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The present paper concerns about finding the impact of applied transverse magnetic field on parallel cylindrical shell of magneto viscous fluid by unit cell model. The considered flow is divided into three regions, bounded fluid region, porous region and inner cavity region, where the flow in the bounded and cavity regions is governed by Stokes equation and flow in the annular porous region is governed by Brinkman's equation in the presence of magnetic field. The boundary conditions used at the fluid-porous interface are continuity of velocity components and stress jump condition for tangential stresses together with Happel and Kuwabara boundary conditions. Expression for volumetric flow rate in the presence of transverse magnetic field is calculated, and limiting cases leads to some well-known results. The effect of Kozeny constant versus fractional void volume for varying permeability, Hartmann numbers, viscosity ratio, separation parameter and stress jump coefficient is tabulated and represented by graphs. In the limits of the motion of porous cylinder and impermeable cylinder in the cell, the numerical values of the Kozeny constant are in good agreement with the available values in the literature.

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The effect of a closed boundary on the hydrodynamic drag of a nonconcentric semipermeable sphere in an incompressible viscous fluid is investigated. Darcy’s law holds in the permeable region and Stokes flow used inside the spherical cavity. Suitable boundary conditions are used on the surface of a semipermeable sphere and spherical cavity. Two spherical coordinate systems are used to solve the problem. By superposition principle, a general solution is constructed from the solutions based on the semipermeable sphere and spherical cavity. Numerical results for the hydrodynamic drag force exerted on the particle is obtained with good convergence for various values of the relative distance between the centers of the inner sphere and spherical cavity, permeability parameter and the separation parameter. The numerical values of the hydrodynamic drag force generalize the results obtained for an eccentric solid sphere.

Slow axisymmetric flow of an incompressible viscous fluid caused by a slip sphere within a non-concentric spherical cell surface is investigated. The uniform velocity (Cunningham's model) and tangential velocity reaches minimum along a radial direction are imposed conditions at the cell surface (Kvashnin's model). The general solution of the problem is combined using superposition of the fundamental solution in the two spherical coordinate systems based on the centers of the slip sphere and spherical cell surface. Numerical results for the correction factor on the inner sphere are obtained with good convergence for various values of the relative distance between the centers of the sphere and spherical cell, the slip coefficient, and the volume fraction. The obtained results are in good agreement with the published results. The effect of concentration is more in the Cunningham's model compared to the Kvashnin's model. The wall correction factor on the no-slip sphere is more compared to that of a slip sphere. The correction factor on the slip sphere is more than that of a spherical gas bubble.