Secondary flows due to axial shearing of a third grade fluid between two eccentrically placed cylinders

In general, purely axial flows of non-Newtonian fluids are not possible in straight pipes of noncircular cross section. The secondary flow pattern for the flow of various non-Newtonian fluids in pipes of non-circular cross se ction has been studied by many authors. The method which is used is invaria bly a perturbation technique using either the driving force for the problem or one of the material constants as the parameter for the expansion. The f ormer implies that the solution is a perturbation of the state of rest, whi le the latter implies that the null solution corresponds to the Newtonian s olution. However, in many problems of practical relevance, flows of a parti cular non-Newtonian fluid, with specific values for the non-Newtonian param eters (not necessarily small), take place under a finite driving force, mak ing such approaches of dubious value. For instance, as a consequence of per turbing in the driving force, the secondary flows appear only at the fourth order. In this paper we use a perturbation technique in which the perturba tion parameter is a geometric measure of the departure from the geometry in which rectilinear flow is possible. Such an approach allows one to study p erturbation of flows which are not the null state, and this, in turn, leads to secondary flows at first order. (C) 1998 Elsevier Science Ltd. All righ ts reserved.