  Non-equilibrium radiation diffusion is an important mechanism of energy
transport in Inertial Confinement Fusion, astrophysical plasmas, furnaces and
heat exchangers. In this paper, an analytical solution to the non-equilibrium
Marshak diffusion problem in a planar slab and spherical shell of finite
thickness is presented. Using Laplace transform method, the radiation and
material energy densities are obtained as a function of space and time. The
variation in integrated energy densities and leakage currents are also studied.
In order to linearize the radiation transport and material energy equation, the
heat capacity is assumed to be proportional to the cube of the material
temperature. The steady state energy densities show linear variation along the
depth of the planar slab, whereas non-linear dependence is observed for the
spherical shell. The analytical energy densities show good agreement with those
obtained from finite difference method using small mesh width and time step.
The benchmark results obtained in this work can be used to validate and verify
non equilibrium radiation diffusion computer codes in both planar and spherical
geometry.
