Abstract
In this article, the method of volume averaging of flow in porous media and averaging theorem was employed to the Navier-Stokes equations. The total drag force per unit volume was considered as the bulk damping resistance due to the porous structure (i.e., the Darcy resistance) and the resistance due to the inertia force (i.e., the Forchheimer resistance), then the Brinkman-Forchheimer extended Darcy model was obtained from average momentum equation. The structural flow in a pipe containing porous medium saturated with power law fluid was applied in the present study. A new theoretical analysis of fully developed non-Darcy flow in a pipe containing a fibrous medium saturated with power law fluid was conducted. Using the integration method, the boundary layer solutions were obtained for flow core velocity and its radius. These theoretical solutions were used to analyze the effects of the Darcy number and inertia parameter on the axial velocity profile in the porous medium pipe.
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