Study on topology optimization for performance improvement of heat transfer resistance

Abstract

In this paper, we propose a formulation of the topology optimization problem based on density variation type to suppress the heat transfer performance of heat conductors. Research on the optimum design of heat conductors has focused exclusively on finding cooling structures that allow heat to escape efficiently. In this study, we review the cost functions used for cooling structures and check that the negative values of those functions can not use for keeping heat. Based on the results, we propose to use the squared L2 norm of heat transfer on the heat transfer boundary as the cost function for heat insulation. In addition, the cost function is extended in the case including radiation. Volume constraint minimization problems of those cost functions are solved by the H¹ gradient method. Based on the numerical examples, there is possibility to use the proposed cost functions to suppress the heat transfer performance of heat conductors.