Theoretical Study of Oldroyd-B Visco-Elastic Fluid Flow Through Curved Pipes with Slip Effects in Polymer Flow Processing

Abstract

The characteristics of the flow field of both viscous and viscoelastic fluids passing through a curved pipe with a Navier slip boundary condition have been investigated analytically in the present study. The Oldroyd-B constitutive equation is employed to simulate realistic transport of dilute polymeric solutions in curved channels. In order to linearize the momentum and constitutive equations, a perturbation method is used in which the ratio of radius of cross section to the radius of channel curvature is employed as the perturbation parameter. The intensity of secondary and main flows is mainly affected by the hoop stress and it is demonstrated in the present study that both the Weissenberg number (the ratio of elastic force to viscous force) and slip coefficient play major roles in determining the strengths of both flows. It is also shown that, as a result of an increment in slip coefficient, the position of maximum velocity markedly migrates away from the pipe center towards the outer side of curvature. Furthermore, results corresponding to Navier slip scenarios exhibit non-uniform distributions in both the main and lateral components of velocity near the wall which can notably vary from the inner side of curvature to the outer side. The present solution is also important in polymeric flow processing systems because of experimental evidence indicating that the no-slip condition can fail for these flows, which is of relevance to chemical engineers.