Effect of magnetic field on the viscous fluid flow in a channel filled with porous medium of variable permeability

The present work concerns the study of the fully developed flow in a channel of an incompressible, electrically conducting viscous fluid through a porous medium of variable permeability under the transverse applied uniform magnetic field. The variation of permeability is taken quadratic on the transverse direction and small. The Brinkman equation is used for flow through porous medium. Numerical expressions by applying Galerkin’s method for the velocity and volumetric flow rate for two cases, Poiseuille and Couette flow are obtained. The influence of the various parameters like Hartmann number, permeability variation, etc. on the velocity profile and flow rate is discussed.