latent heat of vapor-ization, Dq the difference between the liquid and vapor densities(respectively ql and qv ), r the surface tension coefficient, g thegravity acceleration, and Dh the hydraulic diameter. According toEq. (1), which predicts the vapor quality at the minimum heattransfer coefficient (see Fig. 2), the transition is a function of the li-quid-to-vapor density ratio, as well as the mass flux G and the heatflux q, giving results similar to those of Ong and Thome (2011a).Some modifications to the original heat transfer models of Thomeet al. (2004) for elongated bubble flow regime and the annular flowmodel of Cioncolini and Thome (2011) were implemented to im-prove their performance in predicting heat transfer. For instance,the three-zone model of Thome et al. (2004) was modified by set-ting the minimum film thickness to the measured wall roughnesssince the roughness breaks the liquid film. This has been alreadyproposed in the previous studies of Agostini et al. (2008c) in a sili-con test section, Ong and Thome (2011b) in three stainless steelmicrotubes, and Vakili-Farahani et al. (2012) in an aluminum mul-tiport tube, while the study of Costa-Patry et al. (2012a) includedboth silicon and copper test sections. Table 1 gives more detailson the geometrical specifications of the test sections and refriger-ants they have investigated.

The above heat transfer prediction method of Costa-Patry andThome (2012, 2013) along with the Chen (1966)-like heat transfermethod of Bertsch et al. (2009) seem to be the most accurate onesavailable today (Costa-Patry and Thome, 2012, 2013). Fig. 3(a)demonstrates the heat transfer coefficient trends for both of thesemethods in comparison to the experimental results of Szczukie-wicz (2012). Firstly, it is seen that the Bertsch et al. (2009) model,however, does not capture the increasing trend of heat transfer athigher vapor qualities (corresponding to the AF regime). While, theprediction method of Costa-Patry and Thome (2012, 2013) predictsboth the trend and the heat transfer coefficients well. This is espe-cially true at low and high values of vapor quality and the locationof the local minimum of the heat transfer coefficient, given by Eq.(1), representing the CB – AF flow transition. The largest discrepan-cies between the predicted and the experimental values are notice-able at this transition (churn flow), which remains a region ofuncertainty in the multi-microchannel heat transfer studies, andis very complex to mechanistically model. Together with the testslisted in Table 1 and those in the recent work of Szczukiewicz et al.(2012b, 2013b) shown in Fig. 1, their flow pattern based method sofar works for square and rectangular channels with aspect ratiosfrom about 1 to 10, for single circular channels, for multiport tubes,and for numerous refrigerants.

Harirchian and Garimella (2012) also used the three-zone mod-el of Thome et al. (2004) (with some modifications) as the basis topredict their experimental data (Harirchian and Garimella, 2008,2009a,b, 2010) for 7 different microchannel heat sinks. The channellocations where the flow transformed from bubbly to slug and con-sequently to annular flow were determined, and then the pressuredrop for each regime occurring along the channel was separatelycalculated. They also proposed a flow regime-based method thatprovided reliable results, but only for their one fluid (FC-77) atone saturation temperature, and hence only one set of physicalproperties; thus its use with any other fluid is an extrapolation.

Table 1Surface roughness effect in experimental studies.

Reference Test section Channel and fin geometry Surface roughness Test fluid

Agostini et al.(2008d)

Silicon micro-evaporator composedof 67 channels

Lch ¼ 13:2 mm; Wch ¼ 223 lm; Hch ¼ 680 lm; Wf ¼ 178 lm 170 nm R245fa andR236fa

Ong and Thome(2011b)

Single stainless steel microtube D = 1.03 mm, 2.20 mm, and 3.04 mm 595.85 nm, 826.99 nm,and 796.81 nm(respectively)

R245fa,R236fa, andR134a

Vakili-Farahaniet al. (2012,2013)

Extruded aluminum multiport tubecomposed of 7 channels

Dh ¼ 1:4 mm 810 nm R245fa,R1234ze(E),and R134a

Costa-Patry andThome (2012,2013)

Copper micro-evaporator composedof 52 channels (Costa-Patry et al.,2012b)

Lch ¼ 20 mm; Wch ¼ 163 lm; Hch ¼ 1560 lm; Wf ¼ 80 lm 450 nm R245fa,R1234ze(E),and R134a

Silicon micro-evaporator composedof 135 channels (Costa-Patry et al.,2011a)

Lch ¼ 12:7 mm; Wch ¼ 85 lm; Hch ¼ 560 lm; Wf ¼ 47 lm 67 to 90 nm R245fa andR236fa

Single stainless steel microtube (Ongand Thome, 2011b)

See above See above See above

Lch: channel length Hch: channel height Wch: channel width Wf : fin width.

0 0.05 0.1 0.15 0.2 0.25 0.30

0.5

1

1.5

2

2.5

3x 104

x [−]

α w [W

m−2

K−1

]

ExperimentalCosta−Patry and Thome (2012)Bertsch et al. (2009)

0 0.05 0.1 0.15 0.2 0.25 0.30

0.5

1

1.5

2

2.5

3x 104

x [−]

α w [W

m−2

K−1

]

ExperimentalNew buffer for Costa−Patry and Thome (2012)Bertsch et al. (2009)

(a)

(b)

Fig. 3. Experimental two-phase flow heat transfer coefficients of R236fa in the100 � 100 lm2 multi-microchannel with ein;rest ¼ 4 for Gch ¼ 525 kg m�2 s�1 andqw ¼ 155:3 kW m�2 compared to the prediction method of Bertsch et al. (2009), (a)original model of Costa-Patry and Thome (2012, 2013), and (b) the latter with thenew vapor quality buffer ðxbuffer ¼ �2xCB�AFÞ. Figure extracted from Szczukiewicz(2012).

0 0.05 0.1 0.15 0.2 0.25 0.30

5

10

15x 104

x [−]

α w [W

m−2

K−1

]ExperimentalTran et al. (1996)Yu et al. (2002)

Fig. 4. Comparison of the experimental results of Szczukiewicz (2012) with themodels of Tran et al. (1996) and Yu et al. (2002).

S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101 87

They did not unfortunately present any graph with trend lines ofthe heat transfer coefficient data versus local vapor quality, northe trends of their predictions. Hence, the method of Harirchianand Garimella (2012) was not compared with the experimental

results in Figs. 3 and 4 because an initial guess of the liquid filmthickness is required to start their heat transfer calculation (andthey note that the stability of the calculation can depend on thechoice).

To better handle the churn flow regime separating the CB andAF regimes and reflect the experimental U-shaped heat transfercoefficient trend, as presented in Fig. 3(b), Szczukiewicz (2012)proposed a new vapor quality buffer for the width of the CB-AFtransition as an update to the heat transfer prediction method ofCosta-Patry and Thome (2012, 2013). Still, the rise in the AF heattransfer coefficients is more rapid than suggested by their modeland this aspect needs to be further investigated. Also in Fig. 4,the U shape of the heat transfer coefficient trend can be observed,however, in case of the method of Tran et al. (1996), it is hardlynoticeable due to the large scale of the y axis. In this figure, themodels of Tran et al. (1996) and its modified version presentedby Yu et al. (2002) are compared with the experimental data ofSzczukiewicz (2012) and the equations to determine the heattransfer coefficient for both of them are respectively given below:

a ¼ 840;000 ðBo2WelÞ0:3 ql

qv

� ��0:4

ð2Þ

a ¼ 6;400;000 ðBo2WelÞ0:27 ql

qv

� ��0:2

ð3Þ

Flow direction

Created basedon the flowobservationfrom the top

Obtained by means of theIR camera placed at the bottom

(a)

(b)

(c) (d)

Fig. 5. (a) Two-phase flow operational map for R236fa in the micro-evaporatorwith the 50 lm-wide, 100 lm-deep, and 100 lm-long inlet restrictions ðein;rest ¼ 2Þ,where: – single-phase flow, – single-phase flow followed by two-phase flowwith backflow, – (b) single-phase flow followed by two-phase without backflow(desirable operating regime), – two-phase flow with backflow triggered bybubbles formed in the flow loop before the test section, and – (c) flashing two-phase flow without backflow (the most desirable operating regime). (b) Photographof the experimental flow boiling test facility with the optical system. Thisoperational map and the photo of the test rig were extracted from Szczukiewiczet al. (2013a). The thermal maps (c) and (d) were recorded for the two-phase flow ofR245fa in the test section of ein;rest ¼ 2 (Szczukiewicz, 2012).

