Thermal rectification in nonmetallic solid junctions: Effect of Kapitza resistance

Based on Fourierʹs law for heat conduction, we investigate the asymmetric heat flow in two segment rods of nonmetallic materials. Specifically, we study the effect of the Kapitza resistance at the boundary of the segments on the thermal rectification. To understand basic features of the rectification, we first develop analytical calculation for the heat currents in an ideal rod of a macroscopic length. Explicitly, this is made by assuming that the thermal conductivity of each constituent has a power-law dependence on temperature and also assuming the continuity of temperature at the boundary. Then, we introduce the temperature jump at the boundary due to the Kapitza resistance and show that this effect on the thermal rectification becomes significant as the length of the rod decreases typically to submillimeters. In particular, we find that the temperature jump yields a finite rectification even when no asymmetry is predicted in the heat currents from the continuity of temperature at the junction. The obtained results have an important implication for the analysis of the thermal rectification of a rod consisting of semiconductors Ge and Si.