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

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 (generally nongrey) matter. The method provides the nonequilibrium photon distribution from which the effective (variable) absorption coefficients and the variable Eddington factor (VEF) can be calculated. For a single band model, the photon distribution depends explicitly on the frequency dependence of the absorption coefficient. Without introducing artificial fit parameters, multi-group or multi-band concepts, our approach reproduces the exact results in both limits of optically thick (Rosseland mean) and optically thin (Planck mean) media, in contrast to the maximum entropy method. Also the results for general nonequilibrium radiation between the limits of diffusive and ballistic photons are reasonable. We conjecture that the reason for the success of our approach lies in the linearity of the underlying Boltzmann equation of the photon gas. The method is illustrated and discussed for grey matter and for a simple example of nongrey matter with a two-band absorption spectrum. The method is also briefly compared with the maximum entropy concept.