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

Analytical benchmark for non-equilibrium radiation diffusion in finite size systems