Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-23T15:25:21.893Z Has data issue: false hasContentIssue false
  • English
  • Français

On the steady rotation of an axisymmetric solid in a conducting fluid at high Hartmann numbers

Published online by Cambridge University Press:  26 February 2010

W. E. Williams  and
R. Shail
W. E. Williams
Affiliation:
The Department of Mathematics, The University of Surrey, Guildford, Surrey.
R. Shail
Affiliation:
The Department of Mathematics, The University of Surrey, Guildford, Surrey.
Get access

Extract

In an earlier paper [Shail, 1] one of the present authors considered the effect of a magnetic field on the frictional couple experienced by an axisymmetric solid insulator which rotates slowly in a bounded viscous conducting fluid, the applied magnetic field being parallel to the axis of rotation. Results for the couple in various geometrical configurations were obtained in the form of power series expansions in the Hartmann number M, and hence are valid only for M ≪ 1. However, because of the increased rigidity given to the fluid by the applied field, it is physically evident that the magnetic field will have a more dramatic effect on the flow pattern for large values of M. Thus one object of this paper is to investigate the frictional couple on a solid insulator rotating in an unbounded fluid for values of M ≫ 1.

Type
Research Article
Information
Mathematika , Volume 16 , Issue 2 , December 1969 , pp. 295 - 304
Copyright
Copyright © University College London 1969

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

1.Shail, R., Proc. Camb. Phil. Soc., 63 (1967), 1331–1339.CrossRefGoogle Scholar
2.Waechter, R. T., Proc. Camb. Phil. Soc., 65 (1969), 329–350.CrossRefGoogle Scholar
3.Waechter, R. T., Proc. Camb. Phil. Soc., 64 (1968), 1165–1201.CrossRefGoogle Scholar
4.Jones, D. S., Proc Roy. Soc., A239 (1965), 338–348.Google Scholar
5.Noble, B., IEEE Trans. Antennas and Propagation AP-7 (1959), 37–42.CrossRefGoogle Scholar
6.Jones, D. S., Proc. Camb. Phil. Soc., 61 (1965), 223–245.CrossRefGoogle Scholar
7.Hasimoto, H., Prog, of Theoretical Physics, Supplement No. 24 (1963), 35–85.CrossRefGoogle Scholar
8.Stallybrass, M. P., Int. J. Engng. Sci., 5 (1967), 689–703.CrossRefGoogle Scholar
9.Thomas, D. P., Q. Jl. Mech. Appl. Math., 21 (1968), 51–65.CrossRefGoogle Scholar
10.Hasimoto, H., J. Fluid Mech., 8 (1960), 61–81.CrossRefGoogle Scholar
11.Noble, B., Electromagnetic Waves, ed. R. E. Longer (University of Wisconsin Press, 1962).Google Scholar
12.Clemmow, P. C., Q. Jl. Mech. Appl. Math., 3 (1950), 241–256.CrossRefGoogle Scholar