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RESEARCH PAPERS: Porous Media

# Height Effect on Heat-Transfer Characteristics of Aluminum-Foam Heat Sinks

[+] Author and Article Information
W. H. Shih, W. C. Chiu

Department of Mechanical Engineering,  National Chung Cheng University, Chia-Yi, Taiwan, R.O.C.

W. H. Hsieh

Department of Mechanical Engineering,  National Chung Cheng University, Chia-Yi, Taiwan, R.O.C.imewhh@ccu.edu.tw

J. Heat Transfer 128(6), 530-537 (Oct 12, 2005) (8 pages) doi:10.1115/1.2188461 History: Received November 30, 2004; Revised October 12, 2005

## Abstract

This study investigates and demonstrates the two conflicting effects of the height on the cooling performance of aluminum-foam heat sinks, under the impinging-jet flow condition. In addition, the nonlocal thermal equilibrium phenomena are also investigated. When the $H∕D$ (the height to diameter ratio) of the aluminum-foam heat sinks is reduced from 0.92 to 0.15, the Nusselt number of aluminum-foam heat sinks is found to first increase and then decrease. The increase in the Nusselt number is caused by the increased percentage of the cooling air reaching the top surface of the waste-heat generation block, resulting from the reduced flow resistance. The decrease in the Nusselt number is mainly caused by the reduction in the heat-transfer area between the cooling air and the solid phase of the aluminum-foam heat sink. As the porosity and pore density decrease, the Nusselt number increases and the convective heat transfer is enhanced. The correlation between the Nusselt and Reynolds numbers for each of the 15 samples studied in this work is reported. For samples with a $H∕D>0.31$, the temperature difference between the solid and gas phases of aluminum-foam heat sinks decreases with the increase of the distance from the heated surface. The non-local thermal equilibrium regime is observed to exist at low Reynolds number and small dimensionless height. On the other hand, for samples with a $H∕D⩽0.31$, the temperature difference first increases and then decreases with the increase of the distance from the heated surface; the maximum temperature difference is located at $z∕H≒0.25$ and is independent of the Reynolds number.

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## Figures

Figure 1

A photo of the aluminum-foam heat sink showing the dimensions and axes (sample 1-1, 10PPI, ε=0.92, H=60mm, D=65mm)

Figure 2

Experimental apparatus for the measurements of heat transfer characteristics of aluminum-foam heat sinks

Figure 3

Apparatus for measuring heat loss

Figure 4

Effect of Reynolds number on the Nusselt number for samples 2-1–2-7

Figure 5

Effect of Reynolds number on Nu for heat sinks with different pore densities and heights

Figure 6

Effect of Reynolds number on Nu for heat sinks with different porosities and heights

Figure 7

Comparison of NuDe from the present study, Lee and Lee (24), Jiang (25), and Hwang and Chao (26)

Figure 8

(a) Effect of Reynolds number on the distributions of dimensionless solid temperature of samples 2-1 and 2-5. (b) Effect of Reynolds number on the distributions of dimensionless gas temperature of samples 2-1 and 2-5.

Figure 9

Effect of Reynolds number on the distributions of dimensionless temperature difference of sample 2-5

Figure 10

Height effect on the distribution of dimensionless temperature difference

Figure 11

(a) Effects of the Reynolds number and the height on the dimensionless temperatures difference for sample 2-1. (b) Effects of the Reynolds number and the height on the dimensionless temperature difference for sample 2-5.

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