Radiative Transfer and Flux Theory

TL;DR

This paper explores the fundamental principles of radiative transfer using flux and stress theory, deriving classical and generalized results for radiance distribution on the sphere.

Contribution

It introduces a flux and stress theory framework for radiative transfer, deriving Lambert's rule from balance laws and extending it to irregular radiance distributions.

Findings

Lambert's rule derived from flux balance and Cauchy postulates

Extension of radiance distribution theory to irregular measures

Unified approach for classical and irregular radiance cases

Abstract

The fundamental notions of radiative transfer, e.g., Lambert's cosine rule, are studied from the point of view of flux and stress theory of continuum mechanics. For the classical case, where the radiance is distributed regularly over the unit sphere, it is shown that Lambert's rule follows from a balance law for the transfer of radiative power in each direction $\norb$ of the sphere, together with the appropriate Cauchy postulates and the additional assumption that the corresponding flux vector field $\radvec_{\norb}$ be parallel to $\norb$. An analogous theory is presented for the irregular case where the distribution of radiance on the sphere is given as a Borel measure.