Research Papers: Forced Convection

A Semi-Empirical Heat Transfer Model for Forced Convection in Pin-Fin Heat Sinks Subjected to Nonuniform Heating

[+] Author and Article Information
S. S. Feng

School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, P.R. China

T. Kim1

SV Laboratory, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, P.R. Chinatongbeum@gmail.com

T. J. Lu

SV Laboratory, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, P.R. China


Corresponding author.

J. Heat Transfer 132(12), 121702 (Sep 17, 2010) (11 pages) doi:10.1115/1.4002285 History: Received September 24, 2009; Revised May 11, 2010; Published September 17, 2010; Online September 17, 2010

This paper presents a cost effective semi-empirical analytical model for convective heat transfer in pin-fin heat sinks subjected to nonuniform heating set by a circular hot gas impinging jet. Based on empirical correlations taken from the open literature, temperature variations in the heat sink are obtained from the finite volume solution of the semi-empirical model. Based on a purpose-built experimental setup, measurements of a substrate temperature are performed using an infrared camera. These, along with the convective fluid temperature measured at the exit of the pin-fin array, are compared against analytical model predictions, with overall good agreement achieved. Subsequently, the influences of the convection Reynolds number, substrate thickness, and thermal conductivity of material on the distribution of substrate temperature are quantified by the validated model. It is demonstrated that the present model is capable of predicting local thermal behaviors such as the footprints of the pin fins. In addition, with the spreading resistance captured accurately, the model can be used for the design optimization of pin-fin/substrate systems subjected to nonuniform heating.

Copyright © 2010 by American Society of Mechanical Engineers
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Figure 7

Heat flux distribution on substrate surface exposed to fluid flow

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Figure 9

Peak substrate temperature (θpeak) plotted as a function of convection Reynolds number

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Figure 10

Influence of substrate thickness on temperature profiles of outer and inner substrate surfaces along x-axis at y=0 for ReDh=1.0×104: (a) ks=169 W/m K (Al alloy); (b) ks=15 W/m K (stainless steel)

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Figure 11

Distribution of substrate temperature (z=0) along x-axis (y=0) plotted as a function of substrate thermal conductivity for fixed substrate thickness (t/d=0.2) at ReDh=1.0×104

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Figure 6

Fluid temperature in pin-fin heat sink: (a) predicted fluid temperature map at ReDh=1.0×104; (b) comparison of measured temperature profiles at channel exit (x=L/2) along y-axis with those predicted

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Figure 8

Effect of convection Reynolds numbers on substrate temperature profile along x-axis (y=0)

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Figure 1

Schematic of (a) square pin-fin heat sink and (b) test setup for nonuniform impingement heating

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Figure 2

Comparison of presently measured nondimensional adiabatic wall temperature distribution with that of Goldstein (15)

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Figure 3

Heat balance in a representative unit cell of pin-fin heat sink

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Figure 4

Computational mesh for substrate: (a) 3D mesh for half of substrate; (b) plan view from positive z-direction showing pin fins (dark squares)

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Figure 5

Surface temperature mappings on substrate (z=0) at ReDh=1.0×104, with convective flow direction from negative x value to positive x value: (a) experiment; (b) prediction from semi-empirical model



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