Laminar Flow in a Uniformly Porous Channel

Abstract

Abstract The problem of laminar channel flow has been investigated for the case of uniform fluid suction or injection through the channel walls. The solution can be divided into three steps: (a) A judicious choice of stream function reduces the Navier-Stokes equations to an ordinary, fourth-order, nonlinear differential equation, which contains a free parameter R, the Reynolds number based upon fluid velocity through the wall. (b) Since general analysis of this equation is intractable, the parameter R is eliminated by a suitable transformation. (c) The transformed, nonparametric equation yields to a series solution, valid and absolutely convergent for all R. From this general solution, expressions are developed for velocity components, pressure distribution, and wall-friction coefficient.