Analytical Solution to Uniform Flow over a Porous Plane with Downward Suction

Abstract

Studies on open channel flows generally focus on the flow profiles in the longitudinal direction. When generating the analytical solutions, the simplified governing equations are usually employed by neglecting the vertical velocity component, which is much less in quantity than the horizontal one. However, the vertical velocity is actually not negligible, especially at the permeable bottom, as well as the horizontal velocity. In this study, the authors investigate a two-dimensional flow field composed of a fluid (upper) layer and a homogeneous porous medium (lower) layer with downward suction. In the upper layer, Navier-Stokes equations are employed to describe the flow, whereas the porous medium flow theory is addressed in the lower layer. Setting the stream function for the velocity components associated with corresponding boundary conditions, the authors successfully obtain the analytical solutions by the six-order power series method (PSM) and the differential transform method (DTM) respectively, and then acquire the velocity profiles in both layers. Comparing these solutions with previous research, the authors find that the present approach can simplify the algorithm process and the results are in very good agreement.