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Exact solutions of the magnetohydrodynamic equations

Published online by Cambridge University Press:  28 March 2006

W. E. Williams
W. E. Williams
Affiliation:
Department of Applied Mathematics, Liverpool University
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Abstract

Exact one-dimensional solutions of the magnetohydrodynamic equations of an incompressible fluid are considered. It is shown that one class of plane wave solutions of the linearized equations is also a possible class of solutions of the general equations including the effect of displacement current. A similar result is also established for the solutions for a horizontally stratified fluid. For the particular case when the viscosity is equal to the magnetic diffusivity an exact solution is obtained for the magnetohydrodynamic Rayleigh problem for a semi-infinite plate. It is shown that this solution may be employed directly to give the solution for liquids of small, but not necessarily equal, viscosity and magnetic diffusivity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 8 , Issue 3 , July 1960 , pp. 452 - 464
Copyright
© 1960 Cambridge University Press

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