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RESEARCH PAPERS

# Constructal Peripheral Cooling of a Rectangular Heat-Generating Area

[+] Author and Article Information
Alexandre K. da Silva1

Department of Mechanical Engineering, University of Hawaii at Manoa, Honolulu, HI 96822akds@hawaii.edu

Louis Gosselin

Département de génie mécanique, Université Laval, Québec, Québec G1K 7P4, Canada

1

Corresponding author.

J. Electron. Packag 128(4), 432-440 (Feb 27, 2006) (9 pages) doi:10.1115/1.2351909 History: Received October 03, 2005; Revised February 27, 2006

## Abstract

The present paper determines numerically the optimal geometric parameters for the maximal peripheral cooling of a two-dimensional rectangular solid body with internal heat generation. The objective is to maximize the thermal global conductance (i.e., minimize the hot spot temperature on the solid body) by using the minimal cooling space. The flow is conducted around the heated solid body by a sequence of channels of independent width $Di$, where $1⩽i⩽4$. Each configuration is free to morph itself in two directions: (a) the number of cooling channels, and (b) the aspect ratio of the heated body $λ$. The numerical results show that a number of cooling channels greater than one (i.e., $n>1$) is profitable in terms of thermal performance when the heated body resembles a square (i.e., $λ∼1$). However when $λ$ is free to vary, the thermal performance does not necessarily increase with the number of cooling channels. The paper also discusses the importance to allow each configuration to morph itself in multiple directions by comparing the thermal performance of similar configurations with different number of degrees of freedom. Scale analysis is used to verify the results obtained numerically for all the degrees of freedom considered. The numerical results agree with the scaling trends.

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## Figures

Figure 1

Solid body with internal heat generation cooled from the periphery: (a) One cooling side (n=1), (b) four cooling sides (n=4)

Figure 2

Effect of the channel spacings D1 and D2 on the global thermal performance of the assembly (Be=105, Pr=0.7, λ=1, and n=2)

Figure 3

Optimal channel spacing versus the dimensionless pumping power

Figure 4

Maximized thermal performance versus the flow strength (Be)

Figure 5

Effect of the heat source aspect ratio on the thermal performance of the assembly

Figure 6

Effect of the dimensionless pumping power on the optimal channel spacing

Figure 7

Optimal channel spacing and heat source aspect ratio for configurations with one (n=1), two (n=2), and three (n=3) cooling surfaces

Figure 8

Effect of the number of cooling surfaces on the thermal performance

Figure 9

Effect of the cooling area available (i.e., ATot=Asolid+Afluid) on the thermal performance of the assembly

Figure 10

Optimal geometric parameter for an assembly with fixed cooling space versus the dimensionless pumping power

Figure 11

Effect of the number of cooling surfaces on the thermal performance of the assembly

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