Transient rotational flow of an Oldroyd-B fluid over a disk

Abstract

The transient flow of an Oldroyd-B fluid over an infinite disk set in rotation impulsively is studied under the similarity assumption. The unsteady velocity and stress field is calculated exactly for short times by a power series expansion in time. The order of magnitude of the velocity and stress components is found to depend on the relative magnitude of the Deborah number (De) and the ratio of solvent to polymeric viscosities (μr). When either one becomes very small, a solution using singular perturbations and Laplace transforms is developed. It is found that the diffusive mechanism for momentum transfer, which exists for about μr≳0.1 (depending on De) dramatically changes and turns into a propagating wave for μr<0.1. Numerical calculations are used to determine the extent of validity of the present results.