Unsteady rotational flows of an Oldroyd-B fluid due to tension on the boundary

Abstract

Unsteady Taylor–Couette flows of an Oldroyd-B fluid, which fills a straight circular cylinder of radius R, are studied. Flows are generated by the oscillating azimuthal tension which is given on the cylinder surface. As a novelty, authors used in this paper the governing equation related to the tension field. The closed forms of the shear stress and velocity fields corresponding to the flow problems are obtained by means of the integral transforms method. Expressions for the azimuthal tension and fluid velocity were written as sums between the “permanent component” (the steady-state component) and the transient component. By customizing values of parameters from the mathematical model were obtained the corresponding solutions of other types of fluids, namely, Maxwell fluids. By using numerical simulations and diagrams of the azimuthal stress, the fluid behavior has been analyzed. The necessary time to achieve the “steady-state” was, also, determined.

Keywords

• Oldroyd-B fluid
• Exact solutions
• Integral transform
• Velocity field
• Shear stress