Maximal rectification ratios for bi-segment thermal rectifiers

TL;DR

This paper derives the theoretical maximum rectification ratios for bi-segment thermal rectifiers, revealing fundamental limits and providing guidelines for designing high-performance devices.

Contribution

It introduces the first theoretical limits for thermal rectification ratios in bi-segment rectifiers, validated by simulations and experiments, and offers practical manufacturing recommendations.

Findings

Maximum ratio for linear conductivities is 3.

Nonlinear conductivities can achieve ratios up to κ_max/κ_min.

Validated theoretical limits with experiments and simulations.

Abstract

We study bi-segment thermal rectifiers whose forward heat fluxes are greater than reverse counterparts. Presently, a shortcoming of thermal rectifiers is that the rectification ratio, namely the forward flux divided by the reverse flux, remains too small for practical applications. In this study, we have managed to discover and theoretically derive the ultimate limit of such ratios, which are validated by numerical simulations, experiments, and micro-scale Hamiltonian-oscillator analyses. For rectifiers whose thermal conductivities are linear with the temperature, this limit is simply a numerical value of 3. For those whose conductivities are nonlinear with temperatures, the maxima equal $\kappa_{max}/\kappa_{min}$, where the two extremes denote values of the solid segment materials that can be possibly found or fabricated within a reasonable temperature range on earth. Recommendations for manufacturing high-ratio rectifiers are also given with examples.