Asian Journal of Mathematics and Computer Research

An investigation of viscous incompressible fluid flow in a non-uniform rigid channel with permeable walls and slowly varying cross-section is presented. It is assumed that the exchange of fluid across the wall obeys Starling's hypothesis. That is, the rate of flow per unit length of the wall is proportional to the difference between the pressure of the fluid within and outside the wall. The nonlinear equations of motion are linearized by perturbation method by assuming δ as a small parameter and the resulting equations are solved numerically by employing finite difference scheme. The effects of permeability parameter (α), slope parameter (κ) and Reynolds number R_e on the velocity profiles, pressure and flow rate are presented graphically. The flux at the boundary is calculated and a comparison is made between two hypotheses, one that prescribes flux as a decreasing function of axial length and the Starling hypothesis. Results show that the flux at the boundary is similar in trend for both cases.