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The development of magnetohydrodynamic flow due to an electric current discharge

Published online by Cambridge University Press:  29 March 2006

C. Sozou  and
W. M. Pickering
C. Sozou
Affiliation:
Department of Applied Mathematics and Computing Science, University of Sheffield, England
W. M. Pickering
Affiliation:
Department of Applied Mathematics and Computing Science, University of Sheffield, England
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Abstract

The development of the magnetohydrodynamic flow field due to the discharge of an electric current J0 from a point on a plate bounding a semi-infinite viscous incompressible conducting fluid is considered. The flow field is the response of the fluid to the Lorentz force set up by the electric current and the associated magnetic field. The problem is formulated in terms of the dimensionless variable (vt)½/r and solved numerically. Here ν is the coefficient of kinematic viscosity, t the time from the application of the electric current and r the distance from the discharge. It is shown that the streamlines of the developing flow field in a cross-section through the axis of the discharge are closed loops about a stagnation point. As the flow field develops, the stagnation point moves to infinity along a ray emanating from the discharge with a speed proportional to t−½. The steady state, within a distance r from the discharge, is practically established when t = r2/ν.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 3 , 12 August 1975 , pp. 509 - 517
Copyright
© 1975 Cambridge University Press

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