Skip to main content
Log in

Analytic Solution of Boundary Value Problems for the Shakhov Equation with the Collision Frequency Proportional to the Molecule Velocity

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The weak evaporation and temperature jump problems are solved analytically for the Shakhov kinetic equation with a collision frequency proportional to the molecular velocity. The expressions obtained are calculated numerically for the kinetic coefficients. The results obtained are compared with those obtained earlier.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. L. B. Barichello, A. C. R. Bartz, M. Camargo, and C. E. Siewert, "The temperature jump problem for a variable collision frequency model," Phys. Fluid, 14, 382 (2002).

    Google Scholar 

  2. M. M. R. Williams, Mathematical Methods in Particle Transport Theory, Butterworth, London (1971).

    Google Scholar 

  3. E. M. Shakhov,Method of Investigating Motions of a Rarefied Gas [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  4. Takeo Soga, "A kinetic analysis of thermal force on a spherical particle of high thermal conductivity in monatomic gas," Phys. Fluid, 29, 976 (1986).

    Google Scholar 

  5. A.V. Latyshev, "Analytic solution of the Boltzmann model equation with a collision operator of the mixed type," Zh. Vychisl. Matematiki i Mat. Fiziki, 31, 436 (1991).

    Google Scholar 

  6. V.A. Titarev and E. M. Shakhov, "Heat transfer and evaporation from a plane surface into a half-space upon a sudden increase in body temperature," Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 1, 141 (2001).

  7. A.V. Latyshev and A.A. Yushkanov, "Boundary value problems for a model Boltzmann equation with frequency proportional to the molecule velocity," Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 3, 140 (1996).

  8. B. S. Vladimirov and V.V. Zharinov, Equations of Mathematical Physics [in Russian], Fizmatlit, Moscow (2000).

    Google Scholar 

  9. K. M. Case and P. F. Zweifel, Linear Transport Theory, Addison-Wesley, Reading, Mass. (1967).

    Google Scholar 

  10. T.A. Germogenova, "Completeness of the systemof eigenfunctions of a characteristic transport equation," Preprint No. 103 [in Russian], Keldysh Applied Mathematics Institute, Moscow (1976).

    Google Scholar 

  11. F.D. Gakhov, Boundary Value Problems [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  12. S.K. Loyalka, "Kinetic theory of planar condensation and evaporation," Transport Theory and Statist. Physics, 20, 237 (1991).

    Google Scholar 

  13. C. Cercignani, "Solution of the Boltzmann equation," in: J. L. Lebowitz and E. W. Montroll (Eds.) Nonequilibrium Phenomena. I. The Boltzmann Equation. Mathematical Methods in Kinetic Theory, Horth-Holland, Amsterdam, etc. (1983), P. 122.

    Google Scholar 

  14. A.V. Latyshev, "Analytic solution of the ellipsoidal-statistical Boltzmann model equation," Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 2, 151 (1992).

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Latyshev, A.V., Yushkanov, A.A. Analytic Solution of Boundary Value Problems for the Shakhov Equation with the Collision Frequency Proportional to the Molecule Velocity. Fluid Dynamics 38, 632–645 (2003). https://doi.org/10.1023/A:1026338214835

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026338214835

Navigation