Geodesic
Mathematical modeling of transfer processes in the problem of the thermal slip of a~gas along a~flat surface
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 4, pp. 79-87.

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In the framework of the kinetic approach, we construct an analytic solution (in the form of a Neumann series) to the problem of the thermal slip of a gas along a rigid flat surface. As the basic equation, we use the linearized ellipsoidal statistical model of the Boltzmann kinetic equation, and as boundary conditions on the streamlined surface we take the mirror-diffuse reflection model. For the various values of the accommodation coefficient of the tangential momentum of the molecules of the gas, we compute the velocity of the thermal slip of the gas along the surface and find the distributions of the gas velocity and the heat flow vector. A comparison with similar results available in the previously published works is made.
Keywords: Boltzmann kinetic equation, model kinetic equation, boundary condition model, exact analytical solution. 
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V. N. Popov; E. A. Smolenskaya. Mathematical modeling of transfer processes in the problem of the thermal slip of a~gas along a~flat surface. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 4, pp. 79-87. http://geodesic.mathdoc.fr/item/SJIM_2014_17_4_a7/

[1] Lifshits E. M., Pitaevskii L. P., Fizicheskaya kinetika, Nauka, M., 1979 | MR

[2] Maxwell J., “On stress in rarefied gases arising from inequalities of temperature”, Philos. Trans. Roy. Soc., 170:1 (1879), 170–231

[3] Latyshev A. V., Yushkanov A. A., Analiticheskoe reshenie granichnykh zadach dlya kineticheskikh uravnenii, izd. MGOU, M., 2004

[4] Cherchinyani K., Matematicheskie metody v kineticheskoi teorii gazov, Mir, M., 1973 | MR

[5] Kogan M. N., Dinamika razrezhennogo gaza. Kineticheskaya teoriya, Nauka, M., 1967 | Zbl

[6] Siewert C. E., “The linearized Boltzmann equation: concise and accurate solutions to basic flow problems”, Z. Angew. Math. Phys., 54:1 (2003), 273–303 | DOI | MR | Zbl

[7] Siewert C. E.,, “Sharipov F. Model equations in rarefied gas dynamics: viscous-slip and thermalslip coefficients”, Phys. Fluids, 14:12 (2002), 4123–4129 | DOI | MR