Effect of the magnetic field on the hydrodynamic permeability of a membrane

Abstract

The present paper concerns the influence of the magnetic field on the permeability of a membrane of solid cylindrical particles covered with porous layer. Here, we have considered the flow along the axis of cylinder and the alignment of uniform magnetic field is assumed to be perpendicular to the axis. The Brinkman equation is used for flow through porous region and Stokes equation is used for flow through clear fluid region. To model flow through assemblage of particles, cell model technique has been used i.e. the porous cylindrical shell is assumed to be confined within a hypothetical cell of same geometry. The stress jump condition has been employed at the fluid-porous interface and all four alternative conditions Happel, Kuwabara, Kvashnin and Mehta-Morse/Cunningham are used at the hypothetical cell. Effect of the Hartmann number on the hydrodynamic permeability of the membrane is discussed.