Radiative transfer within non Beerian porous media with semitransparent and opaque phases in non equilibrium: Application to reflooding of a nuclear reactor

A local radiative transfer model is developed for strongly anisotropic porous media with an opaque phase and a mixture of two semitransparent phases. At the optically thick limit, the homogenized phase associated with the opaque interfaces is characterized by generalized extinction and scattering coefficients at equilibrium, a phase function and an effective refraction index, by following the model of Taine et al. for non Beerian media. The radiative transfer model is based on a Radiative Transfer Equation (RTE) with three source terms, which are associated with the temperature fields of the opaque interfaces and the two semitransparent phases. This RTE has been solved by a perturbation technique, which allows radiative interfacial fluxes and radiative powers per unit volume, that are exchanged between phases, to be computed at local scale. The main contributions are obtained at zeroth order perturbation. Corrective contributions at first order perturbation are also determined: Radiative fluxes and powers are then expressed from coupled Fourier’s laws, which are characterized by radiative conductivity tensors associated with each phase.