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

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.