An Analytical Solution of the Radiative Transfer Equation for Inhomogeneous Finite Medium with Fresnel Boundary Conditions

The problem of radiation transfer through an inhomogeneous finite medium with internal energy sources and diffusely and specular reflecting boundary conditions is considered (problem 1). The partial heat fluxes for this problem are given in terms of the albedo of the source-free problem with specular-reflecting boundaries (problem 2). We assume that the reflectivity of the surfaces dependent upon the refractive indices and is considered as Fresnel's reflection probability function. The Pomading-Eddington method is used to calculate first the albedo s for problem 2 and then calculate the partial heat fluxes for problem 1. Results are obtained for isotropic scattering in a homogeneous and an inhomogeneous media for uniform and non-uniform internal sources and are compared with the published calculations.