Unsteady Helical Flows of a Maxwell Fluid

where T is the stress tensor, p the hydrostatic pressure, S the extra-stress tensor, A the first RivlinEricksen tensor and μ the dynamic viscosity. Many common fluids show this “Newtonian” behavior and in fact the whole discipline of classical fluid mechanics is based upon this equation. However, the constitutive equation (1) does not show any of the normal stress effects or relaxation phenomena and for many fluids, like dilute polymeric fluids, it is for that reason not acceptable. In cases of time dependent flows, for instance due to abrupt changes in the flow geometry, or to time dependencie of boundary conditions, relaxation phenomena should be included. The simplest way to do this is to use an equation of Maxwell type [1]: