Topology optimization of a thermal cloak in the frequency domain

Abstract

Designing wideband thermal cloaks remains a challenge, especially at high frequencies. We propose an optimization approach for the design of a thermal cloak for an arbitrary object with large thermal conductivity (copper), in a given frequency band and for a specific diffusion direction. Cloaking performance is assessed as a function of frequency (in the optimal direction) and as a function of angle (at the optimal frequency). Near-perfect cloaking is achieved over a finite frequency band, and, moreover, the thermal cloak performs well in the time domain, including in the transient regime, irrespective of the initial temperature distribution. Interestingly, this specially optimized cloak also works fairly well for other objects with large thermal conductivity but breaks down for those of low thermal conductivity.