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
 … show all 3 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessSummary
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.
 Abramowitz, M., Stegun, I. A. (eds.): Handbook of mathematical functions. New York: Dover 1964.
 Benton, E. R., Loper, D. E.: The unsteady hydromagnetic EkmanHartmann boundary layer problems. J. Fluid Mech.39, 561–586 (1967).
 Benton, E. R.: Nonlinear hydrodynamic and hydromagnetic spinup driven by EkmanHartmann boundary layers. J. Fluid Mech.57, 337–360 (1973).
 Benton, E. R., Clark, A.: Spinup. Ann. Rev. Fluid Mech.6, 257–280 (1974).
 Chawla, S. S.: On hydrodynamic spinup. J. Fluid Mech.53, 545–555 (1972).
 Chawla, S. S.: Spinup from a rotating disk. J. Fluid Mech.78, 609–619 (1976).
 Chawla, S. S., Verma, A. R.: Free convection from a disk rotating in a vertical plane. J. Fluid Mech.126, 307–313 (1983).
 Dieke, R. H.: Internal rotation of the sun. Ann. Rev. Astronomy Astrophys.8, 297–329 (1970).
 Eugene, J., Emde, F.: Tables of functions with formulae and curves. New York: Dover 1948.
 Greenspan, H. P., Howard, L. N.: On a timedependent motion of a rotating fluid. J. Fluid Mech.17, 385–404 (1963).
 Hide, R., Roberts, P. H.: The origin of the main magnetic field. Phys. Chem. of the Earth4, 27–98 (1961).
 MacRobert, T. M.: Functions of a complex variable, 4th ed London: Macmillan 1954.
 Mathews, J. L. R., Nath, G.: Spinup or spindown of a rotating electrically conducting fluid with a magnetic field. Phys. Fluids27, 1718–1722 (1984).
 Nakamura, S.: Iterative finitedifference schemes for similar and nonsimilar boundary layer equations. Adv. Eng. Software21, 123–131 (1994).
 Rott, N., Lewellen, W.: Boundary layers due to the combined effects of rotation and translation. Phys. Fluids10, 1867–1873 (1967).
 Sparrow, E. M., Cess, R. D.: Magnetohydrodynamic flow and heat transfer about a rotating disk. J. Appl. Mech.29, 181–187 (1962).
 Thacker, W. T., Watson, L. T., Kumar, S. K.: Magnetohydrodynamic free convection from a disk rotating in a vertical plane. Appl. Math. Modelling14, 527–537 (1990).
 Watson, G. N.: A treatise on the theory of Bessel functions, 2nd ed. London: Cambridge University Press 1944.
 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
 Additional Links
 Topics
 Industry Sectors
 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