Unsteady flow of a generalized Oldroyd-B fluid using a director theory approach

Abstract

Using a 1D model based on the Cosserat theory which reduces the exact three-dimensional equations to a system of partial differential equations depending on time and on a single spatial variable, we analyze the axisymmetric unsteady flow of an incompressible viscoelastic generalized Oldroyd-B fluid with shear-dependent viscosity. In this study we consider an uniform rectilinear pipe with circular cross-section and give the relationship between average pressure gradient and volume flow rate over a finite section of the pipe and the corresponding equation of the wall shear stress. An application to blood flow is also given in the steady case.