MAGNETIC FIELDS EFFECT ON A POROUS SPHERE IN A NONCONCENTRIC SPHERICAL CELL

The effects of uniform transverse magnetic field on the quasi-steady axisymmetrical flow of an incompressible viscous fluid past a porous sphere situated at an arbitrary position within a virtual spherical cell along the line connecting their centers is investigated. At the interface between clear fluid and porous medium, the stress jump boundary condition for the tangential stresses along with continuity of normal stress and velocity components are applied. A semi-analytical approach based on a collocation method is used. The Brinkman model governs the flow inside the porous particle and the flow in the fictitious envelope medium is governed by Stokes equations with different Hartman numbers in the flow regions. A general solution is constructed from the superposition of the fundamental solutions in the two spherical coordinate systems based on both the porous particle and fictitious spherical envelope. Numerical solutions for the hydrodynamic drag force exerted on the porous sphere in the presence of the cell are calculated. The numerical values of the Kozeny factor (often assumed to be constant) are also evaluated for various cases of the effective distance between the center of the porous particle and the fictitious envelope, the volume ratio of the porous particle over the surrounding sphere, the Hartmann numbers, the viscosity ratio, the stress jump coefficient, and a coefficient that is proportional to the permeability. Streamlines through and around porous spherical particles are presented for the Happel and Kuwabara unit cell models at different values of relevant physical parameters. In the limits of the motions of the porous particle in the concentric position with the cell surface and near the cell surface with a small curvature, the numerical results for the Kozeny factor are in good agreement with the available analytical solutions in the literature.