A gradient-based strategy to construct efficient heat conduction path for arbitrary configurations

Abstract

The heat conduction optimization problem is a widely investigated abstraction of various heat dissipation problems in industry and electronics cooling. This paper studies the optimization strategy that produces optimized heat conduction path made of high thermal conductivity materials, with the objective of lowering the hot spot temperature or improving temperature uniformity. The automatic differentiation (AD) technique is a general-purpose method to calculate the partial derivatives of any continuous function composed by elementary functions with respect to multiple independent variables. It is introduced to calculate the gradient of the objective function with respect to the thermal conductivity field, so that the optimization procedure can be guided directly towards the minimization of the desired objective function. This paper investigated the configurations of both continuous-value thermal conductivity and discrete-value thermal conductivity. Results indicate that the present optimization strategy is able to handle various types of boundary conditions and objective functions. The present method is compared with the iterative method based on variational principle (Var), showing that the AD method performs better than the Var method in most situations.