Level-set topology optimization for effective control of transient conductive heat response using eigenvalue

Abstract Designing thermally efficient devices for an instantaneous heating condition is a challenging task, since a structure that simultaneously satisfies a lower peak temperature as well as a slower thermal response time must be achieved. In order to design a structure for both of the requirements, a transient analysis-based structural topology optimization method can be usually employed. However, the overall thermal response time of a heat conduction system can be modelled simply via the fundamental thermal eigenvalue, which is a physical quantity. This suggests that a thermal eigenvalue analysis can be adopted instead of transient analysis for an effective design of the structure controlling its thermal response time. In this study, we aim at developing a level-set topology optimization method to effectively optimize the overall response time of heat conduction systems using the thermal eigenvalue. The proposed level-set thermal eigenvalue topology optimization updates the structural boundary based on the common fixed grid approach, and the adjoint variable method is applied to compute shape sensitivity. Numerical examples clearly show the controllability of overall heat response time through the thermal eigenvalue, and especially, it is demonstrated that the proposed method is useful in designing an effective cooling structure for an instantaneous heating.