Effects of porous-wall acceleration on laminar flows in semi-porous channels with a rectangular cross section

Abstract

This paper aims to examine the effects of wall acceleration on the steady laminar flow of an incompressible Newtonian fluid along a semi-porous channel with a rectangular cross section. The lower wall of the channel is impermeable and at rest, while the upper wall is porous, and experiences longitudinal acceleration so that the flow is steady despite the accelerated movement of the wall. The fluid is injected or suctioned through the porous wall at uniform and constant velocity, orthogonally to the wall. The positive acceleration ratio defined as the ratio of longitudinal and transverse velocities, and the Reynolds number constructed by adding these velocities are the governing parameters. The similarity-solutions method, which is applied for the vorticity stream-function equation, gives numerical solutions using the shooting technique. Results indicate that the flow under study exists in the case of injection if the acceleration ratio does not exceed the value of 1, but in the case of suction, the flow remains unchanged if the acceleration ratio varies above the value of 9.5. For increasing acceleration ratios, the absolute value of transverse velocity decreases, the transverse pressure gradient remains unchanged at a specific fluid layer, the absolute value of longitudinal velocity increases near the porous wall and decreases near the impermeable wall, and in the case of injection, the algebraic wall shear stress decreases for the impermeable wall and increases for the porous wall. In the case of suction, there is a specific fluid layer at which the longitudinal velocity cancels by changing sign.