Spinup and spindown of a viscous fluid over a heated disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force
 A. Slaouti,
 H. S. Takhar,
 G. Nath
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Summary
The hydromagnetic spinup and spindown of an incompressible electrically conducting fluid on a heated infinite disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force have been studied. The flow is nonaxisymmetric due to the imposition of the buoyancy force. We have considered the situation where there is an initial steady state which is perturbed by suddenly changing the angular velocity of the disk. By using suitable transformations the NavierStokes and energy equations with four independent variables (x, y, z, t) are reduced to a system of partial differential equations with two independent variables (η,t ^{*}). Also, these transformations uncouple the momentum and energy equations, resulting in a primary axisymmetric flow with an axial magnetic field, in an energy equation dependent on the primary flow and in a buoyancy induced secondary cross flow dependent on both primary flow and energy.
The results indicate that the effect of the stepchange in the angular velocity of the disk is more pronounced on the primary flow than on the secondary flow and the temperature field. For both spinup and spindown cases the surface shear stress in the nonaxial direction normal to gravity for the primary flow and the surface shear stresses for the secondary flow increase with the magnetic parameter, whilst the surface shear stress in the vertical direction and the heat transfer at the surface decrease as the magnetic parameter increases. Also, the secondary flow near the disk dominates the primary flow. We have also developed an asymptotic analysis for large magnetic parameters which complements well the numerical results obtained in the lower magnetic parameter range.
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 Title
 Spinup and spindown of a viscous fluid over a heated disk rotating in a vertical plane in the presence of a magnetic field and a buoyancy force
 Journal

Acta Mechanica
Volume 156, Issue 12 , pp 109129
 Cover Date
 20020301
 DOI
 10.1007/BF01188745
 Print ISSN
 00015970
 Online ISSN
 16196937
 Publisher
 SpringerVerlag
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 Authors

 A. Slaouti ^{(1)}
 H. S. Takhar ^{(1)}
 G. Nath ^{(2)}
 Author Affiliations

 1. Department of Engineering and Technolgy, Manchester Metropolitan University, M1 5GD, Manchester, UK
 2. Department of Applied Mathematics, Indian Institute of Science, 560012, Bangalore, India