Analytic solution of the Poiseuille Flow problem
V. N. Popov1, I. V. Testova2, A. A. Yushkanov3
| Annotation | Within 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. |
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| Keywords | flow of the gas in the channel, Poiseuille Flow, Boltzmann's kinetic equation, the model kinetic equations, exact analytical solutions. |
1Head of Mathematics Chair, Northern Arctic federal university, Arkhangelsk; popov.vasily@pomorsu.ru.
2The senior teacher of computer science Chair, Pomor state university after M.V. Lomonosov, Arkhangelsk; testovairina@mail.ru.
3Professor of Theoretical Rhysics Chair, Moscow state regional university, Moscow; yushkanov@inbox.ru.
Citation: V. N. Popov, I. V. Testova, A. A. Yushkanov , "[Analytic solution of the Poiseuille Flow problem]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,12:3 (2010) 111–121 (In Russian)
