An analytical solution of the flow of a hydromagnetic fluid through a porous medium between permeable beds is obtained and studied. The fluid is under an exponential decaying pressure gradient and the uniform magnetic field in a direction normal to the flow saturated porous medium is considered. Two governing equations, namely Navier-Stokes equations and Darcy's law, are employed for the flow between and through the permeable beds, respectively. Injection and suction of the fluid through lower and upper permeable beds, respectively, with same velocity are allowed in the presence of porous medium and the uniform magnetic field. The velocity field and the volume flux are calculated analytically and presented graphically for different choices of the parameters exhibiting their phenomenal nature. Additionally if we replace the exponentially decaying pressure gradient by the pulsatile one and porousity of medium tends to zero, the results match excellently with those of Malathy and Srinivas [T. Malathy and S. Srinivas, Pulsatile flow of a hydromagnetic fluid between permeable beds, Int. Comm. In Heat and Mass Transfer 35, 681-688 (2008)].
This paper investigates the unsteady hydromagnetic Couette fluid flow through a porous medium between two infinite horizontal plates induced by the non-torsional oscillations of one of the plates in a rotating system using boundary layer approximation. The fluid is assumed to be Newtonian and incompressible. Laplace transform technique is adopted to obtain a unified solution of the velocity fields. Such a flow model is of great interest, not only for its theoretical significance, but also for its wide applications to geophysics and engineering. Analytical expressions for the steady state velocity and shear stress on the plates are obtained, and the case of single oscillating plate is also discussed. The influence of pertinent parameters on the flow is delineated, and appropriate conclusions are drawn.
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