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Journal of Electronic Packaging | Volume 128 | Issue 1 | Research Paper
RESEARCH PAPERS

A Model for Flow Bypass and Tip Leakage in Pin Fin Heat Sinks

[+] Author and Article Information
M. Baris Dogruoz1

Experimental and Computational Heat Transfer Group, Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721mbd@tx.fluent.com

Alfonso Ortega

Experimental and Computational Heat Transfer Group, Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721ortega@u.arizona.edu

Russell V. Westphal

Department of Mechanical and Materials Engineering, Washington State University, Tri-Cities, Richland, WA 99354westphal@wsu.edu

1

Presently at Fluent Inc.

J. Electron. Packag 128(1), 53-60 (Jul 30, 2005) (8 pages) doi:10.1115/1.2159009 History: Received October 24, 2004; Revised July 30, 2005
Article
References
Figures
Citing Articles

A model for the pressure drop and heat transfer behavior of heat sinks with top bypass is presented. In addition to the characteristics of a traditional two-branch bypass model, the physics of tip leakage are taken into consideration. The total flow bypass is analyzed in terms of flow that is completely diverted and flow that enters the heat sink but leaks out. Difference formulations of the momentum and the energy equations were utilized to model the problem in the flow direction. Traditional hydraulic resistance and heat transfer correlations for infinitely long tube bundles were used to close the equations. Tip leakage mechanisms were modeled by introducing momentum equations in the flow normal direction in both the pin side and bypass channel, with ad hoc assumptions about the static pressure distribution in that direction. Although the model is applicable to any kind of heat sink, as a case study, results are presented for in-line square pin fin heat sinks. Results were compared with the predictions from a two-branch bypass model and previous experimental data. It is shown that tip leakage effects are important in setting the overall pressure drop at moderate and high pin spacing, but have only minor influence on heat transfer.
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Copyright © 2006 by American Society of Mechanical Engineers
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References

