Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-17T18:09:38.377Z Has data issue: false hasContentIssue false
  • English
  • Français

Magnetic levitation of liquid metals

Published online by Cambridge University Press:  20 April 2006

A. J. Mestel
A. J. Mestel
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The process of levitation melting of metals is examined analytically and numerically for the case of axisymmetric toroidal high-frequency currents. The governing equations for the mean-velocity field and associated free-surface shape are derived under the assumption of low magnetic Reynolds number and the neglect of thermal effects. The form of the solution for high Reynolds number is discussed in general, and particularized to the case of high surface tension, in which limit a perturbation analysis about a spherical shape is presented. Finite-difference techniques are used to solve the Navier–Stokes equations in the sphere, and the surface perturbation is calculated. The asymptotic behaviour of the potential vorticity is illustrated by the numerical experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 117 , April 1982 , pp. 27 - 43
Copyright
© 1982 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

Batchelor, G. K. 1956 On steady laminar flow with closed streamlines at large Reynolds number. J. Fluid Mech. 1, 177.Google Scholar
Fautrelle, Y. R. 1981 Analytical and numerical aspects of the electromagnetic stirring induced by alternating magnetic fields. J. Fluid Mech. 102, 405.Google Scholar
Harris, M. R. & Stephan, S. Y. 1975 Support of liquid metal surface by alternating magnetic field. I.E.E.E. Trans. on Magnetics 5, 1508.Google Scholar
Jones, C. A., Moore, D. R. & Weiss, N. O. 1976 Axisymmetric convection in a cylinder. J. Fluid Mech. 73, 353.Google Scholar
Moffatt, H. K. 1965 On fluid flow induced by a rotating magnetic field. J. Fluid Mech. 22, 521.Google Scholar
Moffatt, H. K. 1977 Some problems in the magnetohydrodynamics of liquid metals. Z. angew. Math. Mech. 58, 65–71.Google Scholar
Muck, O. 1923 German Patent no. 422004, Oct. 30, 1923.
Okress, E. C., Wroughton, D. M., Comenetz, C., Brace, P. N. & Kelly, J. C. K. 1952 Electromagnetic levitation of solid and molten metals. J. Appl. Phys. 23, 545.Google Scholar
Peifer, W. A. 1965 Levitation melting ⃛ a survey of the state-of-the-art. J. Metals 17, 487.Google Scholar
Polonis, B. M. & Parr, J. G. 1954 Phase transformations in titanium rich alloys of iron and titanium. Trans. A.I.M.E. 200, 1148.Google Scholar
Sagardia, S. R. 1977 Electromagnetic levitation melting of large conductive loads. Ph.D. thesis, University of Toronto.
Sneyd, A. D. 1979 Fluid flow induced by a rapidly alternating or rotating field. J. Fluid Mech. 92, 35.Google Scholar
Sneyd, A. D. & Moffatt, H. K. 1982 Fluid dynamical aspects of the levitation-melting process. J. Fluid Mech. 117, 45.Google Scholar
Weir, A. D. 1976 Axisymmetric convection in a rotating sphere. Part 1. Stress-free surface. J. Fluid Mech. 75, 49.Google Scholar