Effect of magnetic field on the hydrodynamic permeability of a membrane built up by porous spherical particles

Abstract

In this paper, an analysis of steady, axi-symmetric Stokes flow of an electrically conducting viscous incompressible fluid through spherical particle covered by porous shell in presence of uniform magnetic field is presented. To model flow through the swarm of spherical particles, cell model technique has been used, i.e. porous spherical shell is assumed to be confined within a hypothetical cell of the same geometry. At the fluid-porous interface, the stress jump boundary condition for tangential stresses along with continuity of normal stress and velocity components are used. Four known boundary conditions on the hypothetical surface were considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta−Morse’s) condition. The effect of stress jump coefficient, Hartmann number, and dimensionless permeability of the porous region as well as particle volume fraction on the hydrodynamic permeability and streamlines were discussed. The patterns of streamlines were also obtained.