Minimum entropy production closure of the photo-hydrodynamic equations for radiative heat transfer

TL;DR

This paper introduces a minimum entropy production approach to determine effective radiation transport coefficients in photo-hydrodynamic models, improving accuracy across different optical regimes without fitting parameters.

Contribution

It presents a novel method based on entropy production minimization to derive photon distributions and effective coefficients, enhancing modeling of radiative heat transfer.

Findings

Accurately interpolates between optically thick and thin regimes

Provides effective absorption coefficients without fitting parameters

Offers a new approach compared to maximum entropy methods

Abstract

In the framework of a two-moment photo-hydrodynamic modelling of radiation transport, we introduce a concept for the determination of effective radiation transport coefficients based on the minimization of the local entropy production rate of radiation and matter. The method provides the nonequilibrium photon distribution from which the effective absorption coefficients and the variable Eddington factor (VEF) can be calculated. The photon distribution depends on the frequency dependence of the absorption coefficient, in contrast to the distribution obtained by methods based on entropy maximization. The calculated mean absorption coefficients are not only correct in the limit of optically thick and thin media, but even provide a reasonable interpolation in the cross-over regime between these limits, notably without introducing any fit parameter. The method is illustrated and discussed for grey matter and for a simple example of non-grey matter with a two-band absorption spectrum. The method is also briefly compared with the maximum entropy concept.