Flow past composite cylindrical shell of porous layer with a liquid core: magnetic effect

Abstract

The creeping flow of a magnetic fluid perpendicular to a porous cylindrical shell is investigated, employing the unit cell model. The viscous fluid is assumed to be flowing in three zones divided as fluid, annular porous, and cavity regions, respectively. We apply a uniform magnetic field in a transverse direction of flow and then emphasize the influence of the Hartmann layers which are developed in their vicinity. Modified Stokes and modified Brinkman’s equations are employed in the liquid and porous regions, respectively. Happel and Kuwabara cell models are used as the interface conditions at the cell surface, and at the fluid–porous interface, continuity of velocity components, continuity of normal stresses, and stress jump condition for tangential stresses are applied. An expression for Kozeny constant for the cylindrical shell is presented. Representation of Kozeny constant under the influences of the pertinent parameters such as Hartmann numbers, stress jump coefficient, fractional void volume, viscosity ratios, permeability, and separation is displayed through graphs and a table. The results are compared with the cases which do not involve magnetic effect. They reveal the strong impact of Hartmann’s numbers on the resisting force experienced on the cylindrical shell. The results agree well with previous available works.