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Mathematical Modelling of Transport Processes for Various Regimes of Rarefied Gas Flow in the Channel. P. 124–128

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Section: Physics. Mathematics. Informatics




Lukashev Vyacheslav Valeryevich
Institute of Mathematics, Information and Space Technologies, Northern (Arctic) Federal University named after M.V. Lomonosov (Arkhangelsk, Russia)
Popov Vasily Nikolaevich
Institute of Mathematics, Information and Space Technologies, Northern (Arctic) Federal University named after M.V. Lomonosov (Arkhangelsk, Russia)


In this paper we obtained asymptotic expressions describing mass flows of gas and heat for various regimes of rarefied gas flow in the channel with the temperature gradient parallel to the walls. As original relations we use the results obtained by the authors within the framework of the kinetic approach, based on the solution of the linearized BGK (Bhatnagar, Gross, Krook) model of Boltzmann kinetic equation using diffuse reflection boundary condition on the channel walls. For various tangential momentum accommodation coefficients of gas molecules during their interaction with the channel walls, we studied the transition to the hydrodynamic regime and regime close to the free-molecular one. We proved the existence of a special regime of gas flow in the channel, when, despite the vanishingly small Knudsen number, the gas flow regime differs significantly from the hydrodynamic one. Further, we identified the conditions for transition to this gas flow regime, determined the range of applicability for the obtained asymptotic expressions and compared the obtained results with the similar published ones.


Boltzmann kinetic equation, model kinetic equations, exact analytical solutions, models of boundary conditions
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