On the unsteady non-Newtonian rotating flow induced by torsional oscillations of a disk

The unsteady boundary-layer flow generated in an incompressible homogeneous elastico-viscous fluid bounded by an infinite rigid disk is investigated when the whole system is in a state of solid-body rotation with uniform angular velocity and, at some instant of time, the disk executes small-amplitude torsional oscillations with a given frequency. The analysis is carried out to determine various qualitative and quantitative information about the unsteady and steady velocity distributions, the structure of the associated multiple boundary layers, the effects of the elastic parameter and rotation on the flow, and the Ekman suction velocity with its physical significance. It has been shown that the steady-state flow field consists of the two distinct boundary layers which are modified by the angular velocity of rotation, the elastic parameter, and the frequency of the imposed oscillations. Several known results of physical interest are recovered as special cases.