2012/08/31 by Karabi Ghosh, Ghosh, Karabi
Engineering · Materials Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Fusion materials and technologies #High Energy Astrophysical Phenomena (astro-ph.HE) #Laser-Plasma Interactions and Diagnostics #Mathematical Physics (math-ph) #Nuclear reactor physics and engineering #Plasma Physics (physics.plasm-ph) #astro-ph.HE #math-ph #math.MP #physics.plasm-ph
paper · pdf · doi:10.48550/arxiv.1208.6400
24 pages, 18 figures, under review in Annals of Nuclear Energy
openalex publication_date 2012/08/31 · arxiv created 2013/01/16 · arxiv updated 2013/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.