Kinetic and Related Models (KRM)

Stagnation-point flow of a rarefied gas impinging obliquely on a plane wall

Pages: 935 - 954, Volume 4, Issue 4, December 2011      doi:10.3934/krm.2011.4.935

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Kazuo Aoki - Department of Mechanical Engineering and Science, and Advanced Research Institute of Fluid Science and Engineering, Kyoto University, Kyoto 606-8501, Japan (email)
Yoshiaki Abe - School of Engineering Science, Faculty of Engineering, Kyoto University, Kyoto 606-8501, Japan (email)

Abstract: The steady two-dimensional stagnation-point flow of a rarefied gas impinging obliquely on an infinitely wide plane wall is investigated on the basis of kinetic theory. Assuming that the overall flow field has a length scale of variation much longer than the mean free path of the gas molecules and that the Mach number based on the characteristic flow speed is as small as the Knudsen number (the mean free path divided by the overall length scale of variation), one can exploit the result of the asymptotic theory (weakly nonlinear theory) for the Boltzmann equation, developed by Sone, that describes general steady behavior of a slightly rarefied gas over a smooth boundary [Y. Sone, in: D. Dini (ed.) Rarefied Gas Dynamics, Vol. 2, pp. 737--749. Editrice Tecnico Scientifica, Pisa (1971)]. By solving the fluid-dynamic system of equations given by the theory, the precise description of the velocity and temperature fields around the plane wall is obtained.

Keywords:  Stagnation-point flow, rarefied gas flows, Boltzmann equation, slip flows, kinetic theory of gases.
Mathematics Subject Classification:  Primary: 76P05, 82C40; Secondary: 76D05.

Received: June 2011;      Available Online: November 2011.