Abstract
The equations of motion modeling the flow of an incompressible homogeneous Rivlin-Ericksen fluid of grade 2 between eccentric rotating cylinders are studied by means of a power series expansion in η = Re Γ , where Re is the flow Reynolds number and Γ is a non-dimensional parameter which reflects the non-Newtonian character of the fluid. The zero order perturbation represents the flow of a Newtonian fluid; this flow has been already discussed by San Andres and Szeri ( J. Appl. Mech. 51, 869–878). The present paper examines the equations of the first order perturbation. The flow domain in this paper is not restricted to narrow gaps, inertial effects are not ignored and the eccentricity ratio is arbitrary. The fluid model, however, represents only slight departure from Newtonian behavior. Even so, we find that the non-Newtonian behavior plays a significant role in determining the streamline pattern and in the positioning of separation and reattachment points. The numerical methods employed in this study include Galerkin's method with B-spline test functions.
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