Research Papers

Topology Optimization for an Internal Heat-Conduction Cooling Scheme in a Square Domain for High Heat Flux Applications

[+] Author and Article Information
Jaco Dirker

e-mail: jaco.dirker@up.ac.za

Josua P. Meyer

e-mail: josua.meyer@up.ac.za

Department of Mechanical and
Aeronautical Engineering,
University of Pretoria,
Pretoria 0002, South Africa

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received May 23, 2012; final manuscript received December 6, 2012; published online September 23, 2013. Assoc. Editor: Sujoy Kumar Saha.

J. Heat Transfer 135(11), 111010 (Sep 23, 2013) (10 pages) Paper No: HT-12-1239; doi: 10.1115/1.4024615 History: Received May 23, 2012; Revised December 06, 2012

Conductive heat transfer is of importance in the cooling of electronic equipment. However, in order for conductive cooling to become effective, the use of high-conducting materials and the correct distribution thereof is essential, especially when the volume which needs to be cooled has a low thermal conductivity. An emerging method of designing internal solid-state conductive systems by means of topology optimization is considered in this paper. In this two-dimensional study, the optimum distribution of high conductive material within a square-shaped heat-generating medium is investigated by making use of the “method or moving asymptotes” (MMA) optimization algorithm coupled with a numerical model. The use of such a method is considered for a number of cost (driving) functions and different control methods to improve the definiteness of the boundaries between the heat-generating and high-conduction regions. It is found that the cost function used may have a significant influence on the optimized material distribution. Also of interest in this paper are the influences of thermal conductivity and the proportion of the volume occupied by the high-conducting solid on the resulting internal cooling structure distribution and its thermal conduction performance. For a square domain with a small exposed isothermal boundary centered on one edge, a primary V-shaped structure was found to be predominantly the most effective layout to reduce the peak operating temperature and to allow for an increase in the internal heat flux levels.

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Fig. 1

Two-dimensional domain under consideration

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Fig. 2

Element-centered nodal scheme for node j

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Fig. 3

Two-dimensional validation of the numerical model by comparing it with a solution obtained by ansys fluent

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Fig. 6

Maximum temperature values for the material distribution described in Fig. 5

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Fig. 5

Comparative temperature distributions for (a) a single full-length fin, (b) perpendicularly branched structure, and (c) the topology optimized material distribution of Fig. 4

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Fig. 4

Obtained topology layouts after different number of iterations (effective 80 × 80 mesh size)

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Fig. 7

Converged maximum temperatures for different p-values for ϕmax = 0.1 and γ = 500

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Fig. 8

Converged maximum temperatures in terms of the converged tree definiteness measure for ϕmax = 0.1 and γ = 500

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Fig. 9

Converged maximum temperatures in terms of the converged tree definiteness measure for ϕmax = 0.2 and γ = 500




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