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 β=1β=1. Moreover, in the absence of side walls, all solutions that have been obtained reduce to those corresponding to the motion over an infinite plate.