radiative transfer in a spherical medium

The problem of radiative transfer in a spherical medium is solved by inspection once the slab solution is known. In this work we try to solve the Pseudo-slab problem using a set of trial functions that depend on Case's eigenvalues plus a linear combination of exponential integral functions. The proposed trial functions are used in the integral equation which transforms it to a system of algebraic equations in the expansion coefficients. These expansion coefficients are used to calculate the albedo and the partial heat flux for isotropic scattering in a homogeneous spherical medium.