Hostname: page-component-7479d7b7d-t6hkb Total loading time: 0 Render date: 2024-07-11T15:38:08.234Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of a very strong magnetic cross-field on steady motion through a slightly conducting fluid

Published online by Cambridge University Press:  28 March 2006

G. S. S. Ludford
G. S. S. Ludford
Affiliation:
University of Maryland
Present address: Brown University, Providence, Rhode Island
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow engendered by the steady motion of a cylindrical insulator through an inviscid, incompressible fluid of small conductivity σ is not close to potential flow when the applied magnetic cross-field H0 is sufficiently strong. Here we determine the limiting form of this flow as σ → 0 with $\sigma H^2_0 \rightarrow \infty$, the latter representing the ponderomotive force.

The limit equations do not have a unique solution, but it is possible to make a selection by taking into account the inertia of the fluid during the limiting process, i.e. without recourse to considerations of how the motion was set up from rest. The forces on the cylinder are found to be asymptotically proportional to $\surd {\sigma} H_0$.

The case of an elliptic cylinder and that of a flat plate are worked out in detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 10 , Issue 1 , February 1961 , pp. 141 - 155
Copyright
© 1961 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

Carslaw, H. S. & Jaeger, J. C. 1948 Operational Methods in Applied Mathematics, 2nd ed. Oxford University Press.
Copson, E. T. 1935 An Introduction to the Theory of Functions of a Complex Variable. Oxford University Press.
Copson, E. T. 1946 The Asymptotic Expansion of a Function Defined by a Definite Integral or Contour Integral. Admiralty Computing Service (Ref. No. S. R. E./ACS 106).
Erdélyi, A. 1956 Asymptotic Expansions. New York: Dover.
Goldstein, S. 1960 Lectures on Fluid Mechanics. New York: Interscience.
Jeffreys, H. 1927 Operational Methods in Mathematical Physics (Cambridge Tracts in Mathematics and Mathematical Physics, No. 23). Cambridge University Press.
Ludford, G. S. S. & Murray, J. D. 1960 On the flow of a conducting fluid past a magnetized sphere. J. Fluid Mech. 7, 516–28.Google Scholar
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder. J. Fluid Mech, 2, 237–62.Google Scholar
Stewartson, K. 1956 Motion of a sphere through a conducting fluid in the presence of a strong magnetic field. Proc. Camb. Phil. Soc., 52, 301–16.Google Scholar