On the Flow of a Visco-Elastic Fluid between Two Rotating Non-Concentric Cylinders for Small Eccentricity

Abstract

The motion of a visco elastic fluid contained between two rotating circular cylinders whose axes are set slightly apart is considered. An approximate solution of the Navier Stokes equations is obtained by a perturbation method for the case of small eccentricity. The expansions contain a perturbation parameter Epsional related to the eccentricity e which is assumed to be small. The method entails the employment of asymptotic expansions of Bessel functions and the results thus obtained are valid for finite gap between the two cylinders. The leading terms of the expansions are the exact solution to the Couette flow of Newtonian Fluid between concentric rotating cylinders. The Transverse velocity profiles are presented for small eccentricity and gap, when both the cylinders are rotating with the same angular velocities in the same direction and compared with the corresponding transverse velocity profile in Newtonian flow.