General formulation of coupled radiative and conductive heat transfer between compact bodies

We present a general framework for studying strongly coupled radiative and conductive heat transfer between arbitrarily shaped bodies separated by subwavelength distances. Our formulation is based on a macroscopic approach that couples our recent fluctuating volume-current (FVC) method of near-field heat transfer to the more well-known Fourier conduction transport equation, in which case the former can induce temperature gradients throughout the bodies. Although the FVC framework can in principle be applied to arbitrary geometries, in practice it is most applicable in situations where only one of the bodies undergoes significant temperature gradients. To illustrate the capabilities of this framework, we consider an idealized, proof-of-concept geometry involving two aluminum-zinc oxide nanorods separated by a vacuum gap, with one of the rods heated by a large-temperature reservoir on one side while the other is held at room temperature. We show that the presence of bulk nanorod polaritonic resonances can result in very large radiative heat transfer rates (roughly five times larger than what is achievable in the planar configuration) and leads to nonlinear temperature profiles.