88 S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101

where Bo is the boiling number defined above andWel ¼ G2Dh=ðqlrÞ is the Weber number. In Eq. (2), the lead constantwas changed accordingly to Thome (2010), who noticed a probabletypographical error in the original publication of Tran et al. (1996).Secondly, these constants for Eqs. (2) and (3) are different, whichexplains the difference in their extrapolated simulations presentedin Fig. 4. One order of magnitude of difference in this constant is sig-nificant especially taking into account the fact that the tested geom-etry and the range of experimental conditions were similar,although it is worthwhile to note that the refrigerant-based correla-tion was adapted to fit to the experimental results obtained forwater. Finally, both of them state that heat transfer coefficient isnot a function of G and x, which is in contrast with common trendsof many studies as pointed out in Thome (2010).

2.2. Infra-red camera measurements applied to microchannels

As a replacement of point-wise thermocouple and diode tem-perature measurements, IR thermography has started to be moreextensively explored in the past few years for microchannel heattransfer experiments, providing a very fine spatial resolution andinstantaneous measurement of heat transfer coefficients. Someapplications of IR cameras to convective heat transfer experimentsare highlighted below.

Hapke et al. (2002) used IR thermography to determine localheat transfer coefficients of water and n-heptane evaporating inrectangular microchannels with sizes ranging from 300 to700 lm applying a classical one-dimensional (1D) heat conductionapproach. Diaz et al. (2005) and Diaz and Schmidt (2007b,a) ex-tended the data base of Hapke et al. (2002) to include additionalgeometries, channel sizes, and fluids. In order to improve the accu-racy of their IR temperature measurements, the test sections werepainted black with an emissivity of�0.95. Due to technical difficul-ties, the change in fluid saturation temperature Tsat along the chan-nel was neglected and the fluid temperature was estimated as anaverage of the inlet and outlet temperatures (that is a fixed valueof Tsat for calculating all local heat transfer coefficients), which se-verely influences the values and trends when the fall in Tsat is sig-nificant with respect to the local wall superheat.

Hetsroni et al. (2001, 2006) focused on investigating triangularparallel multi-microchannels down to hundreds of microns in sizeunder uniform and non-uniform heat flux conditions. An IR camerawith an accuracy of ±1 �C was employed to monitor the tempera-ture variations across the uniformly heated test section wall. Thesewere found to be associated with hydraulic instabilities within thetest section and they were significantly enhanced for non-uniformheating. IR camera temperature measurements were also carriedout by Hetsroni et al. (2001, 2003) to study the explosive vaporiza-tion of water in microchannels with periodic wetting and dryoutbehavior. Furthermore, Hetsroni et al. (2002) showed that tempo-ral temperature and pressure fluctuations of the fluid Vertrel XF(DuPontTM) evaporating in their test section corresponded to eachother and they caused a reduction in heat transfer, i.e. unstableflow penalized heat transfer.

Xu et al. (2005, 2006) measured (by means of an IR camera)thermal oscillations for a uniformly heated surface of their silicontest sections, although the recording rate of their IR image systemwas not sufficient to observe the thermal flow patterns in greaterdetail. In particular, Xu et al. (2005) examined flow boiling of ace-tone in silicon parallel triangular microchannels, each having ahydraulic diameter of 155.4 lm. Similar to previous studies, theback of the test section was covered by a thin layer of black lacquerwith an emissivity of 0.94 that improved the accuracy of the IRtemperatures to within ±0.4 �C. Three zones of a full boiling cyclewere described: (i) liquid refilling stage, (ii) bubble nucleation,growth and coalescence stage, and (iii) transient annular flow stage

and the transient boundaries between them were given. Analogousobservations were made in the intercrossed array of triangularmicrochannels and transverse trapezoidal microchannels (Xuet al., 2006).

An experimental investigation of flow boiling of 2-propanol andwater in 50 � 50 lm2 Cyclo Olefin Polymer ðCOPÞ parallel channelswas performed by Hardt et al. (2007). In their experiments, thetemperature measurements were done by means of an IR camera,which was calibrated using a single thermocouple that had anaccuracy of ±1.5 K. Although, the authors stated that their cameraitself measured the temperature with a thermal resolution of

S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101 89

±0.08 K at 30 �C. Patil and Narayanan (2005, 2006) utilized IR ther-mography to obtain spatially-resolved temperature measurementsin a single silicon, uniformly heated microchannel of the samewidth as Hardt et al. (2007), but having a higher aspect ratio. Boththe wall and near-wall fluid temperatures (here water) were mea-sured, depending on the opacity of the channel wall. The IR cameracalibration was done implementing intensity maps during waterflow at the temperature of 23.5 �C, although this does not explainmeasurements at other temperatures. An IR camera was also used(together with a high-speed flow visualization camera) by Barberet al. (2009, 2011) to study flow boiling instabilities of n-pentanein a single rectangular microchannel having a hydraulic diameterof 727 lm under uniform heating. The accuracy of their IR temper-atures was reported to be ±1 �C.

Recently, Szczukiewicz et al. (2012a,b, 2013b) introduced a newin situ pixel by pixel technique to calibrate the raw infra-red imagesignals with an accuracy of ±0.2 �C, and thus converting them intoaccurate two-dimensional temperature fields of 10,000 pixels overthe heated surface of the silicon micro-evaporator. The test facilityand the test sections were designed such that simultaneous two-phase flow patterns (through a transparent Pyrex cover plate) andtemperature visualizations in 67 microchannels of 100 � 100 lm2

cross-sectional areas were possible. To this aim, they used a high-speed video camera placed above the test section and a high-speedinfra-red (IR) camera below, as shown in Fig. 5(b). Their results forR245fa, R236fa, and R1234ze(E) at a variety of the channel massflux Gch and the base heat flux qb were categorized into 8 differenttwo-phase flow operating regimes, among which 2 examples areillustrated in Fig. 5, where TIR is a temperature measured at the baseof the test section, y indicates an axis perpendicular to the flowdirection, while z denotes the distance form the channel entrance.This description applies also to the other thermal maps in this pa-per. The flashing two-phase flow without backflow operating re-gime, shown in Fig. 5(d), was identified as the most desirable one,since it provided the best spatio-temporal temperature and flowuniformities. Moreover, several new two-phase flow operationalmaps were developed for the two-phase flow of refrigerantsR245fa, R236fa, and R1234ze(E) flowing in the test sections with in-let restrictions (used for flow stabilization, as suggested by Kosaret al. (2006); Agostini et al. (2008c); Park et al. (2009)) and withoutany inlet restrictions. An example of such an operational map forR236fa flowing in the test section with the inlet restrictions of theexpansion ratio of ein;rest ¼ 2 is presented in Fig. 5(a). From an engi-neering stand-point of view, these operational maps are veryimportant for specifying the most advantageous operating condi-tions, at which the flow is always going to be stable for eventual ac-tual electronics cooling applications. More details on the two-phaseflow operational study of refrigerants in multi-microchannelevaporators for future high-performance 3D-ICs can be found inSzczukiewicz (2012) and Szczukiewicz et al. (2013a).

3. Numerical simulations of two-phase flow boiling inmicrochannels

In spite of the high resolution of IR cameras and high-speed vi-deo cameras, many dynamic and localized aspects of these two-phase flows and their heat transfer mechanisms remain elusive,or based on conjecture, rather than based on proven principles.This is specifically where numerical simulation of these flows canprovide strategic insight into this complex process and providethe basis for proposing models that incorporate these newly iden-tified aspects. This section introduces this recent work with first anoverview of numerical two-phase models and the following sec-tion gives some insight into their use to improve a mechanisticmodel.

3.1. Numerical models

The computation of evaporating flows in microchannels re-quires the conventional multiphase algorithms for CFD to be cou-pled with specific physical and numerical models to accuratelycapture the interfacial effects which become dominant in themicroscale. These models are briefly summarized below along witha unified formulation of the flow equations for the Volume Of Fluidand Level Set methods. Then, a review of the pertinent numericalfindings so far is presented.

The VOF and LS methods adopt a single-fluid mathematical rep-resentation of the two-phase flow, where the gas and liquid phasesare treated as a single fluid with variable properties across theinterface. A color function c is used to identify each phase on thecomputational domain and a Heaviside step function I is builtaccording to the values of c to compute the fluid properties through-out the computational domain. For instance, for each computationalcell of the flow domain the density is calculated as follows:

q ¼ ql þ ðqv � qlÞI ð4Þ

where 0 6 I 6 1 and qv ; ql are the vapor and liquid phase specificdensities. The liquid–vapor interface is then identified as a transi-tion region for the fluid properties and it has a finite thickness of2–3 computational cells. When the flow problem is treated asincompressible, which is true provided that the variation of the va-por density due to the pressure drop that occurs along the micro-channel is negligible, the mass conservation equation is expressedas:

r � u ¼ _m1qv� 1

ql

� �dS ð5Þ

where u denotes the fluid velocity. The term at the r.h.s. representsthe mass source due to the evaporation, where _m is the interphasemass transfer and dS is a delta function which is non-zero only atthe interface and its expression depends on the specific multiphasealgorithm adopted.

