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 Matem. Mod., 2017, Volume 29, Number 1, Pages 84–94 (Mi mm3808)

Heat transfer process in an elliptic channel

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

a Northern (Arctic) Federal University named after M.V. Lomonosov, Arkhangelsk
b Moscow state regional university, Moscow

Abstract: Consider the problem of heat transfer in the elliptic channel with its axis parallel to the temperature gradient. As the basic equation, that describes the kinetics of the process, the Williams kinetic equation, and as a boundary condition on the wall of the channel — a model of diffuse reflection are used. The deviation from the equilibrium state of the gas is assumed small. In order to find a linear correction to the local equilibrium distribution function the problem is reduced to solving a linear homogeneous differential equation of the first order. It’s solution is constructed using the method of characteristics. An analytical method for calculating the heat flux of rarefied gas through a cross section in the elliptic channel by the using a simple numerical procedures, which are realized in the system of computer algebra of Maple 17, is presented. A comparison with analogical results presented in the open data is done.

Keywords: the gas flow in the channel, a model kinetic equation, analytical solutions, method of characteristics.

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 3628

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English version:
Mathematical Models and Computer Simulations, 2017, 9:4, 521–528

Revised: 29.02.2016

Citation: O. Germider, V. N. Popov, A. A. Yushkanov, “Heat transfer process in an elliptic channel”, Matem. Mod., 29:1 (2017), 84–94; Math. Models Comput. Simul., 9:4 (2017), 521–528

Citation in format AMSBIB
\Bibitem{GerPopYus17} \by O.~Germider, V.~N.~Popov, A.~A.~Yushkanov \paper Heat transfer process in an elliptic channel \jour Matem. Mod. \yr 2017 \vol 29 \issue 1 \pages 84--94 \mathnet{http://mi.mathnet.ru/mm3808} \elib{http://elibrary.ru/item.asp?id=28405094} \transl \jour Math. Models Comput. Simul. \yr 2017 \vol 9 \issue 4 \pages 521--528 \crossref{https://doi.org/10.1134/S2070048217040056} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85024383916} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. O. V. Germider, V. N. Popov, “Matematicheskoe modelirovanie techeniya razrezhennogo gaza v pryamougolnom kanale s vnutrennim tsilindricheskim elementom”, Sib. elektron. matem. izv., 14 (2017), 518–527
2. O. V. Germider, V. N. Popov, “Transport processes at part accommodation by the walls of a rectangular channel”, Math. Models Comput. Simul., 10:4 (2018), 512–518
3. O. V. Germider, V. N. Popov, “Matematicheskoe modelirovanie protsessov perenosa v tsilindricheskom kanale”, Zhurnal SVMO, 20:1 (2018), 64–77
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