AIAA 2005-0958

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Convection Heat Transfer From Tube Banks in Crossflow:

Analytical ApproachM. M. Yovanovich, Fellow AIAA

W. A. KhanJ. R. Culham

Microelectronics Heat Transfer LaboratoryDepartment of Mechanical Engineering

University of Waterloo

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Outline

IntroductionLiterature Review ObjectivesAssumptionsModelingResults and ComparisonsConclusionsAcknowledgments

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

IntroductionIndustrial applications:

Heat exchanger devices (like steam generators, preheaters, oil coolers, power condensers)Process industryAir conditioning and refrigeration industry

Primary interest of thermal engineers:Average heat transfer coefficient for the

entire tube bundle

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Available Correlations (Single Cylinder)

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Available Correlations (Tube Banks)

Zukauskas, 1972:

F = Correction factor for NL ≤ 16

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Available Correlations (Tube Banks)

Zukauskas, 1972:

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Correction Factor F for NL ≤ 16

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Available Correlations (Tube Banks)Grimison, 1937:

F = Correction factor for NL ≤ 10

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Available Correlations (Tube Banks)Grimison, 1937:

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Correction Factor F for NL ≤ 10

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Objectives

Develop analytical correlations to determine heat Develop analytical correlations to determine heat transfer fortransfer for :

In-line tube banks

Staggered tube banks

that can be used for a wide range of geometric parameters

Validate developed correlations with experimental data

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Assumptions

1. Forced Convection

2. Steady, laminar, fully developed and 2-D flow

3. Incompressible fluid with constant properties

4. Reynolds number is based on D and Umax

5. Inviscid flow outside boundary layer

6. Flow normal to tube bank

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Heat Transfer Model

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

In-Line Arrangement

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Staggered Arrangement

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Control Volume

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Boundary Conditions

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Results

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

HTP with ST (In-Line Arrangement)

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

HTP with ST (Staggered Arrangement)

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Effect of Tube Arrangement (1.25 x 1.25)

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Effect of Tube Arrangement (3.0 x 3.0)

ReD

Nu D

102 103 104100

101

102

103

In-Line ArrangementStaggered ArrangementExperimental (Zukauskas, 1985)Analytical Model (Khan, 2004)

Pr = 0.71

ST/D = 3

SL/D = 3

SingleCylinder}

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Staggered Tube Bank (Incropera and DeWitt)

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Comparisons

(ii) Wide Tube Bank (2.1 x 2.1)

(i) Compact Tube Bank (1.25 x 1.25)

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

NuD vs. ReD (In-Line Arrangement)

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

NuD vs. ReD (Staggered Arrangement)

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Summary and Conclusions

Comparisons show that higher heat transfer rates are obtained from:

compact tube banks (any arrangement)

staggered arrangement (any spacing)

Both In-Line and Staggered models are:

applicable over a wide range of parameters

suitable for use in design of tube banks

43rd Aerospace Sciences Meeting & Exhibit, 10-13 January 2005, Reno, Nevada

Acknowledgements

The authors gratefully acknowledge the financial support of

Natural Sciences and Engineering Research Council of Canada

Centre for Microelectronics Assembly and Packaging