The momentum equation for Newtonian fluids in laminar flow,appropriate for microchannels, takes the following form:

@ðquÞ@t

þr � ðqu � uÞ ¼ �rpþr � ½lðruþruTÞ� þ qg

þ rjndS ð6Þ

with t being the time, p the pressure, q and l the single-fluid den-sity and viscosity to be computed as it is shown in Eq. (4), and g thegravity vector. The last term on the r.h.s. represents the surface ten-sion force for a constant surface tension coefficient, where j and nidentify the local interface curvature and unit normal vector. Theinterface topology is not available explicitly in VOF and LS methods,but it can be derived by means of the color function field asn ¼ rc=jrcj and j ¼ �r � n as originally proposed by Brackbillet al. (1992). However, the computation of the interface curvatureby means of derivatives of the color function is known to be of pooraccuracy for VOF methods as pointed out by Cummins et al. (2005),thus generating errors in the estimation of the surface tension force.Since the surface tension is a dominant force in the microscale, theaccuracy of its calculation is fundamental to obtain reliable numer-ical results. Hence, it is preferable that VOF schemes include specificalgorithms for the reconstruction of the interface topology such asthe parabolic fitting of Renardy and Renardy (2002), the HeightFunction method (Cummins et al., 2005), or coupled LS and VOFschemes (CLSVOF) (Sussman and Puckett, 2000).

The energy equation to be solved is given by:

@ðqcpTÞ@t

þr � ðqcpuTÞ ¼ r � ðkrTÞ þ s

: ru� _m½hlv � ðcp;v � cp;lÞT�dS ð7Þ

90 S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101

where T indicates the temperature, cp and k are respectively the sin-gle-fluid specific heat at constant pressure and thermal conductiv-ity, while s represents the shear stress tensor. The second term onthe r.h.s. represents the viscous heating which may become impor-tant for very small channel sizes (negligible for the sizes consideredhere), while the third term implements the enthalpy sink due toevaporation, that of the vapor created and of the liquid that disap-pears. Usually, the temperature variations are sufficiently smallsuch that the physical properties of the phases are considered con-stant. The set of the flow equations is then completed by the trans-port equation for the color function:

@c@tþ u � rc ¼

_mq

dS ð8Þ

which is used to update the position of the interface and then themixture fluid properties as time elapses.

To complete the formulation, an evaporation model to expressthe interphase mass transfer _m as a function of the local tempera-ture and pressure is necessary. If microscale effects on mass trans-fer are neglected, the interface is assumed to be at the saturationtemperature, such that the temperature field is continuous acrossthe interface, and the mass transfer can be computed as_m ¼ krT � n=hlv (Mukherjee and Kandlikar, 2005; Mukherjee,

2009; Mukherjee et al., 2011; Lee et al., 2012; Suh et al., 2008).However, as the scale of the problem is reduced, interphase resis-tance and disjoining and capillary pressures tend to create a dis-continuity in the temperature and pressure fields across theinterface, thus generating an interfacial resistance to mass transferwhich decreases the evaporation rate. In this direction, Schrage(1953) derived a relationship to express the interphase mass trans-fer as a function of the local temperatures and pressures of the li-quid and gas phases at the interface, while Wang et al. (2007)showed that the following linearized expression is a goodapproximation:

_m ¼ CTðTi � TvÞ þ Cpðpl � pvÞ ð9Þ

as long as the temperature difference between the liquid–vaporinterface and the equilibrium saturation temperature is below 5 K.CT and Cp are constants of the model which only involve the fluidproperties, see Wang et al. (2007). Ti is the liquid–vapor interfacetemperature, Tv is the vapor temperature at the interface, andpl � pv is the liquid–vapor pressure jump. Eq. (9) has been imple-mented by various authors to set-up a CFD solver for boiling andcondensing flows in microchannels such as Magnini et al. (2013a),Kunkelmann and Stephan (2009) and Nebuloni and Thome (2010).

In flow boiling in microchannels, liquid dryout at the channelwall may occur as a consequence of the evaporation of the liquidfilm which surrounds an elongated vapor bubble (Thome et al.,2004). In CFD computations, the modeling of wall adhesion in-volves the implementation of a (static or dynamic) contact anglemodel. The contact angle is a condition on the direction of theinterface normal vector at the solid-liquid–vapor three-phase con-tact line, and hence on the local color function field for LS and VOFmethods. In the former, the contact angle is introduced as a bound-ary condition for the color function field at the wall (Mukherjeeand Kandlikar, 2005; Suh et al., 2008; Lee et al., 2012), while inthe latter it is usually enforced by adjusting the components ofthe unit normal vector involved in the surface tension force termin Eq. (6) (Brackbill et al., 1992; Renardy et al., 2001; Afkhamiand Bussmann, 2008). Another issue connected to wall adhesionis the microlayer evaporation process, which is known to increasedramatically the heat transfer in the contact line region in nucleateboiling, and hence may be a significant heat transfer mechanism atthe perimeter of intermittent dry patches in microchannels. Usu-ally, the contact line evaporation is modeled by solving a fourth

order differential equation for the film thickness evolution in theso-called micro-region (Stephan and Busse, 1992), which is discret-ized by a separated computational grid. This solution is then in-cluded in the flow problem for the macro-region by means ofspecific source terms (Kunkelmann and Stephan, 2009; Li and Dhir,2007). However, its short life in the cyclic heat transfer process andsmall footprint in elongated bubble flow tends to reduce it to onlya small influence.

3.2. Literature review

The numerical investigations of flow boiling in microchannelshave focused initially on the fundamental aspects of the flow, suchas bubble dynamics and the flow field induced by the evaporationprocess. In this light, Mukherjee and Kandlikar (2005) simulatedthe growth of a spherical bubble during flow boiling in a squaremicrochannel and observed that the presence of the channel wallstended to elongate the bubble, which grew with an exponentialtime-law, while vapor patches appeared at the centerlines of thechannel walls due to the dryout of the trapped liquid film. Li andDhir (2007) analyzed the bubble growth and detachment from aflat wall in flow boiling conditions and observed that the departurediameter of the bubble decreased as the bulk flow velocity in-creased and it increased with the wall tilt angle. Augmentation ofthe flow velocity suppressed the gravity effect on the bubbledynamics.

Subsequently, as the experimental findings highlighted specificissues which required more detailed knowledge of the local phe-nomena to clarify, e.g. flow instabilities, dominant heat transfermechanisms, heat transfer enhancement, more targeted numericalstudies began to be conducted. The stability of the flow duringevaporation in parallel microchannels was investigated by Suhet al. (2008), who showed that backflow occurred when the forma-tion of vapor bubbles was not simultaneous in adjacent microchan-nels, and thus led to a distribution of the heat flux which was notuniform on the surface of the heater. Dong et al. (2012) studied theeffect of single and multiple growing vapor bubbles on the fluidflow behavior and heat transfer, and reported that the bubble for-mation process induced a flow resistance which increased with thegrowth of the bubble, disappeared with the bubble departure, andwas strongly affected by the presence of multiple bubbles. Muk-herjee and Kandlikar (2009) analyzed the effect of inlet constric-tions to prevent the backflow growth of vapor bubbles in asquare microchannel and showed that, despite the positive effectin stabilizing the flow, they generated a high pressure drop and re-duced the efficiency of the thin-film evaporation mechanism.Diverging microchannels in the direction of the desired flow wereproposed as a better solution. However, the analysis of pressuredrop needs to be applied to the entire two-phase cooling loop toascertain the true impact of such orifices.

The contribution of the evaporation of the thin liquid film sur-rounding an elongated bubble during flow boiling was the subjectof the work of Mukherjee (2009). He simulated the growth of a va-por bubble in contact with the heated surface of a microchanneland observed that the formation of a thin layer of liquid betweenthe bubble and the channel wall, which was promoted by smallercontact angles, increased the wall heat transfer and thus reinforc-ing the interpretation that the heat transfer in microchannels isthin-film evaporation dominated. Magnini et al. (2013a) studiedthe hydrodynamics and heat transfer given by the flow boiling ofsingle elongated bubbles in a circular microchannel and observeda strong increase of the heat transfer coefficient in the vapor bub-ble region due to the evaporation of the thin liquid film, including athermally developing length effect. They obtained good predictionsof the heat transfer coefficient by means of a model based on tran-sient heat conduction across the film, which was an extension of

S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101 91

Thome et al. (2004) steady-state three-zone model, and confirmedthe thin-film evaporation dominance on heat transfer withinmicrochannels. Mukherjee et al. (2011) also attempted to explainsome of the experimentally observed trends for the boiling heattransfer coefficient, see Agostini and Thome (2005) for an earlierreview. The results of their computational study suggested thatthe heat transfer coefficient increased with the heat flux as it aug-mented the bubble growth rate and then the velocity of the liquid,which was pushed against the channel wall by the growing bubble.The authors observed that the liquid mass flux had only a little ef-fect on the heat transfer and this was justified by the high veloci-ties generated by the bubble growth process, which suppressed theeffect of the liquid inlet velocity. This can also be explained byassuming that the heat conduction is the dominant heat transfermechanism across the liquid film. Their conclusions also matchthose that can be deduced from analysis of the three-zone model,where bubble frequency and velocity play important roles whilemass velocity does not influence heat transfer (completely coun-ter-intuitive to single-phase flows). Magnini et al. (2013b) per-formed simulations of the flow boiling of multiple bubbleswithin a microchannel and showed that the interaction amongsequential bubbles generated bubbles of different lengths, veloci-ties and thickness of the liquid film trapped between the liquid–va-por interface and the channel wall. This led to different heattransfer performances, in particular the time-averaged heat trans-fer coefficient for the trailing bubble cycle was much higher thanthat of the leading one (about 60% higher).

