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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

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

Figures

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Figure 1

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

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Figure 2

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

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Figure 3

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

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Figure 4

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

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Figure 5

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

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Figure 6

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

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Figure 7

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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Figure 8

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

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Figure 9

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

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Figure 10

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

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Figure 11

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

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Figure 12

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

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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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Figure 14

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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