One class of analytical self-similar solutions to the system of radiative transfer and energy equations for a homogeneous medium

Abstract

The known class of analytical self-similar solutions of the traveling heat wave type for a nonlinear integro-differential system of equations which describes nonstationary spectral transfer of radiant energy in a kinetic model is generalized to a homogeneous medium. The solutions are constructed in three-dimensional Cartesian geometry with specially chosen absorption and scattering coefficients. No additional terms that might distort the essence of the physical phenomena being described are introduced into the original equations, and the solution is almost completely determined by the functional dependence on a self-similar variable. This class of exact solutions is also applicable to the “gray matter” approximation and can be used to test numerical methods for calculating direct and inverse problems of radiative transfer. Examples of test calculations are given.