Radiative transfer in random media with Rayleigh scattering

Abstract

This paper considers radiation transfer through a finite plane-parallel random medium consisting of two immiscible mixed materials. The mixing statistics of the two components of the medium is assumed to be described by the two-state homogeneous Markovian statistics. The problem treats a medium contains an internal source and has diffusely- and specularly-reflecting boundaries obeying Rayleigh scattering law. The problem with this generalized boundary conditions is solved in terms of the solution of the corresponding free source problem with simple boundary conditions. Pomraning–Eddington approach is used to obtain an explicit solution of the simple problem in the deterministic case. A formalism, developed to treat radiative transfer in statistical mixtures, is used to obtain the ensemble-averaged solution. Numerical results for the ensemble-average partial heat fluxes of the problem under consideration are obtained using three different weight functions for the sake of comparison.