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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.

The characteristic of creeping flow past a fluid sphere enclosed in a spherical envelope bearing fluid of different viscosity has been studied under the impact of transverse magnetic field. Stream functions related to modified Bessel functions are used in order to calculate the solution in closed form. The problem is considered to be parted into two flow regions as inner fluid and outer fluid region respectively, which are supposed to be governed using Stokes equations with different Hartmann number. At the contact layer of outer and inner fluid sphere, we assume the vanishing of normal components of velocity along with continuity of tangential components of velocity and stress respectively as boundary conditions. The condition of vanishing of vorticity (Kuwabara model) is considered to be applicable at the outer layer of fluid envelope. Expression for drag acting on the inner fluid sphere is presented. In limiting cases, several significant results accessible in literature are evaluated.

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