The enhancement of the heat transfer performance of a micro-channel of square cross-section was the objective of the work ofLee et al. (2012), who performed numerical simulations to opti-mize the design of transverse fins on the channel. It was found thatthe heat transfer was significantly improved by those solutionswhich promoted thinner liquid films trapped between the bubbleand the channel walls and larger liquid–vapor–solid interface con-tact regions. It is not known however if this will promote prema-ture dry patch formation and CHF.

10

12

]

4. Discussion on the most recent experimental and numericalresults of heat transfer studies

Some critical discussion on experimental and numerical work ispresented below, whose objective is to highlight some of theachievements but also pitfalls of the current state-of-the-art andalso to illustrate how experimental, theoretical modeling andnumerical simulations can work hand-in-hand to resolve micro-channel evaporation research issues.

0 2 4 6 8 10 12 14 16

2

4

6

8

Time [ms]

Posi

tion

of th

e bu

bble

nos

e [m

m

R113

R245fa

R134a

Fig. 6. Positions of the bubble nose against time in flow boiling conditions, given bysimulations (solid lines) and Consolini and Thome (2010) model (dashed lines).Simulation conditions: D = 0.5 mm, q ¼ 20 kW m�2; G ¼ 600 kg m�2 s�1 (R113,R245fa) and 500 kg m�2 s�1 (R134a), Tsat ¼ 50 �C (R113, R245fa) and 31 �C (R134a).

4.1. Contribution of numerical simulations to the heat transfermodeling

After almost ten years since its publication, the three-zonemodel of Thome et al. (2004) with its related updates (Agostiniet al., 2008d; Harirchian and Garimella, 2012; Costa-Patry andThome, 2012, 2013; Costa-Patry et al., 2012b) is still the best per-forming boiling heat transfer prediction method for slug flow boil-ing in microchannels in circular and non-circular channels,covering numerous fluids and channel sizes down to 85 micronwidths. Even so, numerous simplifications are assumed in thetwo-phase flow structure in developing this mechanistic modeland numerical two-phase simulations constitute a unique tool toinvestigate the local flow phenomena influencing the micro-heattransfer processes involved, and thus can contribute to theimprovement of the sub-models. For example by means of compu-tations, Magnini et al. (2013a) already proved that, for a liquid filmthickness of 1/20 of the channel diameter, the thermal inertia

effect is not negligible when modeling the heat transfer in the li-quid film region by assuming one-dimensional heat conduction.By adding a transient term to the original three-zone model’s for-mulation (which was developed for much thinner liquid films, onthe order of 1/100 of the channel diameter), the time-law of theheat transfer coefficient given by CFD simulations was predictedsatisfactorily. This influence is more significant for shorter bubblessince the thermal boundary layer development length then plays alarger role; hence this effect is more important in the IB regimewhere bubbles are still relatively short ðL < 2DÞ but less so in theCB regime where coalescence of bubbles results in mostly longbubbles ðL > 5DÞ.

With the aim of improving the modeling of the heat transfer inthe liquid slug zone of the three-zone model, consider two bubblesflowing and evaporating in sequence in a circular microchannel.They were simulated using the numerical framework already dis-cussed above by Magnini et al. (2013a), taking advantage of a 2Daxisymmetrical formulation to limit the computational time ofthe simulations. For horizontally oriented channels, this is a validassumption provided that Co > 1, as observed experimentally byOng and Thome (2011a), and hence only working conditionsmatching such criterion were chosen. The reliability of the solverin modeling the flow of axisymmetrical elongated bubbles was as-sessed by a positive comparison of the liquid film thicknesstrapped between the bubbles and the wall in adiabatic conditionswith the Han and Shikazono (2009) correlation, the latter based ontheir measurements with a highly accurate oscillating microscopetechnique. The validation of the numerical results in flow boilingconditions were also proven by comparing the position of the noseof the growing bubble against time with the theoretical model de-rived by Consolini and Thome (2010) for the flow of coalescingbubbles in microchannels. Fig. 6 shows the computational and the-oretical results for three different operating fluids, namely R113,R245fa and R134a, under similar operating conditions. The com-parison is quite positive, where the increasing underestimationsof the model at the highest time steps are due to the assumptionthat the bubble grows only by absorbing the wall heat flux, whilein the numerical simulations the bubble also grows because it re-ceives the sensible heat of the superheated liquid by evaporationacross the nose of the bubble.

92 S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101

In the present simulations, R245fa is employed as the workingfluid. The microchannel has a circular cross-section with a diame-ter of D = 0.5 mm and length of 72 diameters, split into an initialadiabatic region of 16 diameters, then a heated section of 22 diam-eters and finally a terminal adiabatic zone. Two elongated vaporbubbles at the saturation temperature Tsat ¼ 31 �C are initializedat the upstream of the initial adiabatic region of the channel andthe bubbles are 6 diameters apart. The channel is fed with a massflux of G ¼ 550 kg m�2 s�1 of saturated liquid, which pushes thebubbles downstream into the heated region. A constant and uni-form heat flux of q ¼ 5 kW m�2 is applied. The initial conditionsfor the temperature and velocity field of the liquid are obtainedby means of a preliminary liquid-only steady-state simulation. Asthe simulation of the two-phase flow starts, the bubbles quicklyachieve a steady flow in the adiabatic region of the channel andthe flow is characterized by a time-averaged cross-sectional voidfraction of 0.28 and a vapor quality of 0.02. As the bubbles enterinto the diabatic section of the channel, they begin to grow andto accelerate downstream due to the evaporation of the super-heated liquid present in the thermal boundary layer at the walland at the nose. The dynamics of the bubbles during the evapora-tion process and the induced wall heat transfer is different be-tween the leading and the following bubble, because the secondbubble comes across a region which had already been cooled downby the transit of the leading one. Hence, the trailing bubble shows alower evaporation rate and velocity, which results in a 13% thinnerliquid film than the bubble ahead. As an illustration, Fig. 7 plots theheat transfer coefficient versus time after 21 heated diameters forthe simulation and a model which is going to be discussed below.The heat transfer coefficient is computed as:

aðtÞ ¼ qTwðtÞ � Tsat

ð10Þ

where Tw is the wall temperature. The numerical results show thatthe heat transfer increases during the transit of the bubbles, as it isexpected due to the evaporation of the thin liquid film trapped be-tween the bubble and the channel wall, then it reaches a maximumand decreases smoothly as the liquid plugs following each bubblepass by. The second bubble and its liquid slug have significantlyhigher heat transfer than the first bubble, not only relevant forthe heat transfer model but also illustrating the limitation ofsingle-bubble simulations. The local heat transfer behavior in the

15 20 25 30 35 40 451000

1500

2000

2500

3000

Time [ms]

Hea

t tra

nsfe

r coe

ffici

ent [

W/m

2 K]

Simulation

Model

liquidliquid leadingbubble

liquidslug

trailingbubble

Fig. 7. Heat transfer coefficient after 21 heated diameters given by the simulationof two bubbles flowing in the microchannel and by the proposed analytical modelfor the heat transfer. The black vertical lines identify the transit of the bubbles’ noseand rear.

liquid slugs cannot be captured by single-phase methods for heattransfer, such as the Shah and London (1978) correlation imple-mented in the three-zone model, as it is generated by a specific cir-culation flow induced by the two-phase flow at the tails of thebubbles. The flow pattern of the liquid within the slug trapped be-tween the bubbles is obtained by computing the streamlines of thevelocity field relative to the velocity of the nose of the trailing bub-ble, which are displayed in Fig. 8 for the time instant t ¼ 22:4 ms atwhich both the bubbles are growing due to the evaporation.

