Nonlinear thermal conductivity of periodic composites

Abstract

Composites have been widely used to realize various functions in thermal metamaterials, thus becoming important to predict heat transport properties according to geometric structures and component materials. Based on a first-principles approach, namely, the Rayleigh method, here we develop an analytical way to calculate temperature-dependent (i.e., nonlinear) thermal conductivities of a composite with circular inclusions arranged in a periodic rectangular array. We focus on both weak and strong nonlinearity. As a result, we find that the temperature-dependence (nonlinearity) coefficient of the whole periodic composite can be larger than that of the nonlinear component inside this composite. Simulation results from finite element analysis show that the Rayleigh method can be also more accurate than the Maxwell-Garnett or Bruggeman effective medium approximations. As a model application, we further tailor the nonlinearity to design a thermal diode, for which heat flux along one direction is much larger than that along the opposite. This work provides a different theory for handling periodic structure with thermally responsive thermal conductivities, and it could be useful for designing thermal metamaterials with diverse properties including rectification.