Viscoelastic inertial flow driven by an axisymmetric accelerated surface.

A similarity transform is used to analyze the flow of an upper- convected Maxwell fluid in an infinitely-long cylinder whose surface has a velocity that increases in magnitude linearly with axial coordinate. Two types of problem are considered, the accelerated surface flow -when the surface velocity is outward towards the tube ends, and the decelerated surface flow - when it is inward. For the accelerated surface flow, the introduction of elasticity prevents the loss of similarity solution that occurs without elasticity at a Reynolds number (Re) of 10.25; with elasticity, solutions up to a Reynolds number of 95 were computed. A turning point in the nonelastic solution family at Re = 10.25 disappears as elasticity is introduced. For the decelerated surface flow, solutions could not be computed beyond a critical Re that depends on the level of elasticity considered, because at this critical Re, the axial velocity profile at the centerline becomes infinitely blunt.