Unsteady flow of Oldroyd-B fluids in an uniform rectilinear pipe using 1D models

Abstract

Using the one-dimensional approach based on the director theory which reduces the exact threedimensional equations to a system depending only on time and on a single spatial variable, we analyze the axisymmetric unsteady flow of an incompressible viscoelastic fluid of Oldroyd type in an uniform rectilinear pipe with circular cross-section. From this system we obtain the relationship between average pressure gradient and volume flow rate over a finite section of the pipe and the corresponding equation for the wall shear stress. Attention is focused on the steady flow case with rigid and impermeable walls.