Exact Integral Formulation for Radiative Transfer in an Inhomogeneous Scattering Medium

The exact integral formulation in terms of the moments of intensity is developed for radiative transfer hi a three-dimensional, inhomogeneous medium with anisotropic scattering. Since the use of the present formulation in radiation computation requires the integration only over spatial variables, it reduces the labor of computation. Examples, including isotropic scattering and anisotropic scattering in a slab, and isotropic scattering in a two-dimensional, rectangular medium exposed to collimated radiation, are presented to show the effectiveness of the present fomiulation. The examples are solved by die Nystrom method. Numerical results for the one-dimensional, isotropically scattering case show excellent agreement with available solutions reported in the literature. Graphic results of both one- and two-dimensional examples are presented to show the effects of the space-dependent albedo.