A volume averaging approach is used to estimate the porous media permeability. Contrary to traditional methods that rely on solving the Navier–Stokes equations for laminar flow, this approach has the advantage that it does not require the specification of some physical conditions and...

By using spatial averaging methods, in this work we derive a Darcy's-type law from a fractional Newton's law of viscosity, which is intended to describe shear stress phenomena in non-homogeneous porous media. As a prerequisite towards this end, we derive an extension of the spatial averaging...

Up-scaling of the Stokes equations with non-slip boundary condition describing the flow in a porous medium, leads to the Darcy–Brinkman equationɛβμβvD,β=-Kβ·(∇Pm,β-ρβg)+Kβ·μβ∇2vD,β.The second-order term -μβ∇2vD,β recovers the viscous drag effects and uses the fluid...