Some Couette flows of a Maxwell fluid with wall slip condition

Couette flows of a Maxwell fluid produced by the motion of a flat plate are analyzed under the slip condition at boundaries. The bottom plate is assumed to be translated in its plane with a given velocity. The flow of the fluid is studied in the assumption that the relative velocity between the fluid at the wall and the wall is proportional to the shear rate at the wall. Exact expressions for velocity and shear stress are determined by means of a Laplace transform. The velocity fields corresponding to both slip and non slip conditions for Maxwell and Newtonian fluids are obtained. Two particular cases, namely translation with constant velocity and sinusoidal oscillations of the bottom plate, are studied. Results for Maxwell fluids are compared with those of Newtonian fluids in both cases with slip and non slip conditions. Some properties of the flow are also presented.