Milne problem in stochastic plane medium with linear anisotropic scattering

The Milne problem of radiative transfer in planar stochastic medium, with linear anisotropic scattering is considered. The medium is assumed to be consisting of two randomly mixed immiscible fluids, with the mixing statistics described as two state homogeneous Markov process. Pomraning-Eddington approach is used to obtain an explicit form for the radiation energy density in deterministic case. A formalism, developed to treat radiative transfer in binary statistical mixtures, is used to obtain the ensemble averaged energy density in stochastic case for the problem under consideration. It is shown that the statistical nature of the medium leads to two contradictory different definitions for the linear extrapolated distance. In the case of isotropic scattering, numerical results are given with comparisons. Results are also given in the case of linear anisotropic scattering at different values of anisotropic coefficient.