Abstract
A new method is proposed, called the method of “the smoothed distribution function,” which makes possible a considerable simplification in the procedure for calculating moments of the collision integral, and enables us to obtain a solution to the system of Maxvell-Boltzmann moment equations. The approximating distribution function used in the collision integral in the Boltzmann form ensures a limiting process towards continuous expressions for the flux of molecular characteristics. For the example of the solution to the classical problem of heat transfer between two parallel plates with arbitrary Knudsen numbers, a comparison was made of the theoretical results with the results of other analyses, and also with experiment.
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N. A. Fuks and A. G. Sutugin, Highly Dispersed Aerosols [in Russian], Moscow (1989).
E. Davis and A. Ray, “Submicron droplet evaporation in the continuum and noncontinuum regimes,” J. Aerosol Sci.,9, 411 (1970).
Sang-Wook Kang, “Analysis of condensation droplet growth in rarefied and continuum environments,” AIAA J.,5, 1288 (1967).
N. Fukuta and L. A. Walter, “Kinetics of hydrometeor growth from a vapor-spherical model,” J. Atmos. Sci.,27, 1160 (1070).
S. Kotake and J. J. Glass, “Flows with nucleation and condensation,” Prog. Aerosp. Sci.,19, 129 (1981).
J. C. Carstens, “Drop growth in the atmosphere by condensation: Application to cloud physics,” Adv. Colloid Interface Sci.,10, 285 (1979).
L. Lees, “Kinetic theory description of rarefied gas flows,” J. Soc. Industr. Appl. Math.,13, 273 (1965).
M. Krook, “Continuum equations in dynamics of rarefied gases,” J. Fluid Mech.,6, 523 (1959).
B. V. Deryagin, I. N. Ivchenko, and Yu. I. Yalaraov, “Construction of solutions to the Boltzmann equation in the Knudsen layer,” Izv. Akad. Nauk SSSR., Mekh. Zhidk. Gaza, No. 4, 167 (1968).
G. E. Kelly and J. V. Sengers, “Droplet growth in a dilute vapor,” J. Chem. Phys.,61, 2300 (1974).
I. N. Ivchenko and S. M. Muradyan, “Evaporation of spherical droplets in a binary gas mixture at arbitrary Knudsen numbers,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 112 (1932).
I. N. Ivchenko, “Properties of the evaporation (or growth) of spherical droplets at intermediate Knudsen numbers,” Izv. Akad. Nauk SSSR., Mekh. Zhidk. Gaza, No. 2, 185 (1984).
I. N. Ivchenko, “A study of condensation growth and evaporation of water droplets in air,” Dokl. Akad. Nauk SSSR,274, 572 (1984).
E. P. Gross and S. Ziering, “Heat flow between parallel plates,” Phys. Fluids,2, 701 (1959).
W. P. Teagan and G. S. Springer, “Heat-transfer and density-distribution measurements between parallel plates in the transition regime,” Phys. Fluids,11, 497 (1968).
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Shidkosti i Gaza, No. 3, pp. 182–185, May–June, 1986.
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Ivchenko, I.N. A method for solving boundary-value problems of transfer at arbitrary knudsen numbers. Fluid Dyn 21, 495–499 (1986). https://doi.org/10.1007/BF01409741
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DOI: https://doi.org/10.1007/BF01409741