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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.v12.i9.40
pages 869-886

Magnetohydrodynamic Peristaltic Pumping Through Uniform Channel with Porous Peripheral Layer and Hall Currents

Nabil T. M. Eldabe
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Cairo, Egypt
A. Y. Ghaly
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt
H. M. Sayed
Department of Mathematics, Faculty of Education, Ain Shams University, Heliopolis, Roxy, Cairo, Egypt

ABSTRACT

The peristaltic pumping of a biofluid consisting of two immiscible fluids of different viscosity, one occupying the core and the other the peripheral layers on either side, in a two-dimensional channel partially filled with a layer of a porous material is investigated. The core region is described by the Eyring-Powell model and the peripheral region is taken to be electrically conducting Newtonian viscous fluid. The fluid in peripheral region is permeated by an external uniform magnetic field imposed perpendicularly to xy plane on the assumption of a small magnetic Reynolds number in the presence of the effect of Hall currents. The flow is examined in the wave frame of reference moving with the velocity of the wave. The Brinkman extended Darcy equation is utilized to model the flow in a porous layer. A shear stress jump boundary condition is used at the interface. The analytic solutions have been obtained in the form of a stream function from which the velocity fields and axial pressure gradient have been derived. The present analysis has been performed under long wavelength and low Reynolds number assumptions. The effects of various emerging parameters on the flow characteristics are shown and discussed with the help of graphs and the phenomenon of trapping is also discussed.