Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-25T15:31:35.291Z Has data issue: false hasContentIssue false
  • English
  • Français

Steady rotation of a body of revolution in a conducting fluid

Published online by Cambridge University Press:  24 October 2008

R. T. Waechter
R. T. Waechter
Affiliation:
School of Physical Sciences, Flinders University, Bedford Park, South Australia†
Get access Rights & Permissions [Opens in a new window]

Extract

We investigate the steady rotation of an insulating body of revolution in an unbounded electrically conducting fluid permeated by a uniform axial applied magnetic field. The assumptions of a small magnetic Reynolds number (Rm ≪ 1, i.e. the weakly conducting situation) and negligible inertia forces compared with the magnetic forces (R/M2 ≪ 1) permit us to suppress the inflow at the poles and outflow at the equator, which normally occurs for a non-conducting viscous fluid ((12), pp. 436–439). Thus in the case of the sphere, we find an exact solution of the reduced equations in terms of an infinite series of Legendre polynomials of order 1 with coefficients which are the ratios of modified spherical Bessel functions. This is the canonical problem by which results for arbitrary bodies of revolution are obtained.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 1 , January 1969 , pp. 329 - 350
Copyright
Copyright © Cambridge Philosophical Society 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

REFERENCES

(1)Bers, L., John, F. and Schechter, M.Partial differential equations (Interscience, 1964).Google Scholar
(2)Burridge, R.J. Math. Phys. 45 (1966), 322–330.CrossRefGoogle Scholar
(3)Clemmow, P. C.Proc. Cambridge Philos. Soc. 57 (1961), 547–560.Google Scholar
(4)Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.Higher transcendental functions, Vol. 1, Bateman manuscript project (McGraw-Hill, 1954).Google Scholar
(5)Fock, V. A.Electromagnetic diffraction and propagation problems (Pergamon Press, 1965).Google Scholar
(6)Franz, W.Theorie der Beugung elektromagnetischer Wellen. Ergebn. Angew. Math., vol. 4 (Springer Verlag, 1957).Google Scholar
(7)Friedlander, F. G.Sound pulses (Cambridge University Press, 1958).Google Scholar
(8)Hobson, E. W.The theory of spherical and elliptical harmonics (Chelsea Publishing Co., New York, 1955).Google Scholar
(9)Jeffreys, H. and Lapwood, E. R.Proc. Roy. Soc. Ser. A 241 (1957), 455–479.Google Scholar
(10)Levy, B. and Keller, J. B.Comm. Pure Appl. Math. 12 (1959), 159–209.CrossRefGoogle Scholar
(11)Nussenzveig, H. M.Ann. Physics 34 (1965), 23–95.CrossRefGoogle Scholar
(12)Rosenhead, L.Laminar boundary layers (Clarendon Press, Oxford, 1963).Google Scholar
(13)Rubinow, S. I. and Keller, J. B.J. Appl. Phys. 32 (1961), 814–828.CrossRefGoogle Scholar
(14)Van Deb Pol, B. and Bremmer, H.Philos. Mag. 24 (1937), 141–176, 825–864.Google Scholar
(15)Waechter, R. T.Proc. Cambridge Philos. Soc. 64 (1968), 1165–1201.CrossRefGoogle Scholar
(16)Watson, G. N.Proc. Roy. Soc. Ser. A 95 (1919), 83–99.Google Scholar