Starting solutions for oscillating motions of an Oldroyd-B fluid over a plane wall

In this paper, we establish the starting solutions for oscillating motions of an Oldroyd-B fluid between two side walls perpendicular to a plane wall. The expressions for the velocity field and the associated tangential stress at the bottom wall are obtained, presented under integral and series form. These satisfy all imposed initial and boundary conditions. The obtained solutions are graphically analyzed for the variations of interesting flow parameters. In the absence of side walls, all solutions that have been obtained reduce to those corresponding to the motion over an infinite plate. Moreover, the obtained solutions can be specialized to give similar solutions for Maxwell, second grade and Newtonian fluids performing the same motions.