© 1962 by Oxford University Press
ON THE STABILITY OF MAGNETOHYDRODYNAMIC FLOW IN A CURVED CHANNEL
( Mathematicss Department, University College Cardiff )
In this paper the theory of the stability of viscous flow between two concentric cylinders due to a pressure gradient acting round the cylinders is extended to the case where the fluid is electrically conducting and a radial magnetic field acts across the channel. It is assumed that the spacing between the cylinders is small compared with their radii, and the resulting eigenvalue problem is solved approximately using the method of Reid (1). Results are given which describe the inhibiting effect of the magnetic field on the onset of instability. It is found that even for channels for which the ratio of the channel width to the radius of the inner cylinder is as small as 104, the critical Reynolds numbers are well below the corresponding ones predicted by Lock (2) for the analogous problem of flow in a perfectly straight channel under the influence of a traverse magnetic field. The suggestion is therefore advanced that small departures from straightness of the channel may partly account for the discrepancy between the theory of Lock and the experiments of (3).