Abstract
The aim of this research is to establish the validity of the predictions of the theory of slow nonisothermal flows, to study the limits of applicability (with respect to the Knudsen number) of the conclusions reached and to determine the effect of the Knudsen layers on these flows on the basis of a numerical investigation of slow nonisothermal weakly rarefied gas flow in a plane infinite channel with weakly nonequilibrium heating of the walls and a finite wall temperature difference. The gas flow is described by a relaxation transport equation. The results obtained show how quickly, as the Knudsen number decreases, the solutions of the transport equation outside the Knudsen layers tend to the solution of the equations of gas dynamics of slow nonisothermal flows (and not to the solution of the Navier-Stokes equations).
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V. S. Galkin, M. N. Kogan, and O. G. Fridlender, “Some kinetic effects in continuum flows,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 13 (1970).
V. S. Galkin, M. N. Kogan, and O. G. Fridlender, “Free convection in a gas in the absence of external forces,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No, 3, 98 (1971).
M. N. Kogan, V. S. Galkin, and O. G. Fridlender, “Stresses occurring in gases as a result of nonuniformity of the temperature and concentrations: new types of free convection,” Usp. Fiz. Nauk,119, 111 (1976).
V. S. Galkin, “Derivation of the equations of slow gas mixture flows from the Boltzmann equations,” Uch. Zap. TsAGI,5, 40 (1974).
D. R. Willis, “Heat transfer in a rarefied gas between parallel plates at large temperature ratios,” Rarefied Gas Dynamics: Third Sympos., Paris, Vol. 1, Academic Press, New York (1963), p. 209.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover (1964).
A. M. Bishaev and V. A. Rykov, “Solution of steady-state problems of the kinetic theory of gases at intermediate and small Knudsen numbers using an iteration method,” Zh. Vychisl. Mat. Mat. Fiz.,15, 172 (1975).
V. Yu. Aleksandrov, “Nonmonotonic dependence of heat transfer on temperature differentials,” Teplofiz. Vys. Temp.,22, 363 (1984).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 115–121, January–February, 1988.
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Aleksandrov, V.Y., Fridlender, O.G. Weakly rarefied gas flows between nonuniformly heated parallel plates. Fluid Dyn 23, 95–100 (1988). https://doi.org/10.1007/BF01051555
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DOI: https://doi.org/10.1007/BF01051555