Laminar flow of power law fluids in concentric annuli

Abstract

Ranger (1994) demonstrated recently that it is possible to achieve higher volumetric flow rate for the laminar flow of incompressible Newtonian fluids in a hollow annular pipe than that in an annulus with the solid core for equal flow areas and pressure gradients. His calculations reveal enhancements of up to 250% in flow rate for certain combinations of the sizes of pipe involved in it. Aside from the theoretical interest in this problem (e.g. Shivakumar and Ji, 1993), this result is of considerable pragmatic importance when different fluids need to be transported between the same points. However, no physical explanation was presented to explain this phenomenon. This note demonstrates that greater enhancements in flow rate are possible for the laminar flow of incompressible power law fluids under the same circumstances. Representative numerical results are presented for a range of combinations of the flow behavior index and geometric parameters to elucidate the interplay between the nonlinear fluid characteristics and the geometrical parameters. The observed trends are qualitatively explained by considering limiting cases and in terms of the results for known geometries