Fluctuating surface-current formulation of radiative heat transfer: theory and applications

TL;DR

This paper introduces a new surface-current formulation for radiative heat transfer that is flexible for various geometries and leverages surface-integral techniques for efficient analytical and numerical solutions.

Contribution

The paper presents a novel surface-current based approach to radiative heat transfer, enabling fast semi-analytical and numerical computations for complex geometries.

Findings

Applicable to high-symmetry geometries with spectral methods

Can be used with boundary-element method for complex shapes

Demonstrates heat transfer calculations for slabs, cylinders, and cones

Abstract

We describe a novel fluctuating-surface current formulation of radiative heat transfer between bodies of arbitrary shape that exploits efficient and sophisticated techniques from the surface-integral-equation formulation of classical electromagnetic scattering. Unlike previous approaches to non-equilibrium fluctuations that involve scattering matrices---relating "incoming" and "outgoing" waves from each body---our approach is formulated in terms of "unknown" surface currents, laying at the surfaces of the bodies, that need not satisfy any wave equation. We show that our formulation can be applied as a spectral method to obtain fast-converging semi-analytical formulas in high-symmetry geometries using specialized spectral bases that conform to the surfaces of the bodies (e.g. Fourier series for planar bodies or spherical harmonics for spherical bodies), and can also be employed as a numerical method by exploiting the generality of surface meshes/grids to obtain results in more complicated geometries (e.g. interleaved bodies as well as bodies with sharp corners). In particular, our formalism allows direct application of the boundary-element method, a robust and powerful numerical implementation of the surface-integral formulation of classical electromagnetism, which we use to obtain results in new geometries, including the heat transfer between finite slabs, cylinders, and cones.