Unsteady flow of an Oldroyd-B fluid induced by the impulsive motion of a plate between two side walls perpendicular to the plate

Exact solutions for the unsteady flow of an Oldroyd-B fluid produced by a suddenly moved plane wall between two side walls perpendicular to the plane are established by means of the Fourier sine transforms. The similar solutions for Maxwell, Newtonian and second grade fluids, performing the same motion, appear as limiting cases of the solutions obtained here. In the absence of the side walls, the solutions corresponding to the motion over an infinite suddenly moved plate are also obtained as the limiting cases. Finally, for comparison, the velocity field in the middle of the channel and the shear stress at the bottom wall are plotted for different values of the material constants.