Fluid Dynamics

, Volume 2, Issue 4, pp 107–109 | Cite as

Exact and approximate formulations of problems for unsteady flows of conducting fluids in MHD channels

  • A. G. Ryabinin
  • A. I. Khozhainov
Article

Abstract

The exact formulation of problems for the unsteady flows of viscous incompressible conducting fluids in MHD channels with arbitrary wall conductivity envisions the joint solution of the equations for the fluid and for the surrounding medium, connected by the conditions at the interface, where the electric and magnetic fields must be continuous [1, 2]. If the side walls of the channel are made from highly conductive material and are connected with the external circuit, then these equations in the general case must be supplemented by the system of equations for the external circuit, written in accordance with Kirchhoff's second law.

The solution of such problems in the exact formulation presents extreme difficulties. Moreover, in many particular cases which are of practical interest the problem formulation may be simplified, and solutions may be constructed in closed form.

In the following we consider the possibilities of such simplification in studying unsteady flows of a fluid of high conductivity in planar MHD channels with an external electrical circuit.

Keywords

Electrical Circuit Unsteady Flow Surrounding Medium Exact Formulation Conductive Material 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    I. B. Chekmarev, “Unsteady flow of a conducting fluid in a flat pipe with a transverse field”, Zh. tekhn. fiz., vol. 30, no. 3, 1960.Google Scholar
  2. 2.
    Ya. S. Uflyand and I. B. Chekmarev, “Study of unsteady flow of a conducting fluid in a plane channel with moving boundaries”, Zh. tekhn. fiz., vol. 30, no. 5, 1960.Google Scholar
  3. 3.
    A. G. Ryabinin and A. I. Khozhainov, “Study of unsteady flow of a conducting fluid in MHD channels”, Zh. tekhn. fiz., vol. 37, no. 2, 1967.Google Scholar
  4. 4.
    S. A. Regirer, “MHD flows in channels and tubes”, INI AN SSSR, 1966.Google Scholar
  5. 5.
    A. N. Patrashev, A. G. Ryabinin, and A. I. Khozhainov, “Unsteady flow of a conducting fluid in MHD channels with small magnetic Reynolds numbers”, Riga Conference on MHD and MHD Generators [in Russian], Izd. AN LatvSSR, 1966.Google Scholar
  6. 6.
    S. Lundquist, “Survey of studies on MHD,“ Probl. sovrem. fiz., no. 2, 1954.Google Scholar
  7. 7.
    L. A. Bessonov, Transient Processes in Nonlinear Electric Circuits with Steel [in Russian], Gosenergoizdat, 1951.Google Scholar
  8. 8.
    S. A. Regirer, “Unsteady flow of electrically conducting fluid in the presence of a magnetic field”, Inzh. -fiz. zh., vol. 2, no. 8. 1959.Google Scholar
  9. 9.
    Ya. S. Uflyand, “Some questions of unsteady flow of a conducting fluid in pipes of constant section in a transverse magnetic field”, Zh. tekhn. fiz., vol. 31, no. 12, 1961.Google Scholar

Copyright information

© The Faraday Press, Inc. 1971

Authors and Affiliations

  • A. G. Ryabinin
    • 1
  • A. I. Khozhainov
    • 1
  1. 1.Leningrad

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