Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-03T01:39:04.715Z Has data issue: false hasContentIssue false
  • English
  • Français

The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers

Published online by Cambridge University Press:  24 October 2008

D. J. Temperley  and
L. Todd
D. J. Temperley
Affiliation:
The University, Edinburgh; Laurentian University, Sudbury, Ontario
L. Todd
Affiliation:
The University, Edinburgh; Laurentian University, Sudbury, Ontario
Get access Rights & Permissions [Opens in a new window]

Abstract

Laminar motion of a conducting fluid in a rectangular duct is discussed. The applied magnetic field is uniform and parallel to one pair of sides of the duct. Classical theory is used and it is shown that the two successive limiting processes, lim (σwall → ∞; hσ wall → a finite, constant limit) and lim (M → ∞) are not always freely interchangeable; M being the Hartmann number, σwall the electrical conductivity of the duct wall and h the typical ratio of (wall thickness/duct width). A general expansion procedure for M ≫ 1, valid for all types of wall conductivities, is devised. A critical discussion of the deficiencies in the classical model is given.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 69 , Issue 2 , March 1971 , pp. 337 - 351
Copyright
Copyright © Cambridge Philosophical Society 1971

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)Chang, C. C. and Lundgren, T. S. Z.angew. Math. Phys. 12 (1961), 100.CrossRefGoogle Scholar
(2)Chiang, P. and Lundgren, T. S. Z.angew Math. Phys. 18 (1967), 92.Google Scholar
(3)Eckhaus, W. and de Jager, E. M.Arch. Rational Mech. Anal. 23 (1966), 26.Google Scholar
(4)Hunt, J. C. R.J. Fluid Mech. 21 (1965), 577.CrossRefGoogle Scholar
(5)Hunt, J. C. R.Proc. Cambridge Philos. Soc. 65 (1969), 319.Google Scholar
(6)Hunt, J. C. R. and Stewartson, K. J.Fluid Mech. 23 (1965), 563.CrossRefGoogle Scholar
(7)Lock, R. C.Proc. Roy. Soc. Ser. A 233 (1955), 105.Google Scholar
(8)Roberts, P. H.An introduction to magnetohydrodynamics (Longmans, 1967).Google Scholar
(9)Shercliff, J. A.Proc. Cambridge. Philos. Soc. 49 (1953), 136.Google Scholar
(10)Srercliff, J. A. J.Fluid Mech. 1 (1956), 644.Google Scholar
(11)Sloan, D. M. and Smith, P. Z.angew Math. Mech. 46 (1966), 439.CrossRefGoogle Scholar
(12)Todd, L. J.Fluid Mech. 31 (1968), 321.Google Scholar
(13)Uflyand, Y. S.Soviet Phys. Tech. Phys. 5 (1961), 1194.Google Scholar