It is observed that, in agreement with the Thulasidas et al.(1997) experimental measurements, the flow within the liquidslug can be split into a wall-adherent liquid layer which bypassesthe bubbles and a recirculating flow which occurs in the core re-gion of the channel.

By assuming that the heat is transferred by one-dimensionalheat conduction from the channel wall to the recirculating flow re-gion, the transient-heat-conduction-based boiling heat transfermodel for the liquid film region of Magnini et al. (2013a) can be ex-tended to model the heat transfer in the liquid slug region as well,to thus obtain an improved two-zone (liquid dryout is not modeledhere) boiling heat transfer model for slug flow. A schematical rep-resentation of the decomposition of the flow domain adopted bysuch two-zone model is depicted in Fig. 8(b). In the liquid slug re-gion, the heat transfer coefficient is modeled by solving the Fourierequation:

k@2T@y2 ¼ qcp

@T@t

ð11Þ

within the wall-adherent film region bounded by the channel wallat y ¼ 0 and the recirculating flow region at y ¼ ds. An analyticalexpression for the thickness of the wall-adherent liquid layer ds

was provided by Thulasidas et al. (1997). At the boundary, a con-stant heat flux condition is applied at y ¼ 0, while a convection con-dition is employed to model the heat transfer at the fictitiousboundary between the wall-adherent and recirculating regions:

�k@T@y¼ asðT � TsatÞ ð12Þ

where as is the heat transfer coefficient between these regions,which is presently evaluated by means of the following correlationoriginally proposed by He et al. (2010):

as ¼kDð24:7þ 0:54Pe0:45ðLs=DÞ�1:34Þ ð13Þ

where Pe is the Peclet number of the liquid within the slug and Ls isthe length of the liquid slug. Note that, in Eq. (12), the recirculatingflow region is assumed to be at the saturation temperature. The ini-tial temperature profile for the liquid slug region is obtained by themodel itself, as the temperature profile at the end of the previousliquid film region. The so-defined flow problem allows an analyticalexpression for the heat transfer coefficient in the liquid slug regionto be obtained, which is then coupled with the solution presentedby Magnini et al. (2013a) for the liquid film zone. The prediction gi-ven by this updated model is plotted in red in Fig. 7 and it estimatesthe heat transfer trends and magnitude in satisfactory agreementwith the results of the computations. This model can be developedfurther to decrease the overestimation observed in Fig. 7 as shownin Magnini et al. (2013b), and to be made fully stand-alone bymeans of correlations available in the literature to estimate thoseparameters (e.g. thin liquid film thickness, wall-adherent liquidlayer thickness, etc.) provided here by the numerical simulation re-sults. Hence, this case study provides a good example of hownumerical two-phase simulations can be used to identify new as-pects of the heat transfer process in microchannel slug flow andprovide the input to the development of new theoretical models.

24 25 26 27 28 29 30 31 32 33 340

0.1

0.2

0.3

0.4

0.5

Nondimensional axial position

Non

dim

ensi

onal

radi

al

sδ δz

y

T=Tsat

regionliquid film

regionliquid slug

R

Ty

λ l s=h (T−T )s vapor bubble

liquid filmadherent film

recirculating zone

posi

tion

(a)

(b)

Fig. 8. (a) Streamlines of the velocity field relative to the velocity of the nose of the trailing bubble, at t = 22.4 ms. The black lines identify the bubbles profiles which aresuperimposed to the streamlines plot. (b) Scheme of the decomposition of the flow field within the microchannel adopted by the proposed two-zone boiling heat transfermodel for slug flow. Since d; ds R, the radial coordinate is here replaced by the vertical coordinate y.

S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101 93

4.2. Heat transfer coefficient data reduction in multi-microchannels

In order to characterize the heat transfer performance of a mul-ti-microchannel evaporator, the local heat transfer coefficientneeds to be determined. Equation (14) expresses the definition ofthe local wall heat transfer coefficient:

awðzÞ ¼qwðzÞ

TwðzÞ � TflðzÞð14Þ

where z denotes the distance from the channel entrance. To beginwith, the local saturation temperature of the refrigerant ðTflÞ isdetermined by the local saturation pressure, which might signifi-cantly decrease along a microchannel. For instance, Szczukiewicz(2012) showed that the saturation temperature starting at�37.5 �C at the inlet of the channel may fall at the end of the chan-nel anywhere from �28 �C predicted by the homogeneous pressuredrop model up to �35 �C obtained by Lee and Garimella (2008) pre-diction method, leading to a difference of �50% in heat transfercoefficient at a local wall temperature of Tw 42 �C when applyingEq. (14) to reduce the data. Thus, the channel pressure drop, Dpch,needs to be precisely quantified in order to accurately reduce rawdata to heat transfer coefficients. Nonetheless, due to numeroustechnical difficulties in multi-microchannel experiments, the pres-sure drop is commonly measured between the inlet and the outletmanifold’s plenums (referring to the total pressure drop). Whilesome methods of direct local pressure measurements within micro-channels are available in the literature, such as the one of Kohl et al.(2005), applied in a single microchannel down to 25 lm, in the caseof multi-microchannels the applicability of such a single-channelmethod is quite difficult.

When direct experimental measurements are not plausible, thenext best way is to either experimentally measure or compute theinlet pressure at the beginning of the channels, and then the localsaturation pressure (and temperature) profile is obtainable byapplying a well-established two-phase flow pressure drop predic-tion method for the channels. For instance, the prediction methodof Cioncolini et al. (2009) was found by Costa-Patry (2011) to bethe best method in his tests when comparing with their experi-mentally measured channel pressure drops. Such models with

predictive error bands of 20–30%, however, may still have a crucialeffect on the determination of the local heat transfer coefficients(Szczukiewicz, 2012) when applying Eq. (14).

Alternatively, the value of Dpch can be calculated by subtractingthe inlet ðDpin;restÞ and the outlet restriction pressure lossesðDpout;restÞ from the total experimental pressure drop measured be-tween the two plenums. The value of Dpin;rest (usually single-phaseflow) can be obtained by fitting subcooled liquid experimental re-sults to the well known formula of Idelcik (1999) or computedaccording to Lee and Garimella (2008), as was done by Szczukie-wicz (2012). The two-phase flow outlet restriction pressure losses,Dpout;rest , can be obtained by employing the method of Costa-Patryet al. (2011b), knowing the absolute pressure measured in the out-let manifold’s plenum and the saturation pressure at the outlet ofthe channel. The latter can be obtained by imposing an adiabaticzone at the outlet (when using local heaters) to get the exit walltemperature, which matches the local saturation temperature,and thus indirectly yields the local saturation pressure of themicrochannels in a partially heated test section. These tempera-tures might be measured by, for instance, thermal diode sensors(Costa-Patry et al., 2011b) or self-calibrated IR camera (Szczukie-wicz, 2012).

To get the local saturation pressures along the microchannels,one can assume a linear pressure drop over the length of the chan-nel using the values of Dpch and then determine Tfl based on the va-por pressure curve. However, this is only appropriate when thepressure drops are small. Instead of assuming such a linear tem-perature gradient along the channel, Szczukiewicz (2012) reducedher heat transfer data using the annular pressure drop predictionmethod of Cioncolini et al. (2009) combined with the model ofLockhart and Martinelli (1949) for vapor qualities below the iso-lated bubble to coalescing bubble (IB-CB) transition of Ong(2010) and then applying a ratio of the experimental and the pre-dicted pressure drop values to make it match the experimentalpressure at the exit in each case. This emulated the expectednon-linear variation in the pressure gradient and saturation tem-perature, accounting also for the accelerational pressure gradient(all of which would emulate what has to be done in the actual sim-ulation/design of a micro-evaporator). Fig. 9(a) demonstrates anexample of the prorated fluid temperatures compared to the linear

2 4 6 8 1033

35

37

39

z [mm]

T fl [o C]

linearprorated

0 2 4 6 8 100

0.5

1

1.5

2

2.5

3

3.5x 104

z [mm]

α w [W

m−2

K−1

]

linearhomogeneous Δ pchprorated

∼83%

(a)

(b)

Fig. 9. (a) Prorated fluid temperature (Szczukiewicz, 2012), and (b) local heattransfer coefficient trends assuming linear, homogeneous, and prorated pressure(and consequently fluid saturation temperature) profiles along the channel forR236fa flowing in the test section with ein;rest ¼ 4, Gch ¼ 1692 kg m�2 s�1,qb ¼ 47:8 W cm�2 for the experimental channel pressure drop of 46.3 kPa. Notethat in Fig. 9(b), as explained later in the text, the heat transfer coefficients affectedby edge effects are excluded.

