Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-20T09:20:52.124Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 3. Variable-area rectangular ducts with insulating walls

Published online by Cambridge University Press:  29 March 2006

J. S. Walker ,
G. S. S. Ludford  and
J. C. R. Hunt
J. S. Walker
Affiliation:
Department of Theoretical and Applied Mechanics, University of Illinois
G. S. S. Ludford
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University
J. C. R. Hunt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Cambridge University
Get access Rights & Permissions [Opens in a new window]

Abstract

The general analysis developed in Parts 1 and 2 of three-dimensional duct flows subject to a strong transverse magnetic field is used to examine the flow in diverging ducts of rectangular cross-section, the walls of which are electrically non-conducting. A dramatically different flow is found in this case from that studied in Part 2, where the side walls parallel to the magnetic field were highly conducting. Now it is found that the core velocity normalized with respect to the mean velocity is of O(M−½) while the velocity in the side-wall boundary layers is of O(M½), so that these boundary layers carry most of the flow. The problem of entry is solved by analysing the change from fully developed Hartmann flow in a rectangular duct to the flow in the diverging duct. It is found that the disturbance in the upstream duct decays exponentially. The analysis of the side-wall boundary layers is more difficult than that in Part 1 on account of the different boundary conditions and requires the solution of two coupled integro-differential equations. Numerical solutions are obtained for a duct whose width increases linearly in the flow direction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 56 , Issue 1 , 14 November 1972 , pp. 121 - 141
Copyright
© 1972 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

Branover, G. G. & Shcrerbinin, E. V. 1966 Magnetohydrodynamic jet flow in a bounded space. Magnitnaya Gidrodinamika, 2, 55–63.Google Scholar
Hunt, J. C. R. & Hancox, R. 1971 The use of liquid lithium as coolant in a toroidal fusion reactor. U.K.A.E.A. Rep. CLM-R115.Google Scholar
Hunt, J. C. R. & Ludford, G. S. S. 1968 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 1. Obstacles in a constant-area channel. J. Fluid Mech. 33, 693–714.Google Scholar
Hunt, J. C. R. & Shercliff, J. A. 1971 Magnetohydrodynamics at high Hartmann number. Rev. Fluid Mech. 3, 37–62.Google Scholar
Kulikovskii, A. G. 1968 Slow steady state flows of conducting fluid at large Hartmann number. Izv. Akad. Nauk S.S.R., Mekh. Zhid. i Gaza, 2, 3.Google Scholar
Lundgren, T. & Chiang, D. 1967 Solution of a class of singular integral equations. Quart. Appl. Math. 24, 303–313.Google Scholar
Shercliff, J. A. 1953 Steady motion of conducting fluids in pipes under transverse magnetic fields. Proc. Camb. Phil. Soc. 49, 136–144.Google Scholar
Slyusarev, N. M., Shilova, YE. I. & Shcherbinin, E. W. 1970 Experimental study of converging and diverging MHD flow. Magnitnaya Gidrodinamika, 4, 59–67.Google Scholar
Walker, J. S. 1970 Three-dimensional magnetohydrodynamic flow in diverging rectangular ducts under strong transverse magnetic fields. Ph.D. thesis, Cornell University.
Walker, J. S., Ludford, G. S. S. & Hunt, J. C. R. 1971 Three-dimensional MHD duct flows with strong transverse magnetic fields. Part 2. Variable-area rectangular ducts with conducting sides. J. Fluid Mech. 46, 657–684.Google Scholar