On exact solutions of flow problems of a second grade fluid through two parallel porous walls

Exact analytical solutions of two problems of laminar flow of a second grade fluid through two parallel porous walls are obtained. For each problem the rate of injection at one wall is assumed equal to the rate of suction at the other wall. Two geometries are considered: rectangular - when the flow takes place between two parallel flat walls, and cylindrical - when the flow takes place through an annulus. For the exact solution no assumption is made on the size of K, the viscoelastic fluid parameter, or the cross-flow Reynolds number. However, it is assumed that a Taylor series expansion of the solution exists near K = 0. Also assuming K small, perturbation solutions are developed for both the geometries. The exact solutions reveal that the viscoelasticity of the fluid tends to destroy the formation of the boundary layer at the wall where the suction takes place for large values of the cross-flow Reynolds number. It is further shown that the commonly used perturbation technique does not give satisfactory results even for moderate values of the cross-flow Reynolds number. (C) 2002 Elsevier Science Ltd. All rights reserved.