0 2 4 6 8 100

1

2

3

4

5x 105

z [mm]

q ft [W m

−2]

1D

3D

0 0.05 0.1 0.15 0.20

0.5

1

1.5

2

2.5

3

3.5x 104

x [−]

α w [W

m−2

K−1

]

1D

3D

(a)

(b)

Fig. 10. Two-phase flow of R1234ze(E) in the test section with ein;rest ¼ 2 forGch ¼ 1705 kg m�2 s�1 and qb ¼ 32 W cm�2: (a) actual heat flux at the root of thefins along the channel length qft , and (b) local wall heat transfer coefficients, aw ,obtained using the 1D and 3D conduction schemes in function of x. Figure extractedfrom Szczukiewicz (2012).

94 S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101

temperature profile for determining the local heat transfer coeffi-cients (Szczukiewicz, 2012). Fig. 9(b) highlights the important dif-ferences in the local heat transfer coefficients using three differentapproaches: (i) assuming linear, (ii) homogeneous, and (iii) pro-rated pressure (and consequently saturation temperature) profiles.The homogeneous pressure drop model (taken here as an example)overpredicts the values of the channel pressure drop and thus low-ers the value of the local saturation temperature of the refrigerantat the exit and the value of the local heat transfer coefficient, lead-ing to a difference of �83% between the approaches (ii) and (iii) atz = 9.5 mm for this test case. Furthermore, the linear pressure dropassumption artificially brings the local heat transfer coefficients tolower values (except the inlet and the outlet temperatures whichare experimentally measured), which might severely affect theheat transfer coefficients along the length by up to 10%, when com-paring to the approach (iii), i.e. at the CB-AF flow transition. There-fore, the proration method for simulating the fluid temperature isrecommended as the most appropriate one in order to provide themost accurate estimation of the local heat transfer coefficient (fu-ture experimental studies should take note of this).

Turning now to another common data reduction procedure, theconventional 1D heat conduction approach does not take into ac-count the heat spreading towards the colder surrounding regionsthat can be observed due to the strong variation in the local heattransfer coefficient with vapor quality along the channel and at

the boundaries. Costa-Patry (2011) noted that the lateral non-uni-form heat flux distribution changes the local pressure drop andevaporation rates. Consequently, the calculated values of the localwall temperatures and heat fluxes and local vapor qualities areinfluenced by the data reduction procedure. The heat spreading ef-fects can be accounted for by using the pragmatic 3D thermal con-duction scheme of Costa-Patry (2011), where the temperature andheat flux values at the test section’s base are found by spatially dis-cretizing the 3D domain and then solving an energy balance foreach control volume (CV). Afterwards, assuming the external wallsof the silicon test section to be adiabatic, the various nodes arelinked with each other, such that: Q LðnÞ ¼ �Q Rðn� 1Þ,QFðnÞ ¼ �Q Bðn� 1Þ, and Q DðnÞ ¼ �QUðn� 1Þ, where Q is the heatflow rate and n is a natural number indicating the layer’s number.The notations above are as follows: D for down (base for the firstlayer of CVs), U – up, L – left, R – right, F – front, and B – back. Thisprocedure is quite fast and yields comparable results to a full 3Dheat conduction simulation.

Fig. 10 presents the comparison between the 1D and 3D heatconduction schemes (Szczukiewicz, 2012), where the silicon waferwas discretized in 100 � 100 (set to the pixels of the IR tempera-ture measurements) �140 control volumes (and taking into ac-count the thermal conductivity change with respect totemperature). The biggest discrepancy is noticeable at the corners,where the edge effects are most significant and they were bettercaptured by the 3D heat conduction model. As can be seen, the first

(a)

(b)

Fig. 12. The flashing two-phase flow without backflow operating regime of R236fain the micro-evaporator with ein;rest ¼ 4 for Gch ¼ 2096 kg m�2 s�1 andqb ¼ 47 W cm�2: (a) wall heat transfer coefficient, aw , and (b) video image of flow.Figure extracted from Szczukiewicz (2012).

S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101 95

and the last 5 pixels of the IR array include edge effects, and thusthey are discarded. Moreover, the heat spreads towards the coldersurrounding regions (regions of higher heat transfer coefficientsand slope in Tfl), here at the inlet and the outlet, and the actual heatflux in those zones is first higher and then lower than that assumedin 1D calculations. Therefore, the heat transfer coefficients deter-mined assuming 1D conduction from the base of the silicon mi-cro-evaporator to the root of the fins are underpredicted at theinlet and the outlet of the channel, as demonstrated in Fig. 10(b),where the local vapor quality is calculated with corresponding lo-cal heat flux profile of the 1D and 3D calculations. If the heatspreading is not considered, the heat transfer coefficient is over-predicted at the local minimum, which corresponds to a flow tran-sition. The present silicon test section has only a 0.28 mm basethickness, but still exhibits some heat spreading, which will beeven more significant for thicker micro-evaporators. Fig. 11 showsan example of the local wall heat transfer coefficients of R236fa ob-tained through 1D and 3D heat conduction schemes at a wall heatflux of qw ¼ 71 kW m�2 and three different mass fluxes, where forinstance for Gch ¼ 2099 kg m�2 s�1 at z = 9.5 mm the heat transfercoefficient accounting for 3D heat spreading is �14% higher com-pared to 1D heat conduction scheme. Thus, 3D heat spreadingshould be included in all future data reduction procedures inexperimental studies to obtain the most accurate results for thevalues of aw and x, and thus the data trends. Since a real micro-evaporator cold plate is subject to heat spreading effects, it isimportant that test data are reduced and then modeled in the samemanner as the actual application.

Fig. 12(a) illustrates the wall heat transfer coefficient, aw, ob-tained using 3D heat spreading in the silicon micro-evaporator ofSzczukiewicz (2012), plotted versus the longitudinal channel loca-tion, z, and compared to the corresponding flow pattern map tran-sition (vertical blue line). The descending trend of aw at thebeginning of the channel (low vapor quality range) correspondsto the coalescing bubble (CB) region, where the elongated bubblescoalesce and the local intermittent dry-out patches are formed(Thome et al., 2004). The local minimum of the heat transfer coef-ficient is well located by the coalescing bubble – annular flow (CB –AF) transition of Costa-Patry and Thome (2012, 2013), computedaccording to Eq. (1). Fig. 12(b) shows a video image of the flowaligned with the graph at the top. The color changes along thechannel from almost black at the entrance (subcooled flow/bubblyflow) to nearly white (transition region) and becomes gray at the

0 0.1 0.2 0.3 0.4 0.50

0.5

1

1.5

2

2.5

3

3.5x 104

x [−]

α w [W

m−2

K−1

]

Gch = 911 kg m−2 s−1, 1DGch = 911 kg m−2 s−1, 3DGch = 1514 kg m−2 s−1, 1DGch = 1514 kg m−2 s−1, 3DGch = 2099 kg m−2 s−1, 1DGch = 2099 kg m−2 s−1, 3D

Fig. 11. Two-phase wall heat transfer coefficient as a function of local vapor qualityfor R236fa flowing in the test section with the inlet restrictions of ein;rest ¼ 4 forqw ¼ 171 kW m�2. The calculations of the local vapor quality here included the 3Dheat spreading effect.

exit. The blue line indicating the CB – AF transition of Costa-Patryand Thome (2012, 2013) falls between the second and the thirdzone. This means that more than half of the channel is in the annu-lar flow (AF) regime. Due to the convective evaporation across theannular film, this provides an increasing heat transfer rate withincreasing vapor quality. Thus, experimental databases should becoupled with flow visualizations in order to capture the flow pat-tern effects on the major trends in the data, or at least evaluatedand characterized using the best flow pattern map for the applica-tion. In essence, one could consider the experiment to be incom-plete if this is not done. . .imagine presenting single-phase flowdata without indicating the transition point from laminar to turbu-lent flow or the location of fully developed flow.

4.3. Stable and unstable two-phase heat transfer coefficients

Two-phase flow stability is the next important issue to be con-sidered (but often ignored in the microchannel flow boiling litera-ture), which needs to be addressed in any credible heat transferstudy, since its effect might significantly change the heat transfercoefficient trends and values with respect to the vapor quality, asillustrated by a specific experimental comparison performed byConsolini and Thome (2009). Figure 13(a) and (b) shows the two-phase flow boiling of R245fa and the time-averaged temperaturedistribution in the micro-evaporator without any inlet restrictions(micro-orifices). As expected, significant flow instabilities, vaporbackflow, and flow maldistribution occur, which are eventuallygoverned by the pressure drop in each individual channel, whichlead to high-amplitude and high-frequency temperature and pres-sure oscillations (see for instance Wu and Cheng (2003)). It isworthwhile to mention that in such a situation, the assumptionof uniform mass flux in all the channels is invalid and it is not

z [mm]

y [m

m]

2 4 6 8 10

2

4

6

8

10

40

42

44

46

48

50

52

54TIR [oC]

Flow direction

TELNI

TELTU

O

wolfkcab

oN

dev orpmi

ytimrofi nu

wolF

z

y

z [mm]

y [m

m]

2 4 6 8 10

2

4

6

8

10

40

42

44

46

48

50

52

54TIR [oC]

(a) (b)

(c) (d)

Fig. 13. Snapshots of the high-speed flow visualization and the time-averaged IR temperature maps of the test section’s base provided by the two-phase flow boiling ofR245fa for Gch ¼ 2035 kg m�2 s�1 and qb ¼ 36:5 W cm�2: (a), (b) without any inlet restrictions, and (c), (d) with the 50 lm-wide, 100 lm-deep, and 100 lm-long inlet micro-orifices (Szczukiewicz et al., 2012b; Szczukiewicz et al., 2013b). The flow is from left to right in all the presented images for both flow and temperature.

