Torsional oscillations of an infinite plate in an elastico-viscous fluid

Summary

The equations of motion of an infinite plate performing torsional oscillations in Walters elastico-viscous liquid B″ have been solved by expanding the velocity profile in powers of the amplitude of oscillation of the plate. The first order solution consists of a transverse velocity and the second-order solution gives a radial-axial flow composed of a steady part and a fluctuating part. The steady part of the radial flow does not vanish outside the boundary layer and hence the equations are solved by another approximate method for the steady part of the flow. The effects of the non-Newtonian term is to increase the non-dimensional boundary layer to start with and subsequently to decrease it and to increase the shearing stress at the plate. The steady radial and the steady axial velocities fall short of the inelastic flow in the beginning but later on their values lie above.