Flow of a non-newtonian fluid through axisymmetric pipes of varying cross-sections

Abstract

We study the flow of a non-Newtonian fluid through an axisymmetric pipe of slowly varying cross-section by means of a perturbation. The results pertinent to the classical linearly viscous fluid are recovered when the non-Newtonian material parameters are set equal to zero. It is found that the elasticity of the fluid leads to flow separation at nearly half the value of the Reynolds number for the linearly viscous case. It is also found that the absolute value of the shear stress at the wall increases with the retardation parameter, while it decreases with a, another non-Newtonian parameter. Also, in marked contrast with the linearly viscous case closed vorticity lines are possible for the flow under consideration at much lower Reynolds numbers than that for the linearly viscous