Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-12-01T04:37:52.257Z Has data issue: false hasContentIssue false
  • English
  • Français

Application to magnetohydrodynamic duct flows of a singular elliptic problem associated with a rectangle

Published online by Cambridge University Press:  14 November 2011

V. A. Nye
V. A. Nye
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow
Get access Rights & Permissions [Opens in a new window]

Synopsis

The analysis developed by the author in a previous paper is used to discuss two magnetohydrodynamic duct flows for which the boundary conditions are not of Dirichlet type. To the accuracy stated, the results obtained confirm those obtained by previous authors who used different approaches to the problems. A feature of the present analysis is that it yields the magnitude of the error entailed by the use of approximate forms for flow quantities. This has been lacking in previous analyses.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 86 , Issue 3-4 , 1980 , pp. 355 - 365
Copyright
Copyright © Royal Society of Edinburgh 1980

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

1Eckhaus, W. and de Jager, E. M.. Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type. Arch. Rational Mech. Anal. 23 (1966), 26–86.CrossRefGoogle Scholar
2Fraenkel, L. F.. On the method of matched asymptotic expansions. Math. Proc. Cambridge Philos. Soc. 65 (1969), 209–284.CrossRefGoogle Scholar
3Fussey, D. E.. An experimental study of magneto-viscous effects in a combustion plasma. J. Phys. D. Appl. Phys. 4 (1971), 1913–1928.CrossRefGoogle Scholar
4Hunt, J. C. R.. Magnetohydrodynamic flow in rectangular ducts. J. Fluid Mech. 21 (1965), 577–590.CrossRefGoogle Scholar
5Hunt, J. C. R. and Stewartson, K.. Magnetohydrodynamic flow in rectangular ducts. J. Fluid Mech. II 23 (1965), 563–581.CrossRefGoogle Scholar
6Hutson, V.. On the Fredholm integral equations associated with pairs of dual integral equations. Proc. Edinburgh Math. Soc. 16 (1969), 185–194.CrossRefGoogle Scholar
7Kaplun, S. and Lagerstrom, P. A.. Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers. J. Math. Mech. 6 (1957), 583–593.Google Scholar
8Nye, V. A.. Some comments on a singular elliptic problem associated with a rectangle. Proc. Roy. Soc. Edinburgh Sect. A 83 (1979), 283–296.CrossRefGoogle Scholar
9Shercliff, J. A.. A Textbook on Magnetohydrodynamics (London: Pergamon, 1965).Google Scholar
10Shercliff, J. A.. Thermoelectric magnetohydrodynamics. J. Fluid Mech. 91 (1979), 231–251.CrossRefGoogle Scholar
11Sloan, D. M. and Smith, P.. Magnetohydrodynamic flow in a rectangular pipe between conducting plates. Z. Angew. Math. Mech. 46 (1966), 439–443.CrossRefGoogle Scholar
12Sutton, G. W. and Sherman, A.. Engineering Magnetohydrodynamics (New York: McGraw-Hill, 1965).Google Scholar
13Temperley, D. J. and Todd, L.. The effects of wall conductivity in magnetohydrodynamic duct flow at high Hartmann numbers. Math. Proc. Cambridge Philos. Soc. 69 (1971). 337–351.CrossRefGoogle Scholar
14Temperley, D. J. and Todd, L.. Some remarks on a class of plane, linear boundary value problems. J. Inst. Math. Appl. 18 (1976), 309–324.CrossRefGoogle Scholar
15Ursell, F.. Integral equations with a rapidly oscillating kernel. J. London. Math. Soc. 44 (1969), 449–459.CrossRefGoogle Scholar
16Zabreyko, P. P.et al. Integral Equations—a Reference Text. Transi. Shaposhnikova, T.O.et al. (Leyden: Noordhoff, 1976).Google Scholar