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Stability of a Hartmann boundary layer under the influence of a parallel magnetic field

Published online by Cambridge University Press:  28 March 2006

S. Abas
S. Abas
Affiliation:
Department of Applied Mathematics, University College of North Wales. Bangor
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Abstract

Stability to infinitesimal disturbances—when a parallel magnetic field is imposed—is investigated for the flow in the boundary layer set up by two-dimensional motion between parallel planes of a viscous, incompressible, electrically conducting fluid under the influence of a transverse magnetic field. The flow is assumed to take place at low magnetic Reynolds number. The usual asymptotic methods are employed for the solution, but, apart from the Tollmientype power series solution, an exact solution of the inviscid equation is obtained in terms of the hypergeometric function and its analytic continuation. Curves of neutral stability for two-dimensional disturbances are calculated and the results for critical Reynolds number modified to take into account three-dimensional disturbances. The parallel magnetic field is found to have a strong stabilizing influence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 32 , Issue 4 , 18 June 1968 , pp. 721 - 735
Copyright
© 1968 Cambridge University Press

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