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Numerical analysis of a flow induced in a rarefied gas between noncoaxial circular cylinders with different temperatures for the entire range of the Knudsen number. (English) Zbl 0661.76079

A flow induced by the temperature field in a rarefied gas contained between two noncoaxial circular cylinders at rest with different uniform temperatures is analyzed numerically on the basis of the linearized Boltzmann-Krook-Welander equation with the diffuse reflection boundary condition for the entire range of the Knudsen number. The computation is carried out for the case where the radius of the inner cylinder is one- half and the eccentricity is one-fourth of the radius of the outer cylinder. It is demonstrated that two symmetric circulating flows are established, the direction of which does not depend on the Knudsen number. The force acting on the inner cylinder and the energy transmitted to it are also obtained, and their variations with the Knudsen number are investigated in detail. The magnitude of the force takes its maximum at a moderate Knudsen number, and the reversal of the direction of the force, which is predicted from the existing analyses for the two extreme cases of small and large Knudsen numbers, takes place at a small Knudsen number.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76M99 Basic methods in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
35Q99 Partial differential equations of mathematical physics and other areas of application
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