On Stokes' Second Problem for Burgers' Fluid over a Plane Wall

Abstract

The Stokes' second problem for a Burgers' fluid over a plane wall is considered in this paper. The motion of the fluid is induced by the oscillation of the plane wall between two side walls perpendicular to the plane wall. The exact analytical solutions for the velocity field and the adequate shear stress are established in simple forms by means of integral transforms. The solutions that have been obtained, presented as a sum of the steady and the transient solutions, satisfy all imposed initial and boundary conditions. In the absence of the side walls they reduce to the similar solutions over an infinite plate. Finally, the results for the velocity, as well as a comparison between models, are displayed graphically for pertinent parameters to show interesting aspects of the solutions. It is observed that the velocity and the boundary layer thickness were observed to be decreased in the presence of the side walls. Moreover, the Maxwell fluid was observed to be the speediest and the Newtonian was the slowest.

Keywords

• stokes' second problem
• burgers' fluid
• side walls
• exact solution‎