Solid-State Thermal Rectification With Existing Bulk Materials

Abstract

A two-terminal thermal device exhibits thermal rectification if it transports heat more easily in one direction than in the reverse direction. Within the framework of classical heat conduction by Fourier’s law, thermal rectification occurs in a two-segment bar if the thermal conductivities of the segments have different dependencies on temperature. The general solution to this problem is a pair of coupled integral equations, which in previous work had to be solved numerically. In this work the temperature dependencies of the thermal conductivities are approximated using power laws, and perturbation analysis at low thermal bias leads to a simple algebraic expression, which shows that the rectification is proportional to the difference in the power-law exponents of the two materials, multiplied by a geometric correction function. The resulting predictions have no free parameters and are in good agreement with the experimental results from the literature. For maximum rectification, the thermal resistances of the two segments should be matched to each other at low thermal bias. For end point temperatures of 300 K and 100 K, using common bulk materials it is practical to design a rectifier with rectification of well over one hundred percent. A new quantity, the normalized thermal rectification, is proposed to better facilitate comparisons of various rectification mechanisms across different temperature ranges.