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The boundary layer in crossed-fields m.h.d.

Published online by Cambridge University Press:  28 March 2006

W. R. Sears
W. R. Sears
Affiliation:
Center for Applied Mathematics, Cornell University, Ithaca, New York
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Abstract

This study of the boundary layer of steady, incompressible, plane, crossed-fields m.h.d. flow at large Reynolds number Re and magnetic Reynolds number Rm begins with a review of Hartmann's case, where a boundary layer occurs whose thickness is proportional to (Re Rm)−½. Following this clue, it is shown that in general the boundary layer is a ‘local Hartmann boundary layer’. Its profiles are always exponential and it is determined completely by local quantities. The skin friction and the total electric current in the layer are proportional to the square root of the magnetic Prandtl number, i.e. to (Rm/Re)½. Thus the exterior-flow problem, the solution of which precedes a boundary-layer solution, generally involves a current sheet at the fluid-solid interface.

This inviscid-flow problem becomes tractable if (Rm/Re)½ is small enough to permit a linearized solution. The flow field about a flat plate at zero incidence is calculated in this approximation. It is pointed out that the thin-cylinder solutions of Sears & Resler (1959), which pertain to Rm/Re = 0, can immediately be extended to small, non-zero values of this parameter by linear combination with this flat-plate solution.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 25 , Issue 2 , June 1966 , pp. 229 - 240
Copyright
© 1966 Cambridge University Press

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