1
Knight, R. W., Goodling, J. S., and Hall, D. J., 1991, “Optimal Thermal Design of Forced Convection Heat Sinks-Analytical,” ASME J. Electron. Packag., 113 , pp. 313–321.
2
Teertstra, P., Yovanovich, M. M., Culham, J. R., and Lemczyk, T., 1999, “Analytical Forced Convection Modeling of Plate Fin Heat Sinks,” in Proceedings of the 15th IEEE SEMI-THERM Symposium , San Diego, CA, pp. 34–41.
3
Lee, S., 1995, “Optimum Design and Selection of Heat Sinks,” in Proceedings of the 11th IEEE SEMITHERM Symposium , San Jose, CA, pp. 48–54.
4
Butterbaugh, M. A., and Kang, S. S., 1995, “Effects of Airflow Bypass on the Performance of Heat Sinks in Electronics Cooling,” ASME J. Electron. Packag., 10 (2), pp. 843–848.
5
Dogruoz, M. B., Urdaneta, M., Ortega, A., and Westphal, R. V., 2002, “Experiments and Modeling of the Hydraulic Resistance of In-line Square Pin Fin Heat Sinks With Top By-Pass Flow,” in Proceedings of the 8th Inter Society Conference on Thermal Phenomena-ITHERM , San Diego, CA, pp. 251–260.
6
Dogruoz, M. B., Urdaneta, M., and Ortega, A., 2002, “Experiments and Modeling of Heat Transfer of In-line Square Pin Fin Heat Sinks With Top By-pass Flow,” ASME Heat Transfer Div. Publ.-HTD, 372 (7), pp. 195–206.
7
Dogruoz, M. B., Urdaneta, M., and Ortega, A., 2005, “Experiments and Modeling of the Hydraulic Resistance and Heat Transfer of In-line Square Pin Fin Heat Sinks With Top By-pass Flow,” Int. J. Heat Mass Transfer, 48 (23-24), pp. 5058–5071.
8
Shaukatullah, H., Storr, W. R., Hansen, B. J., and Gaynes, M. A., 1996, “Design and Optimization of Pin Fin Heat Sinks for Low Velocity Applications,” in Proceedings of the 12th IEEE SEMI-THERM Symposium , Austin, TX, pp. 151–163.
9
Jubran, B. A., Hamdan, M. A., and Abdualh, R. M., 1993, “Enhanced Heat Transfer, Missing Pin and Optimization for Cylindrical Pin Fin Arrays,” ASME J. Heat Transfer, 115 (3), pp. 576–583.
10
Jonsson, H., and Moshfegh, B., 2001, “Modeling of the Thermal and Hydraulic Performance of Plate Fin, Strip Fin, and Pin Fin Heat Sinks-Influence of Flow Bypass,” IEEE Trans. Compon. Packag. Technol.  [CrossRef], 24 (2), pp. 142–149.
11
Jonsson, H., and Moshfegh, B., 2002, “Enhancement of the Cooling Performance of Circular Pin Fin Heat Sinks under Flow Bypass Conditions,” in Proceedings of the 8th Inter Society Conference on Thermal Phonomena-ITHERM , San Diego, CA, pp. 425–432.
12
Biber, C. R., and Belady, C. L., 1997, “Pressure Drop Predictions for Heat Sinks: What is the Best Method?,” ASME J. Electron. Packag., 19 (2), pp. 1829–1835.
13
Dvinsky, A., Bar-Cohen, A., and Strelets, M., 2000, “Thermofluid Analysis of Staggered and Inline Pin Fin Heat Sinks,” in Proceedings of the 7th Inter Society Conference on Thermal Phonomena-ITHERM , Las Vegas, NV, pp. 157–164.
14
Khan, W. A., Culham, J. R., and Yovanovich, M. M., 2004, “Fluid Flow and Heat Transfer from a Cylinder Between Parallel Planes: Analytical Approach,” AIAA Paper 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, pp. 1182–1194.
15
Kays, W. M., and London, A. L., 1998, "Compact Heat Exchangers", Krieger, Florida, pp. 108–114.
16
Idelchik, I. E., 1989, "Flow Resistance: A Design Guide for Engineers", Hemisphere, New York, pp. 716–720.
17
Zhukauskas, A., 1972, “Heat Transfer from Tubes in Cross Flow,” J.P.Hartnett, T.F.IrvineJr., eds., "Adv. Heat Transfer", Academic, San Diego, CA, Vol. 8 , pp. 93–160.
18
Incropera, F. P., and DeWitt, D. P., 1996, "Fundamentals of Heat and Mass Transfer", Wiley, New York.
19
Urdaneta, M., 2002, “Characterization of Pressure Drop and Heat Transfer on Pin Fin Heat Sinks Under Side-Inlet Side-Exit Configuration With Top and Side Flow Bypass,” M.S. thesis, The University of Arizona, Tucson, AZ.

Figures

Grahic Jump Location
+Illustration of a sample heat sink geometry with a top bypass channel. (a) side-view; (b) top-view
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Illustration of a sample heat sink geometry with a top bypass channel. (a) side-view; (b) top-view
Figure 3

Illustration of a sample heat sink geometry with a top bypass channel. (a) side-view; (b) top-view

Grahic Jump Location
+Control volumes for the finned and the bypass sections in the theoretical model
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Control volumes for the finned and the bypass sections in the theoretical model
Figure 4

Control volumes for the finned and the bypass sections in the theoretical model

Grahic Jump Location
+Overall pressure drop, ΔP vs clearance ratio, CL for PL=2.238 at uapp=4m∕s
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Overall pressure drop, ΔP vs clearance ratio, CL for PL=2.238 at uapp=4m∕s
Figure 5

Overall pressure drop, ΔP vs clearance ratio, CL for PL=2.238 at uapp=4m∕s

Grahic Jump Location
+Overall pressure drop, ΔP vs clearance ratio, CL for PL=3.917 at uapp=4m∕s
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Overall pressure drop, ΔP vs clearance ratio, CL for PL=3.917 at uapp=4m∕s
Figure 6

