Nonlinear thermal conductivities of core-shell metamaterials: Rigorous theory and intelligent application

Abstract

Nonlinear (temperature-dependent) thermal conductivities are common in nature, so their in-depth studies are valuable to practical applications. However, for core-shell metamaterials with nonlinear thermal conductivities, only an approximate theory was proposed to deal with weak nonlinearity, and almost no theory can handle strong nonlinearity strictly. To solve this problem, we propose a rigorous theory under certain conditions to calculate the effective thermal conductivities of core-shell metamaterials with nonlinear thermal conductivities, whether weak or strong. Furthermore, we design intelligent applications with the present theory. We take thermal radiation with the Rosseland diffusion approximation as an example, which is a typical system containing nonlinear thermal conductivities, and further realize switchable functions between concentrating and cloaking. The present theory and application are confirmed by finite-element simulations. Our results lay the theoretical foundation for nonlinear core-shell metamaterials and provide insights into nonlinear thermal management.