On unsteady non-newtonian flows in a rotating system-I

Abstract

An incompressible isotropic visco-elastic liquid is bounded by an infinite rigid horizontal disk atz=0. Both the fluid and the disk are in a state of solid body rotation with a uniform angular velocity Ω about thez-axis. At timet=0+, small amplitude non-torsional oscillations are superimposed on the disk, or the disk is impulsively moved with a constant acceleration so that an unsteady motion is set up in the liquid. An analysis is made of the unsteady flow generated in the visco-elastic liquid. The velocity field is calculated by using the Laplace transform treatment and the structure of the associated boundary layers is determined. This analysis provides the existence of Stokes-Ekman-Elastic boundary layers of thicknesses of the order$\left( {\frac{v}{\Omega }} \right)^{\tfrac{1}{2}} \frac{1}{{\alpha _r }}, r = 1,2$. Special emphasis is given to the limiting behaviour of the solution ast→∞, and the significant interaction of the elastic parameter and rotation is examined. The surface traction at the disk is found and the effects of elasticity on this quantity are discussed. It is shown that in the absence of the elasticity, the results of this paper reduce to the corresponding results of the Newtonian rotating fluid.