Inverse design method of thermal devices with thermal Hall effect

Efficient thermal management is important for both performance and efficiency improvements of thermal devices. For designing reasonable materials and structures of such devices, various design methods were proposed where the material thermal conductivity tensors were positive definite and symmetric based on the physical requirements. Here, we propose an inverse design method for thermal devices considering the thermal Hall effect, which makes the material thermal conductivity tensor asymmetric. Enlarging the design space consisting of the symmetric constitutive tensors to that of the asymmetric ones, there is a possibility of improving the theoretical performance limit of thermal devices. We formulate an inverse problem based on the free material optimization formalism, parameterizing the design space so that the physically available property could be naturally satisfied. Several numerical experiments are provided to show the validity and the utility of the proposed method.