Fluctuational electrodynamics calculations of near-field heat transfer in non-planar geometries: A brief overview

•We review the fluctuational electrodynamics formalism for calculating near-field heat transfer.•We describe partial-wave scattering, boundary element, and FDTD numerical methods.•We compare the computational aspects of these methods in the coupled dielectric sphere heat transfer problem.

Near-field electromagnetic heat transfer is of interest for a variety of applications, including energy conversion, and precision heating, cooling and imaging of nano-structures. This past decade has seen considerable progress in the study of near-field electromagnetic heat transfer, but it is only very recently that numerically exact methods have been developed for treating near-field heat transfer in the fluctuational electrodynamics formalism for non-trivial geometries. In this paper we provide a tutorial review of these exact methods, with an emphasis on the computational aspects of three important methods, which we compare in the context of a canonical example, the coupled dielectric sphere problem.