Time-periodic thermal rectification in heterojunction thermal diodes

Abstract

Thermal diodes that rectify time-periodic temperature (T) fields have been proposed for applications in waste heat scavenging and thermal control. Although these applications involve transient temperatures, prior analytical solutions for heat conduction in thermal diodes have focused on the steady-state response. We use analytical perturbation methods supported by finite-element method (FEM) calculations to study time-periodic rectification in a one-dimensional heterojunction diode consisting of two materials with thermal conductivity k and heat capacity c that each scale linearly with T. One boundary of the diode experiences a sinusoidal boundary condition with an average temperature T0, an angular frequency ω, and a temperature amplitude ΔT, while the other boundary is maintained at a constant T0. The analytical perturbation solution shows that the nonlinear response has frequency components at direct current (dc) and at the second harmonic of ω for small ΔT/T0. We introduce a rectification asymmetry metric φ as the difference in the forward and reverse diode orientation dc heat fluxes and find that φ can be enhanced at large ω by a factor of two compared to the quasi-steady φ at small ω. We identify the optimal dimensionless parameters to maximize φ and find that φ is independent of the heat capacity temperature coefficient for all ω. We use FEM calculations to validate the perturbation solution and to study the effects of larger ΔT oscillations, interface thermal contact resistances, and heat losses. Our modeling results can be used to design heterojunction thermal diodes for applications and experiments involving time-periodic thermal rectification.