Skip to main content
SpringerLink
Log in

Exact solutions of the kinetic-moment equations of a mixture of monatomic gases

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

An extension is given of the class of exact solutions of the kinetic-moment equations for a monatomic gas in the absence of external forces [1] to the case of a mixture of monatomic Maxwellian gases with account for external forces. Very simple solutions of this class are obtained which are examples of the normal solutions of the Boltzmann equations in the Chapman-Enskog sense [2]. Conclusions are summarized concerning the applicability of the various methods of solving the Boltzmann equations and their properties, obtained on the basis of an analysis of the indicated exact solutions.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. S. Galkin, “On a class of solutions of the Grad kinetic moment equations”, PMM, vol. 22, no. 3, 1958.

  2. S. Chapman and T. Cowling, Mathematical Theory of Nonuniform Gases [Russian translation], Izd-vo inostr. lit., 1960.

  3. H. Grad, “On the kinetic theory of rarefied gases”, Comm. Pure Appl. Math., vol. 2, no. 4, 1949.

  4. A. A. Nikol'skii, “On a general class of uniform motions of continuous media and rarefied gas”, Inzh. zh. [Soviet Engineering Journal], vol. 5, no. 6, 1965.

  5. A. A. Nikol'skii, “Three-dimensional homogeneous expansion-contraction of a rarefied gas with power-law interaction functions”, DAN SSSR, vol. 151, no. 3, 1963.

  6. V. S. Galkin, “On a solution of the Boltzmann kinetic equation”, PMM, vol. 20, no. 3, 1956.

  7. C. Truesdell, “On the pressures and the flux of energy in a gas according to Maxwell's kinetic theory.” J. of Rational Mechan. and. Anal., vol. 5, no. 1, 1956.

  8. V. S. Galkin, “One-dimensional unsteady solution of the kinetic moment equations of a monatomic gas”, PMM, vol. 28, no. 1, 1964.

  9. A. S. Borisov, “Asymptotic behavior of some solutions of the Grad kinetic moment system”, Inzh. zh. [Soviet Engineering Journal], vol. 5, no. 6, 1965.

  10. V. Zhdanov, Yu. Kagan, and A. Sazykin, “Effect of viscous momentum transport by diffusion in a gas mixture”, ZhETF, vol, 42, no. 3, 1962.

  11. H. Grad, “Asymptotic Solution of the Boltzmann equation.” The Physics of Fluids, vol. 6, no. 2, 1963.

  12. V. S. Galkin, “On the applicability limits of the relaxation model of Boltzmann's kinetic equation”, Inzh. zh., vol. 1, no. 3, 1961.

  13. E. Kamke, Handbook on Ordinary Differential Equations [Russian translation], Izd-vo Nauka, 1965.

  14. H. Bateman and A. Erdelyi, Higher Transcendental Functions; The Hypergeometric Function; Legendre Functions [Russian translation], Izd-vo Nauka, 1965.

Download references

Author information

Authors and Affiliations

  1. Moscow

    V. S. Galkin

Authors
  1. V. S. Galkin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The author wishes to thank M. N. Kogan and A. A. Nikol'skii for their interest in the study.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Galkin, V.S. Exact solutions of the kinetic-moment equations of a mixture of monatomic gases. Fluid Dyn 1, 29–34 (1966). https://doi.org/10.1007/BF01022146

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01022146

Keywords

Search

Navigation