An effective method for hot spot temperature optimization in heat conduction problem

Abstract

Heat conduction problem for the optimization of thermal conductivity distribution is gaining considerable concerns in electronics cooling. Previous studies usually adopted optimization criteria to solve this problem. However, it still remains a big challenge for minimization of hot spot temperature, which is a core issue for electronics cooling. In this study, an iterative method based on a novel criterion is developed to minimize the hot spot temperature of customized regions in heat conduction problems. The optimization criterion for minimizing the hot spot temperature is derived using variational principle, which reveals that the optimization mechanism is the synergy of temperature gradient field and multiplier gradient field. An iterative method based on this criterion is developed to adjust the thermal conductivity field for minimization of hot spot temperature. The volume-to-point (VP) heat conduction problem is introduced to validate the proposed method. The results show that the proposed method reduces the hot spot temperature rise in customized regions by 44 %–47 % compared with those with uniform thermal conductivity distribution. Moreover, the developed criterion is also adopted in an allocation and reallocation method for the VP problems with discrete thermal conductivities, reducing the hot spot temperature rise by 88% ∼ 89%.