Radiative Heat Transfer and Effective Transport Coefficients

TL;DR

This paper reviews the radiative transfer theory, emphasizing a moment expansion approach that derives effective transport coefficients, with an application to electrical arcs, advancing the modeling of radiative heat transfer.

Contribution

It introduces a moment expansion method with entropy production rate minimization for closure, providing a new way to compute transport coefficients in radiative heat transfer.

Findings

Derivation of effective transport coefficients using the moment approach.

Application of two-moment equations to electrical arc modeling.

Validation of the method through practical example.

Abstract

The theory of heat transfer by electromagnetic radiation is based on the radiative transfer equation (RTE) for the radiation intensity, or equivalently on the Boltzmann transport equation (BTE) for the photon distribution. We focus in this review article, after a brief overview on different solution methods, on a recently introduced approach based on truncated moment expansion. Due to the linearity of the underlying BTE, the appropriate closure of the system of moment equations is entropy production rate minimization. This closure provides a distribution function and the associated effective transport coefficients, like mean absorption coefficients and the Eddington factor, for an arbitrary number of moments. The moment approach is finally illustrated with an application of the two-moment equations to an electrical arc.