Starting Solutions for Motion of a Maxwell Fluid Over an Infinite Plate that Applies an Oscillating Shear to the Fluid

Abstract

Unsteady motion of a Maxwell fluid over an infinite plate that applies an oscillating shear to the fluid is studied by means of integral transforms. The obtained solutions satisfy all initial and boundary conditions. They are presented as a sum of steady-state and transient solutions and can easily be reduced to the similar solutions for Newtonian fluids. They describe the motion of the fluid some time after its initiation. After that time, when the transients disappear, the motion of the fluid is described by the steady-state solutions which are periodic in time and independent of the initial conditions. However, they satisfy the governing equations and boundary conditions. Finally, the required time to reach the steady-state, as well as a comparison between models, is determined by graphical illustrations.