96 S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101

advised to be used to reduce the data for local heat transfer coeffi-cients. This illustrates the necessity of developing new measure-ment techniques for determining the mass flux in each individualchannel within multi-microchannel test sections.

As demonstrated in Fig. 13(c), such undesired phenomenamight be prevented by using an inlet slit to create restrictions atthe entrance of each channel, which tend to stabilize the two-phase flow (Agostini et al., 2008c). For the same reason, Parket al. (2009) used inlet restrictions for each channel in their coppertest section. These restrictions and the channels in their case werefabricated separately and then aligned within the multiple-micro-channel element tested. Nonetheless, such a solution is not appli-cable for silicon chips, where the restrictions are generallyfabricated along with the channels, applying the same manufactur-ing process. Recently, Szczukiewicz et al. (2012b, 2013b), usedrectangular orifices at the inlet of each channel (they were manu-factured in one etching process together with the microchannels)with expansion ratios varying from ein;rest ¼ 1:33 to 4. However,they saw that the micro-orifices of ein;rest ¼ 1:33 did not stabilizethe two-phase flow of R236fa within the range of the tested exper-imental conditions. Such geometries were also previously studiedby Peles and co-workers, i.e. Kosar et al. (2006), Schneider et al.(2006, 2007), Kosar and Peles (2007).

Fig. 14 illustrates the two-phase flow and temperature patternsof R236fa for three different micro-orifices sizes tested by Szczu-kiewicz (2012) at the same experimental conditions. The channelswere 100 � 100 lm2 of cross-sectional area, while the expansionratio of the inlet restrictions was varied from 1.33 to 4. As can beseen, the overall two-phase flow stability improves with increasingthe expansion ratio of the inlet restrictions. In Fig. 14(b), the testsection’s base temperature appears to have medium values,

although the two-phase flow is always unstable within the testedrange of the experimental conditions. Whereas, as noticeable inFig. 14(d) and (f), the temperature increases with increasing theexpansion ratio from 2 to 4 (experimentally, the outlet tempera-ture was controlled to a fixed value). As pointed out by Mukherjeeand Kandlikar (2009), the inlet restriction increases the velocity ofthe liquid and consequently the liquid flow rate which by-passesthe bubble through the liquid film. This generates a hydrodynamiceffect which squeezes the bubble, thus thickening the liquid filmand reducing the thin-film evaporation heat transfer rate. In orderto explore the effect of the size of the inlet restriction on the ther-mal behavior of the micro-evaporator under stable conditions, Ta-ble 2 lists the spatio-temporal average temperatures of the testsection’s base for ein;rest ¼ 2 and 4, for a base heat flux ranging from25 to 48 W cm�2. It is seen that the difference of the average basetemperature Tb;ave between these cases decreases with increasingheat flux. This may be interpreted as a consequence of the higherevaporation rate which tends to thin the liquid film, thus opposingand then suppressing the hydrodynamic effect of the inletrestriction.

In order to determine the effect of the expansion ratio on the lo-cal heat transfer coefficient, a comparison was performed forR236fa flowing in the micro-evaporators with different inletrestrictions. Fig. 15 reports that the average level of the heat trans-fer coefficient decreases when increasing the expansion ratio of theinlet restriction. The red vertical line corresponds to the predictedCB – AF flow transition of Costa-Patry and Thome (2012, 2013). Therepresented points are from the flashing two-phase flow withoutbackflow operating regime (Szczukiewicz et al., 2012b, 2013b).This regime was found to provide the best flow and temperaturestability. Based on the high-speed flow visualization videos, it

TIR [oC]

z [mm]

y [m

m]

2 4 6 8 10

2

4

6

8

10

36

38

40

42

44

46

TIR [oC]

z [mm]

y [m

m]

2 4 6 8 10

2

4

6

8

10

36

38

40

42

44

46

TIR [oC]

z [mm]

y [m

m]

2 4 6 8 10

2

4

6

8

10

36

38

40

42

44

46

(a) (b)

(c) (d)

(e) (f)

Fig. 14. Snapshots of the high-speed flow visualization and the time-averaged IR temperature maps of the test section’s base provided by the two-phase flow boiling ofR236fa for Gch 1100 kg m�2 s�1 and qb 36 W cm�2: (a), (b) ein;rest ¼ 1:33, (c), (d) ein;rest ¼ 2, and (e), (f) ein;rest ¼ 4. The flow is from left to right in all the presented images forboth flow and temperature.

Table 2Spatio-temporal average temperatures of the test section’s base forGch ¼ 2094 kg m�2 s�1 of channel mass flux, the base heat flux, qb , ranging from 25to 48 W cm�2 and the expansion ratios of the inlet restrictions of ein;rest ¼ 2 and 4,where DT ¼ Tb;aveðein;rest ¼ 4Þ � Tb;aveðein;rest ¼ 2Þ.

qb Tb;aveðein;rest ¼ 2Þ Tb;aveðein;rest ¼ 4Þ DT

W cm�2 �C �C K

25.0 42.6 45.2 2.629.0 43.5 46.0 2.532.6 44.3 46.8 2.536.6 45.3 47.3 2.040.0 46.1 48.1 2.044.4 47.0 48.9 1.948.0 47.6 49.5 1.9

S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101 97

was determined that bubbly flow was initiated at the beginning ofeach channel from the flashing and almost immediately developedinto slug and consequently annular flow.

In Fig. 15 at low vapor qualities, the descending trend of aw cor-responds to the coalescing elongated bubble region, as predictedby the three-zone model of Thome et al. (2004). In this zone, thehigher expansion ratio leads to a drop of the heat transfer coeffi-cient, as explained previously. After reaching the local minimum,which corresponds relatively well to the CB – AF flow transitionof Costa-Patry and Thome (2012, 2013), the heat transfer increaseswith increasing vapor quality. In the annular flow regime, the heattransfer coefficient for the higher expansion ratio grows more sig-nificantly. This can be ascribed to the instability of the vapor–li-quid interface triggered by the higher velocities associated withthe smaller restriction that gives a more irregular bubble interface,thus enhancing the time-averaged heat transfer coefficient (Tibiri-ca et al., 2012). In addition the perturbed interface promotes moreliquid to be entrained in the vapor core, which was shown byCioncolini and Thome (2011) to have a positive effect on the heattransfer performance (of course as long as dryout is avoided).

0 0.05 0.1 0.15 0.2 0.250

0.5

1

1.5

2

2.5

3

3.5x 104

x [−]

α w [W

m−2

K−1

]

ein,rest = 2

ein,rest = 4

CB−AF transition of Costa−Patry and Thome (2012)

Fig. 15. Two-phase wall heat transfer coefficient as a function of local vapor qualityfor R236fa in the test section with the inlet restrictions of ein;rest ¼ 2 and 4 forGch ¼ 2081 kg m�2 s�1 and qw ¼ 173 kW m�2 (stable two-phase flows).

0 0.05 0.1 0.15 0.2 0.25 0.30

0.5

1

1.5

2

2.5

3

3.5x 104

x [−]

α w [W

m−2

K−1

]

Gch = 906 kg m−2 s−1, qb = 16.8 W cm−2

Gch = 2099 kg m−2 s−1, qb = 16.9 W cm−2

Gch = 2096 kg m−2 s−1, qb = 48.0 W cm−2

Fig. 16. Two-phase wall heat transfer coefficient of R236fa in the micro-evaporatorwith the inlet restrictions of the expansion ratio of ein;rest ¼ 4 as a function of localvapor quality, where solid lines correspond to experimental results, while thedashed ones represent the simulated (steady) values obtained using the flowpattern-based heat transfer model of Costa-Patry and Thome (2012, 2013).

