Unsteady Plane Couette Flow of an Incompressible Couple Stress Fluid with Slip Boundary Conditions

Abstract

In this work, the unsteady flow of an incompressible couple stress fluid between two parallel plates is studied. Slip boundary conditions are applied on the two plates and vanishing couple stress condition at the boundaries is assumed. The upper plate is suddenly moved with time dependent velocity while the other plate is fixed. The problem is solved analytically in the Laplace domain through the use of Laplace transform technique. The inverse transform of the fluid velocity is obtained numerically. The velocity profiles for different times and different physical parameters are plotted and the numerical results are discussed.