Analysis of perturbed flows of a second-order fluid using a 1D hierarchical model

Abstract

The aim of this paper is to analyze the unsteady flow of a non-Newtonian incompressible second-order fluid in a straight rigid axisymmetric tube with circular crosssection of constant radius. To study this problem, we use the 1D nine-director Cosserat theory approach which reduces the exact three-dimensional equations to a system depending only on time and on a single spatial variable. From this onedimensional system we obtain the relationship between mean pressure gradient and volume flow rate over a finite section of the tube. Attention is focused on some numerical simulation of steady/unsteady flows for specific mean pressure gradient and on the analysis of perturbed flows.