EXACT SOLUTIONS FOR THE FLOW OF A GENERALIZED OLDROYD-B FLUID INDUCED BY A SUDDENLY MOVED PLATE BETWEEN TWO SIDE WALLS PERPENDICULAR TO THE PLATE

The unsteady flow of an incompressible generalized Oldroyd-B fluid induced by a suddenly moved plate between two side walls perpendicular to the plate is studied by means of Fourier sine and Laplace transforms. The velocity field v(y,z,t), written in terms of the generalized G(a,b,c)(.,.) functions, is presented as a sum between the Newtonian solution and the corresponding non-Newtonian contribution. The solutions corresponding to the generalized Maxwell fluids, as well as the solutions for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, are obtained as limiting cases of the general solutions. In the absence of side walls, namely when the distance between walls tends to infinity, the solutions corresponding to the motion over an infinite suddenly moved plate are recovered. Finally, the effect of fractional parameters on the velocity field, as well as the influence of the side walls on the fluid motion, is spotlighted by graphical illustrations.