Maximal rectification ratios for idealized bi-segment thermal rectifiers

Thermal rectifiers whose forward heat fluxes are greater than reverse counterparts have been extensively studied. Here we have discovered, idealized, and derived the ultimate limit of such rectification ratios, which are partially validated by numerical simulations, experiments, and micro-scale Hamiltonian-oscillator analyses. For rectifiers whose thermal conductivities (κ) 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 κ(max)/κ(min), where two extremes denote values of the solid segment materials that can be possibly found or fabricated within a reasonable temperature range. Recommendations for manufacturing high-ratio rectifiers are also given with examples. Under idealized assumptions, these proposed rectification limits cannot be defied by any bi-segment thermal rectifiers.