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Journal of Porous Media
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ISSN Imprimer: 1091-028X
ISSN En ligne: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v21.i7.50
pages 637-664

EFFECT OF MAGNETIC FIELDS ON THE MOTION OF POROUS PARTICLES FOR HAPPEL AND KUWABARA MODELS

El-Sayed Ibrahim Saad
Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt; Department of Mathematics, Faculty of Science, Shaqra University, Dawadmi, Saudi Arabia

RÉSUMÉ

The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of porous spheres subject to a uniform transverse magnetic field is analytically studied through the use of unit cell models. Both flows are also considered parallel and perpendicular to assemblages of porous circular cylinders-in-cell models under the effect of uniform magnetic fields. At the porous-medium/clear-fluid interface, the stress jump boundary condition for the tangential stresses along with continuity of normal stress and velocity components are employed. The flow inside the porous particleis governed by the Brinkman model and the flow in the fictitious envelope medium is governed by Stokes equations with different Hartman numbers in the flow regions. The analytical solutions for the hydrodynamic drag force exerted on the porous particle-in-cell models, the volume flow rate of fluid through the cylindrical regions, and the expressions of Kozeny constant are obtained for parallel and perpendicular flow. For various cases, the Kozeny constant is analyzed against the fractional void volume, the Hartmann numbers,the viscosity ratio, the stress jump coefficient, and a coefficient that is proportional to the permeability of the porous region. Streamlines in and around the porous particle are constructed for the Happel and Kuwabara unit cell models at different values of relevant physical parameters. In the limits of the motions of impermeable spheres and cylinders in the cell surface and near the cell surface with a small curvature, the numerical values of the Kozeny constant are in good agreement with the available values in the literature.


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