Skip to main content
Log in

Approximate system of equations for describing nonstationary natural concentration convection in binary gas mixtures

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

Analysis of the Navier-Stokes equations at small values of the hydrostatic compressibility parameter leads to the formulation of an approximate system of equations for describing nonstationary natural convection in isothermal binary mixtures of gases with arbitrary ratio of the densities. A system of equations for nonstationary concentration convection is also obtained in the Boussinesq approximation, and it is shown that its use in the solution of the considered class of problems may lead to not only quantitative errors but also to a qualitative distortion of the results.

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

Literature cited

  1. G. Z. Gershuni and E. M. Zhukhovitskii, Convective Stability of an Incompressible Fluid [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  2. G. B. Petrazhitskii and V. I. Polezhaev, “Investigation of heat transfer regimes and the structure of a vortex flow in the case of free motion of a viscous compressible gas in two-dimensional cavities,” Tr. MVTU im. N. É. Baumana, No. 222 (1976).

  3. J. M. Mihaljan, “A rigorous exposition of the Boussinesq approximation applicable to a thin layer of fluid,” Astrophys. J.,136, No. 3 (1962).

  4. E. A. Spiegel and G. Veronis, “On the Boussinesq approximation for a compressible fluid,” Astrophys. J.,131, No. 2 (1960).

  5. D. D. Gray and A. Giorgini, “The validity of the Boussinesq approximation for liquids and gases,” Int. J. Heat Mass Transfer,19, No. 5 (1976).

  6. R. Cordon Perez and M. G. Velarde, “On the (nonlinear) foundations of Boussinesq approximation applicable to a thin layer of fluid,” J. Phys. France,36, No. 7–8 (1975).

  7. P. J. Roache, Computational Fluid Dynamics, Hermosa Publ., Albuquerque USA (1976).

    Google Scholar 

  8. L. G. Loitsyanskii, Mechanics of Liquids and Gases, Pergamon Press, Oxford (1966).

    Google Scholar 

  9. J. D. Ramshaw and J. A. Trapp, “A numerical technique for low-speed homogeneous twophase flow with sharp interfaces,” J. Comput. Phys.,21, No. 4 (1976).

  10. A. J. Chorin, “A numerical method for solving incompressible viscous flow problems,” J. Comput. Phys.,2, No. 1 (1967).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 57–61, September–October, 1980.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikulin, D.A., Potekhin, G.S. & Strelets, M.K. Approximate system of equations for describing nonstationary natural concentration convection in binary gas mixtures. Fluid Dyn 15, 679–683 (1980). https://doi.org/10.1007/BF01089639

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01089639

Keywords

Navigation