Casson fluid flow in a pipe filled with a homogeneous porous medium

The Bow characteristics of a Casson fluid in a tube filled with a homogeneous porous medium is investigated by employing the Brinkman model to account for the Darcy resistance offered by the porous medium. This analysis can model the pathological situation of blood flow when fatty plaques of cholesterol and artery-clogging blood clots are formed in the lumen of the coronary artery. Two cases of permeability of the porous medium are considered, namely (i) permeability has a constant value K-0, and (ii) permeability varies in radial direction according to K(r) = K-0(1 - r)/r. The generalized equation of motion, which is an integral equation for shear stress, is solved iteratively and is coupled with the Casson constitutive equation to find the velocity distribution. For the case of constant permeability, the analytical solution is found for the shear stress distribution in terms of modified Bessel functions of order 0 and 1. Finally, the effect of permeability factor K-0 and yield stress a of the fluid on shear stress distribution, wall shear stress, plug flow radius, Bow rates and frictional resistance are examined. Copyright (C) 1996 Elsevier Science Ltd