Non-Darcy Couette Flow in a Porous Medium Filled With an Inelastic Non-Newtonian Fluid

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Abstract
Newtonian and non-Newtonian Couette flows through inelastic fluid saturated porous media due to a moving plate boundary have been investigated analytically. The momentum equation which includes both the viscous and inertia terms is solved to examine the effects of the pseudoplasticity, boundary friction, and porous inertia on the velocity profile and wall shear stress at the moving wall. Closed-form exact solutions are presented for three distinct cases of practical interest. A simple expression for the wall shear stress valid for all Newtonian and non-Newtonian cases of small Darcy number has been also derived through an integral treatment, and found to agree closely with the exact values obtained from direct numerical integrations of the momentum equation. The analytical results presented here can be used for possible applications to highly sensitive viscosity measuring devices.

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