Perturbation method for laminar flow of viscous incompressible fluid between two porous boundary walls

The present study focuses on the investigation of the velocity profile of viscous fluid between two parallel porous walls while fluid is being ejected from both channel walls at the same rate. The distributions of velocity, pressure and shear stress were determined theoretically for incompressible, steady, fully developed laminar flow past a porous boundary wall. Due to the pressure difference across the porous wall, there is ejection or injection into the wall. The velocity specified as the boundary condition at the wall has been used to explore fluid flow phenomena in porous tubes and ducts. The variable wall velocity is based on the pressure differential across the wall, the fluid characteristics, the thickness of the wall, and the permeability of the structure. An appropriate wall condition must take these factors into account. This paper discusses a Reynolds number solution. We seek formulas for the velocity component. The perturbation approach is used to solve the governing differential equation and the general solution of the velocity is obtained for higher terms of Re. Fifth term of perturbation is used in the perturbation method. The velocity of the fluid is analyzed for different values of Re for a boundary condition. Finally, the result is analysis graphically for the range of Re from .1 to 50. In addition, another strategy is used to keep the Reynolds number constant when the diameter of the hole in the porous wall changes, i.e., changing the value of λ.