Flow of a third grade fluid through a porous flat channel

The steady, laminar flow of a third grade fluid through a porous flat channel is considered, when the rate of injection of the fluid at one boundary is equal to the rate of suction at the other boundary. The flow is governed by a non-linear boundary value problem (BVP) in which the order of the differential equation is three, but only two boundary conditions are available. Two numerical schemes are developed to obtain the appropriate solution of the BVP. In the first scheme the dilemma is resolved by assuming that the solution is analytical in the neighborhood of K = 0, where K is the non-dimensional viscoelastic fluid parameter. This scheme is practical to use only up to certain values of T, the third grade fluid parameter. The second scheme allows arbitrary values of T, but,is restricted to small values of K and R, the cross-flow Reynolds number. A perturbation solution valid for small values of T is also derived. Finally two approximate solutions, based on Collatz' iterative scheme, but with different starting trial solutions are obtained. A comparison is made of the results computed by using various methods and appropriate conclusions are drawn. (C) 2003 Elsevier Science Ltd. All rights reserved.