Skip to main content
Log in

Controllable equilibrium of an inhomogeneously heated liquid in a vibrational field

  • Statistical, Nonlinear, and Soft Matter Physics
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

Equations of thermal vibrational convection of an inhomogeneously heated liquid are analytically solved for arbitrary orientation of vectors determining the heating direction, force of gravity, and vibrations in a closed cavity in the shape of an infinite horizontal cylinder. It is demonstrated that for any orientation of these vectors in the plane perpendicular to the cylinder, the gravitational and vibrational convection mechanisms can completely compensate each other. The ratio is determined between the vibrational and the gravitational Grashof numbers such that mechanical equilibrium conditions are satisfied. This ratio is proved by direct numerical calculation of complete equations of thermal vibrational convection.

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. A. V. Zyuzgin, G. F. Putin, N. G. Ivanova, A. V. Chudinov, A. I. Ivanov, A. V. Kalmykov, V. I. Polezhaev, and V. M. Emelianov, Adv. Space Res. 32, 205 (2003).

    Article  ADS  Google Scholar 

  2. V. A. Demin, G. Z. Gershuni, and I. V. Verholantsev, Int. J. Heat Mass Transfer 39, 1979 (1996).

    Article  Google Scholar 

  3. E. M. Zhukhovitskis-, Prikl. Mat. Mekh. 18, 205 (1954).

    Google Scholar 

  4. S. M. Zen’kovskaya and I. B. Simonenko, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 51 (1966).

    Google Scholar 

  5. G. Z. Gershuni and E. M. Zhukhovitskis-, Dokl. Akad. Nauk SSSR 249(1-3), 580 (1979) [Sov. Phys. Dokl. 24 (11), 894 (1979)].

    ADS  Google Scholar 

  6. G. Z. Gershuni and E. M. Zhukhovitskis-, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 12 (1981).

    Google Scholar 

  7. G. Z. Gershuni, E. M. Zhukhovitskis-, and A. N. Sharifulin, Chislennye Metody Mekh. Sploshnos- Sredy 14, 21 (1983).

    Google Scholar 

  8. A. N. Sharifulin, Convective Flows (Perm State Pedagogical Institute, Perm, Soviet Union, 1981), p. 22 [in Russian].

    Google Scholar 

  9. J. P. McHugh, Q. Appl. Math. LVIII, 425 (2000).

    MathSciNet  Google Scholar 

  10. G. Z. Gershuni and E. M. Zhukhovitskis-, Convective Stability of an Incompressible Liquid (Nauka, Moscow, 1972) [in Russian].

    Google Scholar 

  11. V.I. Chernatynskis- and M. I. Shliomis, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 64 (1973).

    Google Scholar 

  12. A. I. Nikitin and A. N. Sharifulin, in Processes of Heat and Mass Transfer of an Viscous Liquid (Ural Scientific Centre, Academy of Sciences of the Soviet Union, Sverdlovsk, Soviet Union, 1986), p. 32 [in Russian]; A. I. Nikitin and A. N. Sharifulin, Heat Transfer-Sov. Res. 21, 213 (1989).

    Google Scholar 

  13. A. N. Sharifulin, in Hydrodynamic and Convective Stability of an Incompressible Liquid (Ural Scientific Centre, Academy of Sciences of the Soviet Union, Sverdlovsk, Soviet Union, 1984), p. 27 [in Russian]; A. N. Sharifulin, Fluid Mech.-Sov. Res. 15, 28 (1986).

    Google Scholar 

  14. F. T. Ferguson and L. U. Lilleleht, Int. J. Heat Mass Transfer 39, 2895(1996). Translated by E. Baudina

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. N. Sharifulin.

Additional information

Original Russian Text © A.N. Sharifulin, 2010, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ-Fiziki, 2010, Vol. 137, No. 1, pp. 177–182.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharifulin, A.N. Controllable equilibrium of an inhomogeneously heated liquid in a vibrational field. J. Exp. Theor. Phys. 110, 157–161 (2010). https://doi.org/10.1134/S1063776110010188

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776110010188

Keywords

Navigation