A Mixture theory approach for a power-law fluid flow through a porous channel

Abstract

The steady-state saturated flow of an incompressible power-law  fluid  through  a porous channel limited by two impermeable flat plates is modeled using a mixture theory, which considers fluid and porous matrix as superimposed continuous constituents of a binary mixture. After some simplifying assumptions, the mechanical model gives rise to a coupled system of ordinary differential equations that is simulated by employing a Runge-Kutta method coupled with a shooting strategy. Despite the strong  nonlinearity  of  the  problem,  this  simple methodology provides stable and accurate results, for both shear-thinning and shear-thickening behaviors.