Initial and boundary conditions for equilibrium diffusion theory

Abstract The problem of specifying the initial and boundary temperatures to be used in conjunction with the equilibrium diffusion description of radiative transfer is considered. For this purpose, both an initial and a boundary layer problem arising from an asymptotic analysis of the equation of transfer are analyzed. The initial layer problem is very simple and leads to an exact algebraic result. The boundary layer problem is much more complex and is solved approximately by a variational procedure. Comparisons with exact results in a special simple case indicate that the variational estimate is very accurate for this special case. This allows one to conjecture that the variational result is probably sufficiently accurate in the general case for practical applications of the equilibrium diffusion description of radiative transfer.