Flow of a generalized second-grade fluid between two side walls perpendicular to a plate with a fractional derivative model

In this paper, the exact analytic Solutions are obtained for flow of a generalized second-grade fluid between two side walls perpendicular to a plate. The fractional calculus approach in the constitutive relationship model of a non-Newtonian fluid is used. The exact analytic solutions are constructed by using Fourier sine transforms and the discrete Laplace transform of the sequential fractional derivatives. The Solutions for a second-grade fluid appear as the limiting cases of the presented Solutions on taking beta = 1. Moreover, in the absence of side walls, all solutions that have been obtained reduce to those corresponding to the motion over all infinite plate. (c) 2007 Elsevier Ltd. All rights reserved.