Abstract
We analyze the laminar flow and heat transfer induced by a slightly curved wall oscillating in a viscous, electrically conducting fluid which is otherwise at rest, under the action of a transverse magnetic field. The electrically insulating wall as well as the fluid at infinity are maintained at different constant temperatures. The analysis is based on perturbative solutions and special attention is paid to the effect that the magnetic field has on the non-linear streaming contributions. The competing action of inertial transfer and magnetic suppression in the transport of vorticity in the boundary layer is analyzed. Diffusive heat transfer solutions including viscous and ohmic dissipation are found. The convective effect of the streaming flow in the boundary layer is also discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Telionis, D. P. (1981) Unsteady Viscous Flows, Springer-Verlag, New York.
Swift, G. W. (1988) A liquid-metal magnetohydrodynamic acoustic transducer, J. Acoust. Soc. Am., 83, 350–361.
Munakata, T. and Tanasawa, I. (1990) Onset of oscillatory flow in Czochralski growth melt and its suppression by the magnetic field, J. Crystal Growth, 106, 566–576.
Lighthill, M. J. (1954) The response of laminar skin friction and heat transfer to fluctuations in the stream velocity, Proc. Roy. Soc. A, 224, 1–23.
Gould, R. K. (1961) Effects of acoustic streaming on heat transfer, Ph.D. Thesis, Brown Univ., Providence, Rhode Island.
Rayleigh, Lord, (1884) On the circulations of air observed in Kundt’s tubes and on some allied acoustical problems, Phil. Trans. A, 175, 1. Rayleigh, Lord, (1945) The Theory of Sound, vol. 2, Dover, New York, 333–342.
Faraday, M. (1831) Phil. Trans. Roy. Soc. London, 121, 229.
Schlichting, H. (1932) Berechnung ebner periodischer Grenzschichtstromungen, Phys. Z., 33, 327–335.
Stuart, J. T. (1966) Double boundary layers in oscillatory viscous flow, J. Fluid Mech., 24, 673–687.
Riley, N. (1965) Oscillating viscous flow, Mathematika, 12, 161–175.
Riley, N. (1967) Oscillatory viscous flows. Review and extension, J. Inst. Math. Appl., 3, 419–434.
Riley, N. (1975) Unsteady boundary layers, SIAM Review, 17, 274–29.
Richardson, P. D. (1967) Heat transfer from a circular cylinder by acoustic streaming, J. Fluid Mech., 30, 337–355.
Davidson, B. J. (1973) Heat transfer from a vibrating circular cylinder, Int. J. Heat Mass Transfer, 16, 1703–1727.
Gopinath, A. and Mills, A. F. (1993) Convective heat transfer from a sphere due to acoustic streaming, ASME J. Heat Transfer, 115, 332–341.
Gopinath, A. and Mills, A. F. (1994) Convective heat transfer due to acoustic streaming across the ends of a Kundt tube, ASME J. Heat Transfer, 116, 47–53.
Cuevas, S and Ramos, E. (1997) Steady streaming in oscillatory viscous flow under a transverse magnetic field, Phys. Fluids, 9, 1430–1434.
Moffatt, H. K. and Toomre, J. (1967) The annihilation of a two-dimensional jet by a transverse magnetic field, J. Fluid Mech., 30, 65–82.
Moreau, R. (1990) Magnetohydrodynamics, Kluwer Academic Publishers, Dordrecht.
Lighthill, J. (1978) Acoustic streaming, J. Sound Vibration, 61, 391–418.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cuevas, S., Ramos, E. (1999). Transport of Momentum and Heat in Oscillatory MHD Flow. In: Alemany, A., Marty, P., Thibault, J.P. (eds) Transfer Phenomena in Magnetohydrodynamic and Electroconducting Flows. Fluid Mechanics and Its Applications, vol 51. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4764-4_8
Download citation
DOI: https://doi.org/10.1007/978-94-011-4764-4_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6002-8
Online ISBN: 978-94-011-4764-4
eBook Packages: Springer Book Archive