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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