Influence of a magnetic field on the flow of a micropolar fluid sandwiched between two Newtonian fluid layers through a porous medium
Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, 211004, Allahabad, India
2 School of Computing and Engineering, University of Huddersfield, HD1 3DH, Queensgate, Huddersfield, UK
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Accepted: 23 May 2018
Published online: 3 July 2018
The present paper is concerned with the flow of a micropolar/Eringen fluid sandwiched between two Newtonian fluid layers through a horizontal porous channel. The flow in both regions is steady, incompressible and the fluids are immiscible. The flow is driven by a constant pressure gradient and a magnetic field of uniform strength is applied in the direction perpendicular to the flow. The flow of electrically conducting fluids, in the three regions, is governed by the Brinkman equation with the assumption that the effective viscosity of each fluid is the same as the viscosity of the fluid. No-slip conditions at the end of the plates, continuity of velocity, continuity of shearing stress and constant rotational velocity at the interface have been used as the boundary conditions to get the solution of the considered problem. The numerical values of the solution obtained are used to analyse graphically the effect of various transport parameters, such as permeability of the porous region, magnetic number, viscosity ratio, etc., on the velocity profile and microrotational velocity profile. Also, the variations in the flow rate and the wall shear stress with respect to the governing parameters are presented in tabular form.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018