Unsteady flow of a second grade fluid between two side walls perpendicular to a plate

Exact solutions for the unsteady flow of a second grade fluid induced by the time-dependent motion of a plane wall between two side walls perpendicular to the plane are established by means of the Fourier sine transforms. The similar solutions for Newtonian fluids, performing the same motions, are obtained as limiting cases for α1→0α1→0. The steady solutions, the same for Newtonian and non-Newtonian fluids, are also obtained as limiting cases for t→∞t→∞. In the absence of the side walls, all solutions that have been obtained reduce to those corresponding to the motion over an infinite plate. Graphical illustrations show that the diagrams corresponding to the velocity field in the middle of channel and the shear stress at the bottom wall for a second grade fluid are going to be those for a Newtonian fluid if the normal stress module α1→0α1→0.