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Magnetohydrodynamics

  • A. C. Eringen
  • G. A. Maugin

Magnettofluid dynamics or magnetohyrodynamics—abbreviated MHD—is concerned with the interactions of free currents and magnetic fields with fluids matter, liquids and gases, which have so high an electrical conductivity that a quasi–static magnetic field model is appropriate for describing the electromagnetic contributions to the system. Magnetohydrodynamics finds practical use in many areas of engineering and pure science. Areas of applications are, e.g., pumping and levitation of liquid metals, orientation and confinement of extremely hot ionized gases or plasmas as in thermonuclear fusion experiments, electric power generation from ionized gases or from heat produced in a fission reaction, and gases.

Keywords

Shock Front Couette Flow Poiseuille Flow Jump Condition Alfven Wave 
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Notes

  1. 1.
    Many books exist that deal exclusively with MHD, e.g., Alfvén and Fälthammar [1963], Anderson [1963], Cabannes [1970], Hughes and Young [1966], Jeffrey [1966], and Pai [1962]. See also Landau and Lifshitz [1960, Chap. VIII] and Dragos [1975]. Extensive studies on the dynamo problems include Moffatt [1976], [1978]. Application to industrial devices are given in Lielausis [1975]. Instabilities of the resistive type are given by Paris [1984].Google Scholar
  2. 3.
    Landau and Lifshitz [1960, Sect. 15] arrive at a similar expression through a different approach.Google Scholar
  3. 4.
    However, a relativistically invariant theory of magnetohydrodynamics can be formulated. In this regard, see Lichnerowicz [1967], Grot and Eringen [1966b], and Chapter 15.Google Scholar
  4. 5.
    Of course, P could not be discarded in studies involving the propagation of ultrasound in solids in Chapters 7 and 8.Google Scholar
  5. 7.
    Eringen [1980, Sect. 10.26].Google Scholar
  6. 8.
    See, for instance, Jeffrey and Taniuti [1964].Google Scholar
  7. 9.
    After J. Hartmann [1937] who first studied the magnetohydrodynamic Poiseuille flow.Google Scholar
  8. 11.
    See Problem 10.10.Google Scholar
  9. 12.
    We follow essentially the works of Bazer and Ericson [1959] and Jeffrey [1966, Chap. 6]; see also Anderson [1963] and Katayev [1966].Google Scholar
  10. 13.
    For a detailed discussion of these shocks the reader is referred to the work of Friedrichs and Kranzer [1958].Google Scholar
  11. 14.
    See Hughes and Young [1966, pp. 466–471].Google Scholar
  12. 15.
    See Germain [1959], [1972].Google Scholar
  13. 16.
    See Germain [1960].Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • A. C. Eringen
    • 1
  • G. A. Maugin
    • 2
  1. 1.Princeton UniversityPrincetonUSA
  2. 2.Laboratoire de Modélisation en MécaniqueUniversité Pierre et Marie Curie et C.N.R.S.Paris 05France

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