Radiative transfer equation in spherically-symmetric non-scattering media

Abstract

The equation of radiative transfer in spherically symmetric shells with arbitrary internal sources is solved. The equation of transfer is integrated on a discrete grid of angle and radius. The size in angle coordinates is determined by the roots of a quadrature formula, while the size in radial coordinates is determined by the non negativity of the reflection and transmission operators. Two cases of variation of the Planck formula are considered: (1) constant throughout the medium and (2) varying as 1/r-squared. It is found that in the inner shells the radiation directed toward the center of the sphere is greater than that directed away from the center. In the outer shells the converse is true.