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Mathematical modelling of processes of carry in flat channels

V. V. Lukashev1, V. N. Popov2, A. A. Yushkanov3

AnnotationWithin the kinetic approach limit, in the isothermal approximation the analytical (in the form of Neumann's series) solution of the problem on flow of the rarefied gas in the flat channel with the infinite walls, caused by a pressure gradient parallel to walls (Poiseuille Flow) it is constructed. As the basic equation the BGK model of the Boltzmann's kinetic equation is used. As a boundary condition the model of diffusion reflections is used. In view of the constructed distribution function the flow of gases mass in a direction of a gradient of the pressure, falling unit width of the channel and the structure of mass speed of gas in the channel are constructed. Comparison with the similar results received Numerical method is leads..
Keywordsflow of the gas in the channel, Poiseuille Flow, Boltzmann's kinetic equation, the model kinetic equations, exact analytical solutions.

1Post graduate student, Northern Arctic federal university, Arkhangelsk; rarugg@yandex.ru.

2Head of Mathematics Chair, Northern Arctic federal university, Arkhangelsk; popov.vasily@pomorsu.ru.

3Professor of Theoretical Rhysics Chair, Moscow state regional university, Moscow; yushkanov@inbox.ru.

Citation: V. V. Lukashev , V. N. Popov , A. A. Yushkanov , "[Mathematical modelling of processes of carry in flat channels]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,13:2 (2011) 81–91 (In Russian)