Exact solutions of system of equations of radiation and energy transfer in 3D spherically nonsymmetrical geometry

摘要

Exact self-similar solutions are constructed in the form of a traveling heat wave for nonlinear integro-differential equations describing nonstationary kinetic radiation and energy transfer in 3D spherically nonsymmetrical geometry. Solutions for simpler geometries are the particular cases of the solution obtained. The solutions are obtained for specially selected absorption and scattering coefficients. The class of exact solutions obtained is applicable both to gray medium and to spectral radiation transfer, and can be used to test numerical methods for direct and inverse transfer problems. An example of a 3D boundary problem is presented.