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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1011–1023 (Mi semr970)

Computational mathematics

Mathematical simulation of heat and mass transfer processes in a rectangular channel depending on the accommodation coefficient of tangential momentum

O. V. Germidera, V. N. Popova, A. A. Yushkanovb

a Northern Arctic Federal University named after M. V. Lomonosov, Severnaya Dvina Emb., 4, 163002, Arkhangelsk, Russia
b Moscow region state university, Radio str., 10a, 107005, Moscow, Russia

Abstract: The article proposes method of solving the problem of heat and mass transfer in a long rectangular channel using Maxwell's mirror-diffusive boundary conditions. A rarefied gas flow trough cross section is studied on the basis of the Williams model kinetic equation. Expressions are obtained for heat and mass fluxes as linear functions of the temperature gradient supported in the channel. The profiles of the heat flux vector and the mass velocity of the gas in the channel are constructed depending on the accommodation coefficient. The specific gas mass flux and the heat flux through the channel cross section have been calculated. A numerical analysis of the results is carried out in the case when the tangential momentum accommodation coefficient is close to unity. It is shown that if one of the channel dimensions is much smaller than the other, the obtained results coincide with the analogous results for channels with infinite parallel walls. The results were compared with the analogous results found in the open press.

Keywords: The Williams equation, the model of mirror-diffuse reflection, analytical solutions, method of characteristics.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-302-0000117-47-500752

DOI: https://doi.org/10.17377/semi.2018.15.085

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Document Type: Article
UDC: 517.9
MSC: 35Q20
Received March 13, 2018, published September 14, 2018

Citation: O. V. Germider, V. N. Popov, A. A. Yushkanov, “Mathematical simulation of heat and mass transfer processes in a rectangular channel depending on the accommodation coefficient of tangential momentum”, Sib. Èlektron. Mat. Izv., 15 (2018), 1011–1023

Citation in format AMSBIB
\Bibitem{GerPopYus18} \by O.~V.~Germider, V.~N.~Popov, A.~A.~Yushkanov \paper Mathematical simulation of heat and mass transfer processes in a rectangular channel depending on the accommodation coefficient of tangential momentum \jour Sib. \Elektron. Mat. Izv. \yr 2018 \vol 15 \pages 1011--1023 \mathnet{http://mi.mathnet.ru/semr970} \crossref{https://doi.org/10.17377/semi.2018.15.085} `