External boundary effects on the velocity profile for generalized Newtonian fluid flow inside a homogeneous porous medium

Analytical expressions for the velocity profiles of different types of generalized Newtonian fluids are derived for fluids traversing a porous domain enclosed between two stationary parallel plates, as well as for free-flow over and flow through a porous domain. In the first scenario a Brinkman-like equation was solved where a no-slip boundary condition was enforced at the macroscopic external boundaries. In the composite domain, analytical expressions have been derived by matching Stokes flow to the solution of the Brinkman equation after assuming a continuity in the shear stress at the fluid-porous interface. For shear thinning and shear thickening fluids, in both scenarios, an inverse approach had to be considered to obtain the average velocity profile within the porous region. The permeability of a porous structure for a specific traversing fluid subjected to a specific pressure gradient is approximated by means of a representative unit cell that is applicable to an infinite porous region. The validity of this analytical modeling approach is established by comparing it to numerical results obtained from an in house developed numerical code.