Skip to main content
SpringerLink
Log in

The analogy between a problem of magnetohydrodynamics and the Benard problem in the Boussinesq approximation

  • Published:
Technical Physics Letters Aims and scope Submit manuscript

Abstract

It is shown that the equations of motion written in a longitudinal plane of symmetry of a liquid-metal current-carrying conductor of rectangular cross section are identical with the equations that describe heat conduction in a flat layer of liquid heated from below in the Boussinesq approximation. The main parameters that determine the threshold of the convective instability that develops under the action of Lorentz forces in a current-carrying liquid metal are found.

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. N. B. Volkov and A. M. Iskol’dskii, JETP Lett. 51, 634 (1990).

    ADS  Google Scholar 

  2. A. M. Iskoldsky, N. B. Volkov, and N. M. Zubarev, Phys. Lett. A 217, 330 (1996).

    Article  ADS  Google Scholar 

  3. A. M. Iskoldsky, N. B. Volkov, and O. V. Zubareva, Physica D 91, 182 (1996).

    Article  MATH  Google Scholar 

  4. N. B. Volkov, N. M. Zubarev, O. V. Zubareva, and V. T. Shkatov, Pis’ma Zh. Tekh. Fiz. 22(13), 43 (1996) [Tech. Phys. Lett. 22, 538 (1996)].

    Google Scholar 

  5. N. B. Volkov, N. M. Zubarev, O. V. Zubareva, and V. T. Shkatov, Physica D 109, 315 (1997).

    Article  ADS  Google Scholar 

  6. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media (Nauka, Moscow, 1982; Pergamon Press, Oxford, 1960).

    Google Scholar 

  7. G. Z. Gershunin, E. M. Zhukhovitskii, and A. A. Nepomnyashchii, Stability of Convective Currents, (Nauka, Moscow, 1989).

    Google Scholar 

  8. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Nauka, Moscow, 1986; Pergamon Press, Oxford, 1987).

    Google Scholar 

  9. Rayleigh, Philos. Mag. 32, 529 (1916).

Download references

Author information

Authors and Affiliations

  1. Electrophysics Institute, Ural Branch, Russian Academy of Sciences, Ekaterinburg

    N. B. Volkov, N. M. Zubarev & O. V. Zubareva

Authors
  1. N. B. Volkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. M. Zubarev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. V. Zubareva
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Pis’ma Zh. Tekh. Fiz. 25, 1–6 (May 26, 1999)

Translated by W. J. Manthey

Rights and permissions

Reprints and permissions

About this article

Cite this article

Volkov, N.B., Zubarev, N.M. & Zubareva, O.V. The analogy between a problem of magnetohydrodynamics and the Benard problem in the Boussinesq approximation. Tech. Phys. Lett. 25, 380 (1999). https://doi.org/10.1134/1.1262489

Download citation

  • Received:

  • DOI: https://doi.org/10.1134/1.1262489

Keywords

Search

Navigation