Flow Through Porous Media Induced by an Impervious Rotating Disk in the Presence of Magnetic Field
Abstract
The flow of an electrically conducting viscous incompressible fluid, due to an infinite impervious rotating disk bounded by porous medium is discussed. It is assumed that the flow between the disk and the porous medium is governed by Navier-Stokes equations and that in the porous medium – by Brinkman equations. A uniform magnetic field is applied in the direction normal to flow. At the interface (porous medium – clear fluid boundary), a modified set of boundary conditions is applied. Analytical expressions for the velocity and shearing stress are calculated and effects of various parameters upon them are examined.Keywords:
incompressible fluid, porous medium, MHD, rotating diskReferences
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2. R.E. CUNNINGHAM and R. J. WILLIAMS, Diffusion in gases and porous media, Pleanum Press, N. Y., 1980.
3. H. DARCY, The flow of fluids through porous media, Mc-Graw Hill Book Co. N. Y., 1937.
4. H.C. BRINKMAN, Calculation of viscous force exerted by a flow in fluid on a dense swarm of particles. Appl. Sci. Res., Al, 27–36, 1947.
5. I.P. JONES, Low Reynolds number flow past a porous spherical shell, Proc. Camb. Phil. Soc., 73, 231–237, 1973.
6. D.D. JOSEPH and L.N. TAO, Ground flow induced by a moving cylinder, Phys. of Fluids, 8, 1438–1449, 1965.
7. M.P. SINGH and J.L. GUPTA, Flow of a viscous fluid past an inhomogeneous porous cylinder. ZAMM, 51, 17–24, 1971.
8. B.S. PADMAVATHI and J. AMARNATH, A solution for the problem of Stokes flow past a porous sphere, ZAMP, 44, 178–184, 1993.
9. A.C. SRIVASTAVA and B.R. SHARMA, The flow and heat transfer of a porous medium of finite thickness, J. Math Phys. Sci., 26, 539–547, 1992.
10. T. KATUKANI, Hydromagnetic flow due to a rotating disk, J. Phys. Soc. Japan, 17, 14961506, 1962.
11. E.M. SPARROW and R.D. CESS, Magnetohydrodynamics flow and heat transfer about a rotating disk, J. Appl. Mech. Trans., ASME, 29, 181–187, 1962.
12. T. WATANABE and T. OYAMA, Magnetohydrodynamic boundary layer flow over a rotating disk, ZAMM, 71, 522–524, 1991.
13. S.K. KUMAR, W.I. THACKER and L.T. WATSON, Magnetohydrodynamic flow and heat transfer about a rotating disk with suction and injection at the disk surface, Computers Fluids, 16, 183–193, 1988.
14. P.D. ARIEL, On computation of MHD flow near a rotating disk, ZAMM, 82, 235–246, 2002.
15. W.O. WILLIAM, On the theory of mixtures, Arch. Rat. Mech. Anal., 51, 239–260, 1973.
16. A.C. SRIVASTAVA and B. BARMAN, The flow of a non-Newtonian fluid confined between impervious rotating disk and a porous medium, Proc. Nat. Acad. Sci. India, 67 (A), II, 165–174, 1997.
