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The Quarterly Journal of Mechanics and Applied Mathematics 1972 25(3):333-348; doi:10.1093/qjmam/25.3.333
© 1972 by Oxford University Press
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THE LINEAR STABILITY OF FLOW IN A CIRCULAR PIPE IN THE PRESENCE OF A STRONG TRANSVERSE MAGNETIC FIELD

P. BALDWIN

( Department of Engineering Mathematics, University of Newcastle upon Tyne )

Electrically conducting fluid with constant fluid properties flows in a circular pipe with an insulating wall, under the action of a strong uniform transverse magnetic field. A linear stability analysis of the MHD equations governing the flow, in the small magnetic Reynolds number approximation, shows that instabilities arise in the Hartmann layer, on the plane of symmetry parallel to the applied magnetic field, where velocity gradients are greatest. The first two terms in asymptotic expansions for the Reynolds number, and for the wave number and wave speed of the disturbance, are obtained for the onset of marginal stability at large Hartmann number.


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