Oscillatory viscoelastic flow in rectangular tubes

The longitudinal flow of a Green-Rivlin fluid in rectangular ducts subject to a small pressure gradient is investigated. An exact solution of the momentum equation is developed. The velocity field is computed for several aspect ratios and for several values of the fluid parameters. The elasticity of the fluid is shown to create complex patterns of flow, as depicted by the instantaneous isovels of the flow. The flow patterns depend mainly on the viscosity index of the fluid, the aspect ratio of the tube and of the selected iinstant of time. These results are useful for understanding both the intrinsic axial flow behavior, and related phenomena such as mass and heat transfer, and secondary flows in the case of fluids best described by constitutive models of the multiple-integral type.