Hostname: page-component-77c89778f8-m8s7h Total loading time: 0 Render date: 2024-07-19T23:41:54.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetohydrodynamic flow due to the discharge of an electric current in a hemispherical container

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
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we consider the flow field induced in an incompressible viscous conducting fluid in a hemispherical bowl by a symmetric discharge of electric current from a point source at the centre of the plane end of the hemisphere. This plane end is a free surface. We construct an analytic solution for the slow viscous flow and a numeriacl solution for the nonlinear problem. The streamlines in an axial cross-section form two sets of closed loops, one on either side of the axis. Our computations indicate that, for a given fluid, when the discharged current reaches a certain magnitude the velocity field breaks down. This breakdown probably originates at the vertex of the hemispherical container.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 73 , Issue 4 , 24 February 1976 , pp. 641 - 650
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Kublanov, V. & Erokhin, A. 1974 Int. Inst. Weld. Document, no. 212–810 74.
Lundquist, S. 1969 Ark. Fys. 40, 89.
Shercliff, J. A. 1970 J. Fluid Mech. 40, 241.
Sozou, C. 1971 J. Fluid Mech. 46, 25.
Sozou, C. 1974 J. Fluid Mech. 63, 665.
Sozou, C. & English, H. 1972 Proc. Roy. Soc. A, 329, 71.
Sozou, C. & Pickering, W. M. 1975 J. Fluid Mech. 70, 509.
Squire, H. B. 1952 Phil. Mag. 43(7), 942.