Investigation of Inlet Boundary Conditions on Capillary Membrane with Porous Wall during Dead-End Backwash

under investigation. The early models to solve Navier-Stokes equation for a laminar flow in porous tube were proposed in Berman [1] and Yuan [2] and extended by Bernales [3]. Berman [1] presented a solution to the two-dimensional model in laminar flow in channels with uniform wall suction. This study was extended to cylindrical coordinates to investigate suction as well as injection in flow along a porous channel [2]. Also there is a description of the flow in the porous wall for a circular tube with uniform suction [4-6] and for different permeability [7]. Further investigation was performed for a tube with variable wall suction [8]. Karode [9] derived analytical solution for the pressure drop in a rectangular slit and cylindrical tube with porous walls for a constant permeability. This expression was in an agreement with the solution proposed by Berman [1]. Another expression for the pressure drop and velocity was derived by Kim [10]. It is obtained by applying the perturbation theory to a dead-end cylindrical porous tube. More recently [11], one dimensional model is introduced to determine the fluid in a porous channel with wall suction or injection based on the analytical solution proposed by Berman and Yuan [1, 2].