# Thermal radiative energy exchange between a closely-spaced linear chain of spheres and its environment

## TL;DR

This paper derives general expressions for radiative heat transfer between coated spheres in a linear chain and their environment, applicable to small, closely-spaced spheres, with validation against established numerical methods.

## Contribution

It introduces new analytical formulas for radiative transfer applicable to arbitrary-sized, coated spheres in close proximity, extending classical models.

## Key findings

- Validated formulas against discrete dipole and boundary element methods.
- Applicable to small, closely-spaced, coated spheres.
- Implications for near-field radiative heat transfer experiments.

## Abstract

In this work, we present expressions for radiative heat transfer between pairs of spheres in a linear chain and between individual spheres and their environment. The expressions are valid for coated spheres of arbitrary size, spacing, and isotropic optical properties. The spheres may be small and closely-spaced, which violates the assumptions foundational to classical radiative transfer. We validate our results against existing formulations of radiative heat transfer, namely the thermal discrete dipole and boundary element methods. Our results have important implications for the modeling and interpretation of near-field radiative heat transfer experiments between spherical bodies.