Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-13T01:32:42.744Z Has data issue: false hasContentIssue false
  • English
  • Français

A periodic boundary-layer flow in magnetohydrodynamics

Published online by Cambridge University Press:  28 March 2006

D. L. Turcotte  and
J. M. Lyons
D. L. Turcotte
Affiliation:
Graduate School of Aerospace Engineering, Cornell University
J. M. Lyons
Affiliation:
Graduate School of Aerospace Engineering, Cornell University
Get access Rights & Permissions [Opens in a new window]

Abstract

It is the purpose of this paper to solve a boundary-value problem posed by induction electromagnetic pumps and generators. Solutions are obtained by an expansion technique and a momentum method for the laminar, incompressible flow problem. For large values of the interaction parameter (μ2σH20λ/ρμe viscous effects are shown to be restricted to periodic boundary layers. In regions of high-field strength a local Hartmann solution is valid. Where the applied field is weak an inertial boundary layer is present which thickens in the upstream direction.

A logical explanation of this phenomenon is given. The condition that a boundary-layer type flow exist is obtained and is shown to be in general satisfied. The results show that inviscid theory may be used to calculate the overall performance of electromagnetic pumps and generators while the boundary-layer theory developed here may be used to obtain the wall shear stress.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 13 , Issue 4 , August 1962 , pp. 519 - 528
Copyright
© 1962 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

Bernstein, I. B., Fanucci, J. B., Fischbeck, K. H., Lessen, M., Ness, W., Jaren, J. & Kulsrud, R. M. 1961 Second Symposium on the Engineering Aspects of Magnetohydrodynamics. University of Pennsylvania, Philadelphia.
Blake, L. R. 1957 Proc. Instn elect. Engrs, A, 104, 49.
Blake, L. R. 1959 J. Nucl. Energy, B, 1, 65.
Harris, L. P. 1960 Hydromagnetic Channel Flows. New York: John Wiley and Sons.
Hartmann, J. 1937 K. danske vidensk. Selsk. (Math.-fys, Meddel.), 15, 6. Copenhagen.
Lyons, J. M. & Turcotte, D. L. 1962 A study of magnetohydrodynamic induction devices. A.F.O.S.R. Tech. Rep. no. 1864.Google Scholar
Panofsky, W. K. H. & Phillips, M. 1955 Classical Electricity and Magnetism, p. 149. Reading, Mass.: Addison-Wesley.
Schlichting, H. 1955 Boundary Layer Theory. New York: McGraw-Hill.