Influence of slip velocity on the flow of viscous fluid through a porous medium in a permeable tube with a variable bulk flow rate

A mathematical model is presented for an axisymmetric flow of a Newtonian fluid through a permeable tube filled with porous medium and slip at the wall. The bulk flow rate is prescribed as a decreasing function of axial distance. The governing coupled partial differential equations are solved analytically using Adomian decomposition method and numerically using a second order finite difference scheme. Numerical method is validated by already published work and a good agreement is observed between the two solutions. Trusting this validity, effects of pertinent parameters on the flow variables such as velocity components, wall shear stress and pressure drop are discussed graphically. This study reveals that the slip parameter (phi), reabsorption parameter (alpha) and permeability parameter (k) have significant influences on flow variables involved in the problem. Creeping flow (Re = 0), flow without porous medium (k -> 8) and flow with no slip (phi = 0) at the wall are the limiting cases of this study.