Laminar flow of a viscous incompressible fluid in a long porous wavy channel

The linearization technique is used to study viscous incompressible fluid laminar flows in a long, porous, wavy channel, through the simplification and solution of the governing equations of motion under the assumption that the fluid velocity consists of a primary mean flow, perturbed flows, and a secondary mean flow. Long wave approximations are used in obtaining the solution for the perturbed flow velocity and secondary mean flow, and numerical results reveal such qualitatively interesting flow characteristics as the significant contribution to fluid velocity from the waviness of the walls, the strong influence of the suction parameter and Reynolds number, and the tendency of the fluid near the wavy wall to move upstream before proceeding on its downstream course, as a consequence of the fluid suction through the wavy wall in a direction normal to it.