Geodesic
Mathematical modeling of heat transfer process in a rectangular channel in the problem of Poiseuille flow
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1401-1409

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We propose an analytical solution of problem of heat transfer in a long channel with a rectangular cross section. A rarefied gas flow trough cross section is studied on the basis of Williams kinetic equation in the whole range of the Knudsen number varying from the free molecular regime to the hydrodynamic one. A wide range of the aspect ratio is considered. The heat flow is calculated as a function of a constant pressure gradient supported in the channel.
Keywords: Boltzmann kinetic equation, Williams equation, model of diffuse reflection, analytical solutions, Knudsen number. 
@article{SEMR_2016_13_a100,
     author = {O. V. Germider and V. N. Popov},
     title = {Mathematical modeling of heat transfer process in a rectangular channel in the problem of {Poiseuille} flow},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1401--1409},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a100/}
}
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O. V. Germider; V. N. Popov. Mathematical modeling of heat transfer process in a rectangular channel in the problem of Poiseuille flow. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 1401-1409. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a100/