Extension of Planck’s law to steady heat flux across nanoscale gaps

Abstract

Recent experiments report that the radiative heat conductance through a narrow vacuum gap between two flat surfaces increases as the inverse square of the width of the gap. Such a significant increase of thermal conductivity has attracted much interest because of numerous promising applications in nanoscale heat transfer and because of the lack of its theoretical explanation. It is shown here that the radiative heat transport across narrow layers can be described in terms of conventional theory adjusted to non-equilibrium structures with a steady heat flux.

Extension of Planck's law of thermal radiation to systems with a steady heat flux

“…In a closely related paper [30] we considered radiative heat transport between two dielectric half-spaces separated by a gap of small width d, and we obtained agreement with recent experimental observation, that the conductance becomes unbounded as O (1/d 2 ) between two materials at different temperatures as the gap's width d vanishes. This was done without employing extraneous point sources, roughness, or non-linearities, which are often introduced to explain the difference between experimental data and the conventional theories.…”

Equilibrium ensembles of electromagnetic thermal radiation in layered media

“…The results presented in [6][7][8] show correct orders of magnitude Kapitsa resistance for the first time without any added elements such as surface roughness. Inspired by this success we applied our methodology to another notorious problem, that of nano-scale thermal radiation across a narrow vacuum gap [9], and we obtained agreement with recent experimental observations that the radiative conductance between two identical materials at different temperatures becomes unbounded as O(1/H 2 ) as the gap's width H vanishes. This was accomplished without employing extraneous point sources, roughness, or non-linearities, which are commonly used without foundation to improve the predictions based on the classical approach..…”

Heat transfer across a nanoscale pressurized air gap and its application in magnetic recording

“…To evaluate q rad , we adopt the theoretical model that extends the classical Planck’s law into the near field radiation regime 26,27 and demonstrates qualitative agreement with experiments conducted using a real magnetic head 28 . In the studied temperature range, the model shows that the radiative heat transfer coefficient h rad (defined by q rad /( T s  −  T d )) is a strong function of the spacing d, in contrast to its weak dependence on T s and T d 28 .…”