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Journal of Porous Media

Impact factor: 1.035

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v11.i4.50
pages 389-400

Some MHD Flows of a Second Grade Fluid through the Porous Medium

I. Khan
Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000, Pakistan
R. Ellahi
Department of Mathematics and Statistics, FBAS, IIUI, Islamabad, Pakistan; Department of Mathematics, Faculty of Science, Taibah University, Al-Madeenah, Saudi Arabia
Constantin Fetecau
Department of Mathematics, Technical University of Iasi, R-6600 Iasi, Romania; Academy of Romanian Scientists, 050094 Bucuresti, Romania

ABSTRACT

In this article, we investigate the effects of magnetic field and porous medium on some unidirectional flows of a second grade fluid. These magnetohydrodynamic (MHD) flows are produced by the application of periodic pressure gradient or by the impulsive motion of one or two boundaries or by an oscillating plate. Modified Darcy's law has been used for the flow modeling. Seven illustrative examples have been taken into account and exact analytic solutions for velocity are obtained. Besides that analytic expressions for frictional forces have been established. The corresponding results of velocity and frictional forces in the absence of a porous medium and applied magnetic field Rajagopal, 1982; Hayat et al., 2000, can be obtained from the present analysis by taking M → 0 and K → 0. The similar results for a Newtonian fluid can also be gotten as a limiting case.