Overall pressure drop, ΔP vs clearance ratio, CL for PL=3.917 at uapp=4m∕s

Grahic Jump Location
+Variation of bypass ratio, BR and leakage ratio, LR with respect to PL for CL=2.0 at uapp=4m∕s
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Variation of bypass ratio, BR and leakage ratio, LR with respect to PL for CL=2.0 at uapp=4m∕s
Figure 14

Variation of bypass ratio, BR and leakage ratio, LR with respect to PL for CL=2.0 at uapp=4m∕s

Grahic Jump Location
+Flow visualization of a heat sink with top bypass flow, PL=2.0, H/df=14.0, CL=0.5
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Flow visualization of a heat sink with top bypass flow, PL=2.0, H/df=14.0, CL=0.5
Figure 1

Flow visualization of a heat sink with top bypass flow, PL=2.0, H/df=14.0, CL=0.5

Grahic Jump Location
+Illustration of the flow passing through a heat sink with top bypass duct
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Illustration of the flow passing through a heat sink with top bypass duct
Figure 2

Illustration of the flow passing through a heat sink with top bypass duct

Grahic Jump Location
+Variation of u, ub, vH with respect to x for PL=2.238 at CL=1.0 and uapp=4m∕s
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Variation of u, ub, vH with respect to x for PL=2.238 at CL=1.0 and uapp=4m∕s
Figure 7

Variation of u, ub, vH with respect to x for PL=2.238 at CL=1.0 and uapp=4m∕s

Grahic Jump Location
+Variation of u, ub, vH with respect to x for PL=2.238 at CL=2.0 and uapp=4m∕s
View Large  |  Save Figure  |  Download Slide (.ppt)
Variation of u, ub, vH with respect to x for PL=2.238 at CL=2.0 and uapp=4m∕s
Figure 8

Variation of u, ub, vH with respect to x for PL=2.238 at CL=2.0 and uapp=4m∕s

Grahic Jump Location
+Variation of u, ub, vH with respect to x for PL=3.917 at CL=1.0 and uapp=4m∕s
View Large  |  Save Figure  |  Download Slide (.ppt)
Variation of u, ub, vH with respect to x for PL=3.917 at CL=1.0 and uapp=4m∕s
Figure 9

Variation of u, ub, vH with respect to x for PL=3.917 at CL=1.0 and uapp=4m∕s

Grahic Jump Location
+Variation of u, ub, vH with respect to x for PL=3.917 at CL=2.0 and uapp=4m∕s
View Large  |  Save Figure  |  Download Slide (.ppt)
Variation of u, ub, vH with respect to x for PL=3.917 at CL=2.0 and uapp=4m∕s
Figure 10

Variation of u, ub, vH with respect to x for PL=3.917 at CL=2.0 and uapp=4m∕s

Grahic Jump Location
+Thermal resistance, Rth vs clearance ratio, CL for PL=2.238 at uapp=2,4m∕s
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Thermal resistance, Rth vs clearance ratio, CL for PL=2.238 at uapp=2,4m∕s
Figure 11

Thermal resistance, Rth vs clearance ratio, CL for PL=2.238 at uapp=2,4m∕s

Grahic Jump Location
+Thermal resistance, Rth vs clearance ratio, CL for PL=3.917 at uapp=2,4m∕s
View Large  |  Save Figure  |  Download Slide (.ppt)
Thermal resistance, Rth vs clearance ratio, CL for PL=3.917 at uapp=2,4m∕s
Figure 12

Thermal resistance, Rth vs clearance ratio, CL for PL=3.917 at uapp=2,4m∕s

Grahic Jump Location
+Variation of bypass ratio, BR and leakage ratio, LR with respect to PL for CL=1.0 at uapp=4m∕s
View Large  |  Save Figure  |  Download Slide (.ppt)
Variation of bypass ratio, BR and leakage ratio, LR with respect to PL for CL=1.0 at uapp=4m∕s
Figure 13

Variation of bypass ratio, BR and leakage ratio, LR with respect to PL for CL=1.0 at uapp=4m∕s

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