Geodesic
Study of different approximations for solving heat transfer
Matematičeskoe modelirovanie, Tome 32 (2020) no. 7, pp. 77-97

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The objective of this work is to study and compare different approximations to the system of equations which describe radiative heat transfer in optically thick and thin media. Asymptotic analysis is used for optically thick media. For optically thin media we use an approach that reduces diffusion equations to the kinetic one. Results of our study suggest that for optically thick media, solutions obtained with the approximations do converge to the solution of the kinetic equation as optical thickness increases. This follows from asymptotic analysis. For optically thin media, the convergence is only possible to quasitransport and quasi-diffusion solutions.
Keywords: radiative heat transfer, radiative heat transfer approximations. 
@article{MM_2020_32_7_a4,
     author = {A. A. Shestakov},
     title = {Study of different approximations for solving heat transfer},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {77--97},
     publisher = {mathdoc},
     volume = {32},
     number = {7},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_7_a4/}
}
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A. A. Shestakov. Study of different approximations for solving heat transfer. Matematičeskoe modelirovanie, Tome 32 (2020) no. 7, pp. 77-97. http://geodesic.mathdoc.fr/item/MM_2020_32_7_a4/