Radiative transfer equation in spherically-symmetric non-scattering media

Abstract

We solved the equation of radiative transfer in spherically-symmetric shells with arbitrary internal sources. We integrated the equation of transfer on the discrete grid of angle and radius given by [μ_j−1, μ_j] [r_i−1, r_i]. The size in the angle coordinates is determined by the roots of a quadrature formula where as the size in the radial coordinate is determined by the non-negativity of the reflection and transmission operators. We considered two cases of variation of the Planck function. (1) Constant throughout the medium and (2) varying as 1/r ². We find that in the inner shells, the radiation directed toward the centre of the sphere is more than that directed away from the centre of the sphere. In the outer shells the converse is true.