Exact formulas for radiative heat transfer between planar bodies under arbitrary temperature profiles: modified asymptotics and sign-flip transitions

TL;DR

This paper provides exact formulas for radiative heat transfer between planar bodies with arbitrary temperature profiles, revealing diverse asymptotic behaviors and enabling tunable heat flux control, including sign-flip transitions at nanometric distances.

Contribution

The authors derive exact analytical formulas for radiative heat transfer under arbitrary temperature profiles, uncovering new asymptotic regimes and the possibility of flux sign-flips, enhancing control over near-field heat exchange.

Findings

Different asymptotic behaviors depending on temperature derivatives

Sign-flip transitions in heat flux at tunable distances

Relevance to experiments on near-field heat transfer

Abstract

We derive exact analytical formulas for the radiative heat transfer between parallel slabs separated by vacuum and subject to arbitrary temperature profiles. We show that, depending on the derivatives of the temperature at points close to the slab--vacuum interfaces, the flux can exhibit one of several different asymptotic low-distance ($d$) behaviors, obeying either $1/d^2$, $1/d$, or logarithmic power laws, or approaching a constant. Tailoring the temperature profile within the slabs could enable unprecedented tunability over heat exchange, leading for instance to sign-flip transitions (where the flux reverses sign) at tunable distances. Our results are relevant to the theoretical description of on-going experiments exploring near-field heat transfer at nanometric distances, where the coupling between radiative and conductive heat transfer could be at the origin of temperature gradients.