Study of shear thinning fluid flow through highly permeable porous media

The Brinkman equation is used to model the flow of power-law fluids in a highly permeable porous medium. Isothermal flow of shear thinning fluids in a porous medium between two impermeable parallel walls at different Darcy parameters (Da) and power-law index is studied. Both finite element method and analytical solutions are applied to solve the Brinkman equation. The analytical solution is based on a trial and error procedure. This solution reveals a channelling in the flow regime within the thin near walls boundary layer. Finite element solution is, in general, unstable but can be stabilised for a limited rang of Darcy parameter and power-law index.