Numerical simulation of generalized second-grade fluids using a 1D hierarchical model

Abstract

We consider the flow of a non-Newtonian incompressible second-grade fluid in an uniform rec- tilinear pipe and generalize it by introducing a shear-dependent viscosity function of power law type. The full 3D set of equations is reduced to a one-dimensional problem involving only time and one spatial variable. This is done using a director theory for fluid dynamics, also called Cosserat theory. An axisym- metric unsteady relationship between mean pressure gradient and volume flow rate over a finite section of the pipe and the corresponding equation to the wall shear stress are derived from this theory.