Flow of A Non-Newtonian Liquid through Two Coaxial Curved Pipes

Abstract

The steady motion of a non-Newtonian liquid through two coaxial curved pipes is discussed on assumptions and approximations similar to those taken by Jones for the case of a single curved pipe. Many theoretical results are supported by numerical calculations.
Discussions are made amongst others about (i) the relation between the pressure gradient and the rate of outflow (to the first order of approximation in the curvature), (ii) the secondary flow produced by the curvature of the pipes, and (iii) the effect of the curvature and the cross-viscosity parameter S on the stress components on the boundaries. The streamlines in a normal section are plotted for some different values of S. The corresponding results for the Newtonian liquids follow when S=0.