1208.6400 (Karabi Ghosh)
Karabi Ghosh
An analytical solution to the non-equilibrium Marshak diffusion problem in a planar slab of finite thickness is presented. Analytic expressions for the radiation and material energy densities as a function of space and time are derived using the Laplace transform method by summing over the first few residues at the poles of the transcendental equation. Integrated energy densities and leakage currents are also obtained in analytical form. Results for a planar slab of any finite thickness can be generated using the analytic expressions of these quantities unlike the previous works wherein numerical results were generated to a specified degree of accuracy for a semi-infinite medium with semi analytical solutions. The benchmark results obtained in this work can be used to validate and verify non equilibrium radiation diffusion computer codes.
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http://arxiv.org/abs/1208.6400
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