Systematically engineered thermal metastructure for rapid heat dissipation/diffusion by considering the thermal eigenvalue

Abstract This study proposes a systematic inverse design method of a novel thermal metastructure that improves the thermal dynamic characteristics by considering thermal eigenvalues for the first time. To this end, we apply topology optimization and introduce a relaxation scheme to address the design-dependent heat convection boundary on the implicit interfaces between solid and (ambient) fluid phases updated during the optimization process. With the proposed inverse design method, optimization of various thermal metastructures with enhanced thermal dynamic characteristics is performed. A physical interpretation of the heat transfer mechanism for each optimized thermal metastructure is also carried out by employing two dimensionless numbers, in this case Biot and Fourier numbers. Through this interpretation, it is demonstrated that among many design factors, the heat convection effect with an ambient fluid is the most important factor when seeking to improve the thermal dynamic characteristics. Also, performance of the optimized thermal metastructures is physically analyzed through thermal energy. Moreover, we find that the thermal eigenvalue physically corresponds to a time constant related to the response rate in a first-order linear system. The thermal eigenvalue-based inverse design method to improve the thermal dynamic characteristics is computationally very efficient, as it predicts the dynamic characteristics from an eigenvalue analysis instead of a full time-dependent analysis. It also has the advantage of providing more physically quantifiable insight regarding optimized thermal metastructures. In this regard, the proposed inverse design method can be an important and critically useful design tool for improving the dynamic characteristic of various thermal actuator and sensor systems.