Skip to main content
SpringerLink
Log in

Free-convection Flow of a Binary Mixture in a Thin Porous Ring

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The problem of natural convection of a binary mixture in a thin porous ring is considered. In the simplified formulation steady-state solutions of the problem are obtained. The stability of these solutions is investigated and a stability map is plotted in the plane of the Rayleigh numbers calculated from the temperature and concentration. It is shown that an auto-oscillation convection regime is established in the ring under certain conditions. It is also found that there is a region of variation of the seepage and diffusion-seepage Rayleigh numbers in which three steady-state solutions are stable.

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. M. C. Charrier-Mojtabi, A. Mojtabi, M. Azaiez, and G. Labiosse, “Numerical and experimental study of multicellular free convection flow in an annular porous layer,” Intern. J. Heat and Mass Transfer, 34, 3061 (1991).

    Article  MATH  Google Scholar 

  2. Kh. G. Magomedbekov, G. M. Gaydarov, and Sh. S. Osman-zade, “Hydrothermal convection in fault zones,” in: Geothermy, Issue 1 [in Russian], Nauka, Moscow (1991) p. 1–13.

    Google Scholar 

  3. Kh. G. Magomedbekov and M. M. Ramazanov, “Hydrothermal convection in a thin porous ring”, Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 4 (1994).

    Google Scholar 

  4. M. E. Taslim and U. Narusawa, “Binary fluid convection and double-diffusive convection in a porous medium,” Trans. ASME, J. Heat and Mass Transfer, 108, 221 (1986).

    Article  Google Scholar 

  5. D. A. Nield, “Onset of thermohaline convection in a porous medium,” Water Resources Res., 4, 553 (1968).

    Article  ADS  Google Scholar 

  6. R G. Bendrikovatskii, D. G. Polonskii, and A. A. Shapiro, “Analysis of the convective instability of a binary mixture in a porous medium”, Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 1, 110 (1993).

    Google Scholar 

  7. D. D. Joseph, Stability of Fluid Motions, Springer, Berlin (1976).

    MATH  Google Scholar 

  8. S. T. Tsien, Physical Mechanics [in Russian], Mir, Moscow (1965) (translated from the Chinese).

    Google Scholar 

  9. L. D. Landau and E. M. Lifshitz, Theoretical Physics. Vol. 6. Hydrodynamics [in Russian], Nauka, Moscow (1986).

    Google Scholar 

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

    MATH  Google Scholar 

  11. V. R. Isachenko, B. A. Osipova, and A. S. Sukomel, Heat Transfer [in Russian], Energiya, Moscow (1969).

    Google Scholar 

  12. N. V. Butenin, Yu. I. Neimark, N. A. Fufaev, Introduction to the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1987).

    MATH  Google Scholar 

  13. J. H. Wilkinson and C. H. Reinsch. Linear Algebra (Handbook for Automatic Computation. B. d. 186), Springer-Verlag, Berlin (1971).

    Book  Google Scholar 

  14. E. Hairer, S. R. Norsett, and G. Wanner, Solving Ordinary Differential Equations, Springer-Verlag, Berlin (1987).

    Book  MATH  Google Scholar 

Download references

Authors
  1. Kh. G. Magomedbekov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Magomedbekov, K.G. Free-convection Flow of a Binary Mixture in a Thin Porous Ring. Fluid Dyn 32, 841–849 (1997). https://doi.org/10.1007/BF03374541

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03374541

Search

Navigation