on the analysis of laminar flow of viscous fluid through a porous channel with suction/injection at slowly expanding or contracting walls

The vast biological and industrial applications of laminar flow of viscous fluid through a porous channel with contracting or expanding permeable wall have attest to the importance of studying the flow process. in this paper, two-dimensional flow of viscous fluid in a porous channel through slowly expanding or contracting walls with injection or suction is analyzed using variation parameter method. from the parametric studies using the developed approximate analytical solutions, it is shown that increase in the reynolds number of the flow process leads to decrease in the axial velocity at the center of the channel during the expansion. the axial velocity increases slightly near the surface of the channel when the wall contracts at the same rate. also, as the wall expansion ratio increases, the velocity at the center decreases but it increases near the wall. the results of the approximate analytical solution are verified by numerical solution using shooting method coupled with runge-kutta method. the results of the variation parameter method are in excellent agreement with the results obtained using numerical method.