Axisymmetric Flow of a Generalized Newtonian Fluid in a Straight Pipe Using a Director Theory Approach

Abstract

The aim of this paper is to analyze the axisymmetric unsteady flow of an incompressible gen- eralized Newtonian °uid in a straight rigid and impermeable tube with circular cross-section of constant radius. To study this problem, we use an approach based on the Cosserat theory (also called director the- ory) related to °uid dynamics which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. From this system we obtain for a °ow without swirling motion the relationship between mean pressure gradient and volume °ow rate over a ¯nite section of the pipe for the speci¯c case of the power law viscosity function. Moreover, we compare the 3D exact solution for steady volume °ow rate with the corresponding solution obtained by the Cosserat theory using nine directors.