Hall Current Effects on Unsteady MHD Flow in a Rotating Parallel Plate Channel Bound-ed by Porous Bed on the Lower Half—Darcy Lapwood Model

M. Veera Krishna¹, Jagdish Prakash^2*

¹Department of Mathematics, Rayalaseema University, Kurnool, India.
²Department of Mathematics, University of Botswana, Gaborone, Botswana.

DOI: 10.4236/ojfd.2015.54029                

Abstract

We discussed the unsteady flow of an incompressible viscous fluid in a rotating parallel plate channel bounded on one side by a porous bed under the influence of a uniform transverse magnetic field taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate. The flow in the clean fluid region is governed by Navier-Stoke’s equations while in the porous bed the equations are based on Darcy-Lapwood model. The exact solutions of velocity in the clean fluid and the porous medium consist of steady state and transient state. The time required for the transient state to decay is evaluated in detail and ultimate quasi-steady state solution has been derived analytically and also its behaviour is computationally discussed with reference to different flow parameters. The shear stresses on the boundaries and the mass flux are also obtained analytically and their behaviour is computationally discussed.

Keywords

Darcy Lapwood Model, Hall Effects, MHD Flows, Porous Bed, Unsteady Flows and Rotating Parallel Plate Channels

Conflicts of Interest

The authors declare no conflicts of interest.

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