An analytical (in the form of the Neumann series) solution of the Couette flow problem has been constructed with the use of the kinetic approach. For the basic equation the Williams equation was used, and for the boundary condition on the channel walls the mirror-diffuse model was applied. With account for the constructed distribution function the value of the gas mass flow per unit width of the channel through its upper half has been calculated and a viscous stress tensor component other than zero has been found. A comparison with analogous results obtained by numerical methods has been made.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 87, No. 4, pp. 953–960, July–August, 2014.
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Gulakova, S.V., Popov, V.N. Analytical Solution of the Couette Flow Problem for Arbitrary Values of the Knudsen Number. J Eng Phys Thermophy 87, 988–996 (2014). https://doi.org/10.1007/s10891-014-1096-z
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DOI: https://doi.org/10.1007/s10891-014-1096-z