A qualitative investigation of the equations of quasi-one-dimensional magnetohydrodynamic channel flow

  • F. A. Slobodkina


A qualitative investigation of the system of differential equations describing the quasi-one-dimensional flow of an electrically conducting medium at small magnetic Reynolds numbers gives an idea of the different possible flow patterns occuring when the electromagnetic field and channel shape are given in different ways. Such a treatment is essential for the calculation of one-dimensional flows, and also for the solution of variational problems [1].

In the literature devoted to this question studies have been made of flow in a one-dimensional electromagnetic field and a channel of constant cross section [2], as well as of the flow when the magnetic field is described by specially given functions of the flow velocity [3]. These cases reduce to the analysis of integral curves in a plane.

In the present paper the investigation is carried out for an arbitrary distribution of the electric and magnetic fields and channel shape, which leads to a consideration of the behavior of integral curves in three-dimensional space. The qualitative results are illustrated by examples.


Magnetic Field Reynolds Number Flow Velocity Flow Pattern Electromagnetic Field 
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  1. 1.
    A. N. Kraiko and F. A. Slobodkin, “Toward a solution of variational problems of one-diniensional magnetohydrodynamics,” PMM, vol. 29, no. 2, 1965.Google Scholar
  2. 2.
    E. Resler and W. Sears, “The prospects for magnetoaerodynamics,” J. Aeronaut. Soc., vol. 25, no. 4, 1958.Google Scholar
  3. 3.
    F. E. C. Culik, “Compressible magnetogas-dynamic channel flow,” Z. angewandte Math. und Phys., vol. 15, no. 2, 1964.Google Scholar
  4. 4.
    V. V. Nemytskii and V. V. Stepenov, Qualitative Theory of Differential Equations [in Russian], Gostekhizdat, 1949.Google Scholar

Copyright information

© The Faraday Press, Inc. 1969

Authors and Affiliations

  • F. A. Slobodkina
    • 1
  1. 1.Moscow

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