A CLASS OF EXACT SOLUTIONS FOR A SYSTEM OF RADIATIVE HEAT TRANSFER EQUATIONS

B. P. Tikhomirov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1986. Вып.2. С. 3-8.

      A spectral formulation and a grey matter problem are used to derive an exact solution for a nonequilibrium heat wave propagating with a constant velocity across a cold (nontransparent) material. Absorption, radiation, and isotropic scattering are accounted. Absorption and scattering coefficients are chosen in a special way. The system of energy and radiation transport equations and that of diffusion equations are considered both with and without an energy source (sink), depending on temperature. The exact solutions obtained may be used for numerical method improvements and program debugging.