An Analytical Study of Fluid Flow Through a Porous Filled Channel with Permeable Wall: Suction/Injection Wall Conditions

Abstract

To depict fluid movement in a channel with a rectangle-shaped cross-section and porous walls, the twodimensional Darcy Brinkman equation of motion with uniform suction and injection is analytically solved using the perturbation method. The analytical expressions for non-dimensional axial velocity, normal velocity, skin friction coefficient and pressure drop are obtained using the perturbation method at a low Reynolds number. Graphical analysis has been done for the derived quantities for different Darcy and Reynolds numbers. At higher Reynolds numbers, the emergence of the velocity overshoots and the presence of an unfavourable pressure gradient zone are significantly less noticeable. The streamlines follow the same pattern since the flow is steady. When the Darcy number is large, the non-dimensional stream function expression reduces to the stream function expression available in the literature. Non-dimensional pressure drop increases up to a specific entry length. The skin friction coefficient decreases as the Reynolds number increases. Acceleration of the fluid in the porous region leads to lesser skin friction; hence, pressure drop rises.