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Solution of the linearized couette-flow problem in a rarefied gas by the integral-diffusion method

  • A. T. Onufriev
Article
  • 39 Downloads

Abstract

In ordinary diffusion theory the transfer of properties is determined by the local gradients of the corresponding fields. As the mean free path increases, the flux density becomes an integral quantity and is determined by a neighborhood of the point under consideration of the order of a few mean free paths. In a previous article [1], the author proposed a model for a one-dimensional transfer process in linear rarefield-gas problems based on the analogy with radiative transfer. The same approach, though without directional averaging, is used in the present paper to analyze the linearized Couette flow problem. The solution obtained here has the properties of the solution obtained by more exact methods based on the solution of the Boltzmann equation [3-4].

Keywords

Mathematical Modeling Mechanical Engineer Flux Density Industrial Mathematic Transfer Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

pxy

shear stress

c

mean thermal velocity of molecules

2/3 A

mean free path

d

half-width of channel

±w0

plate velocity

ρcϕ

“nonequilibrium”value of momentum flux density

y

transverse coordinate

γ

ratio of specific heats

W

dimensionless velocity

Pxy

shear stress scaled with respect to the shear stress in free-molecule flow

Y

dimensionless coordinate

W1(y)

velocity distribution according to Millikan's solution

μ

coefficient of viscosity

R

Reynolds number

K

Knudsen number

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References

  1. 1.
    A. T. Onufriev,“A model for nonequilibrium processes in some problems in the mechanics of continua,” Zhurnal prikladnoi mekhaniki i tekhnicheskoi fiziki, 1, 1963.Google Scholar
  2. 2.
    D. R. Willis, “Comparison of kinetic theory analyses of linearised Couette flow,” Phys. Fluids, vol. 5, no. 2, 127–135, 1962.Google Scholar
  3. 3.
    F. S. Sherman and L. Talbot, “Comparison of kinetic theory with experiment for rarefied gases,” in: Rarefied Gas Dynamics (F. M. Devienne, ed.), Proc. I International Symp. on Rarefield Gas Dynamics, Nice 1958, Pergamon Press, 1960.Google Scholar
  4. 4.
    R. E. Street, “Study of the boundary conditions in the aerodynamics of slip flow,” in: Rarefied Gas Dynamics (F. M. Devienne, ed.), Proc. I International Symp. on Rarefield Gas Dynamics, Nice 1958, Pergamon Press, 1960.Google Scholar
  5. 5.
    R. A. Millikan, Phys. Rev., 21, 217–238, 1923.Google Scholar
  6. 6.
    C. T. Zahn, “Absorption coefficients for thermal neutrons,” Phys. Rev., vol, 52, no. 2, 67–71, 1937.Google Scholar
  7. 7.
    L. V. Kantorovich and V. I. Krylov, Approximate Methods of Higher Analysis [in Russian], Gostekhizdat, 1950.Google Scholar

Copyright information

© The Faraday Press, Inc. 1966

Authors and Affiliations

  • A. T. Onufriev
    • 1
  1. 1.Novosibirsk

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