0 10 20 30 40 5030

35

40

45

50

55

60

t [s]

T b [o C]

(a)(b) (c)(d) (f)

(e)

(g)(h)

Fig. 17. Temporal temperature fluctuations at the base of the silicon micro-evaporator of ein;rest ¼ 2: (a) single-phase flow in the entire test section with thevapor bubbles appearing only at the manifold’s outlet plenum, (b) single-phase flowfollowed by two-phase flow with backflow into the inlet header, (c) unstable two-phase flow with backflow developing into jet flow, (d) jet flow, (e) single-phase flowfollowed by two-phase flow without backflow, (f) two-phase flow with backflowtriggered by bubbles formed in the flow loop before the test section, (g) flashingtwo-phase flow (at exit of inlet micro-orifices) with backflow, and (h) flashing two-phase flow without backflow. Figure extracted from the Ph.D. thesis of Szczukiewicz(2012).

98 S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101

The further analysis includes the impact of two-phase flowinstability on the value and trend of the heat transfer coefficient.Fig. 16 shows a comparison of three sets of data: two at similarheat flux (green and red lines) and two at similar mass flux (redand blue lines). For the lowest heat flux and mass flux (green col-or), significant flow instability, vapor backflow, and flow maldistri-bution were present. In the second case (red color), the flowinstabilities were prevented and the vapor backflow was sup-pressed. However, the flow experienced a severe flow maldistribu-tion, which increased and then decreased the heat transfercoefficients by about 30%, showing the maldistribution is mostlydetrimental to heat transfer. As the mass flux and the heat flux in-creased (blue color), the stable two-phase flow with a flashed va-por injected into the channel was achieved. The solid linescorrespond to experimental results, whereas the dashed ones rep-resent the simulated (steady) heat transfer coefficients for compar-ison. The experimental trends of the heat transfer coefficient are U-shaped (over the applicable ranges of vapor qualities) in all threecases. The stable two-phase flow with flashing (blue line) lead tothe highest rise of the heat transfer coefficient as the vapor qualityincreases in the annular flow regime. Furthermore, since in thesimulations the local heat transfer coefficient in the annular flowregime does not depend on the heat flux, the dashed red and bluelines overlap. This tendency is usually observed experimentally,but it is not present here due to the maldistributed flow. Therefore,a clear distinction between steady, unsteady, well- and maldistrib-uted flows needs to be made when presenting the heat transfercoefficient trends.

For unstable two-phase flow (green line in Fig. 16), the experi-mental heat transfer coefficient trend is nearly flat over a widerange of vapor quality (0.02 < x < 0.17 in the present conditions)and the unstable values are about the same as those predictedfor stable flow in this case. This may confuse the situation whena limited number of temperature sensors are adopted and theexperimental trends are extrapolated. For instance, Consolini andThome (2009) showed that the local heat transfer coefficients un-der unsteady conditions were independent of local vapor quality.Nonetheless, they used only 5 sensors along the channel length,which is much less than the present case, and thus the increaseof the heat transfer coefficient toward the inlet and outlet couldnot be captured in their tests.

The results presented above are time-averaged; however, atemporal analysis is needed to provide a full overview on the mul-ti-microchannel heat transfer performance and reliability during

its whole lifetime in practical applications. To this aim, the temper-ature fluctuations for a selected pixel of the IR camera’s sensor ar-ray are assessed in Fig. 17. Note that the highest standard deviationof the temperature fluctuation, 0.82 K, is detected for the unstabletwo-phase flow with backflow developing into jet flow operatingregime (c), but as shown in Szczukiewicz (2012) it can be muchhigher. On the other hand, the flashing two-phase flow withoutbackflow, defined as the most optimum operating regime, providesvery stable flow with a temperature standard deviation of �0.04 K.Additionally, the current analysis reveals that the frequency of thetemperature oscillations is about 2 to 6 Hz for unstable two-phaseflow (c). The frequency increases with mass and heat fluxes (g, h),simultaneously with decreasing the amplitude of the oscillations,such that above a certain threshold for heat and mass flux theoscillations disappear and the flow can be regarded as stable. The

0 2 4 6 8 101.4

1.6

1.8

2

2.2

2.4

2.6

2.8x 104

y [mm]

α w [W

m−2

K−1

]

z = 2 mm, ein,rest = 2z = 2 mm, ein,rest = 4z = 5 mm, ein,rest = 2z = 5 mm, ein,rest = 4z = 8 mm, ein,rest = 2z = 8 mm, ein,rest = 4

Fig. 18. Width-wise heat transfer coefficient profiles for two-phase flows of R236fain ein;rest ¼ 2 (unsteady case) and ein;rest ¼ 4 (steady case) at the longitudinal channellocation of z ¼ 2, 5, and 8 mm for Gch ¼ 1292 kg m�2 s�1 and qb ¼ 43:2 W cm�2,considering an array of 90 � 90 IR temperatures.

S. Szczukiewicz et al. / International Journal of Multiphase Flow 59 (2014) 84–101 99

frequency of the present temperature oscillations for unstableflows agrees quite well with the ones given by Consolini andThome (2009).

As a last point, the width-wise heat transfer coefficient profilesfor steady (in ein;rest ¼ 4) and unsteady (in ein;rest ¼ 2) two-phaseflows of R236fa at the longitudinal channel location of z = 2, 5,and 8 mm for Gch ¼ 1292 kg m�2 s�1 and qb ¼ 43:2 W cm�2 are pre-sented in Fig. 18. The first two locations correspond to the churnflow, while the last one represents the annular flow. It is evidentthat average level of the heat transfer coefficient decreases withincreasing the expansion ratio of the inlet restriction, which isassociated with higher flow velocities in ein;rest ¼ 4. Those ones ex-tend the region of churn flow. Whereas, in annular flow forz = 8 mm, the difference in heat transfer coefficient betweenein;rest ¼ 2 and 4 becomes less significant. Secondly, the heat trans-fer coefficient for the unsteady case is characterized by significantfluctuations in the lateral direction. Whereas, in ein;rest ¼ 4, wherethe flow is very stable in time (see the flashing two-phase flowwithout backflow operating regime in Fig. 17), the heat transfercoefficient profile is more uniform between y = 2 mm and 8 mm,with y being a coordinate perpendicular to the flow direction. Inthis test section, due to the heat spreading in the lateral direction,the local heat transfer coefficient at the boarders rises proportion-ally to the dissipated heat flux, since the heat tends to conduct to-wards the cooler regions (for more detail, refer to Section 4.2). Thishighlights again that 3D heat conduction analysis needs to be ta-ken into account to provide the most accurate heat transfer resultsand data trends.

5. Conclusions

This paper illustrates the most recent experimental and numer-ical outcomes on two-phase flow boiling in microchannels. Thenumerical simulations of boiling flows performed by the authorsshow that the proper modeling of the thermal inertia of the liquidfilm trapped between an elongated bubble and the channel wall,and of the flow recirculation in the liquid slug between two bub-bles, provides very valuable local information on the heat transfercoefficient. This may aid to improve physics-based boiling heattransfer prediction methods, for instance the broadly-used three-zone model of Thome et al. (2004). A better understanding of thelinkage between flow patterns and heat transfer trends in micro-channels is also obtained by coupling the very fine spatial

temperature measurements allowed by IR thermography with flowvisualization techniques. Such analysis confirmed that flow patterntransitions need to be further investigated to clarify the observedtrends in the heat transfer coefficient with respect to the local va-por quality. High emphasis is here given to the heat transfer coef-ficient data reduction process which, in order to conduct a faircomparison among independent experimental studies, has to ac-count for peculiar microscale effects associated with the miniatur-ization of the tested evaporators. In particular, when the pressuredrop is significant, the saturation temperature involved in the heattransfer coefficient estimation cannot be assumed to be constant orlinear along the channel length; it was illustrated how linear, pre-diction method-based, and prorated reconstructions of the pres-sure profile along the microchannel may lead to remarkabledifferences in heat transfer trends and magnitudes. Moreover, themeasured wall temperature and the actual local heat flux seenby the two-phase flow are affected by the heat spreading acrossthe micro-evaporator due to the slopes in the heat transfer coeffi-cients themselves and by the edge effects in proximity of its man-ifold. Therefore, an accurate 3D modeling of the heat conductionfrom the base of the heat sink to the channels walls is recom-mended, in order to obtain a heat transfer coefficient which prop-erly reflects the performance of the microchannel two-phase flow.In addition, the spatio-temporal local heat transfer coefficient anal-ysis revealed that the two-phase flow instability and flow maldis-tribution among the channels may have predominant influence onthe experimental results and data trends, and thus add to confuseof the situation. Therefore, a clear distinction between mal- andwell-distributed flows, unsteady, and steady flows needs to bemade in order to properly reduce and compare the results fromindependent studies. Finally, it was shown that the inlet micro-ori-fices are an effective solution to stabilize the two-phase flow inmicrochannels, and thus greatly extend the reliable range of oper-ating conditions of the micro-evaporator.

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