A simplified couette flow solution of non‐newtonian power‐law fluids in eccentric annuli

Abstract

Flow of non‐Newtonian fluids in both the concentric and eccentric annuli is of great importance in extruders for molten plastics and wellbore fluid circulation for the removal of drilling cuttings. The steady laminar couette flow of non‐Newtonian power‐law fluids in eccentric annulus is employed in this study to analyze the problems of surge or swab pressures encountered when running or pulling tubular goods (pipes) in a liquid filled borehole. This is similar to the annular space created by two long co‐axial cylinders with the inner cylinder in motion at a steady velocity, and a stationary outer cylinder. The solutions of the equations of motion are presented in both dimensionless form and as a family of curves for different pipe/borehole eccentricity ratios and power‐law fluid index values for a more general application. The expected error in surge computation for concentric annulus as a result of eccentricity is evaluated.

Laminar, transitional and turbulent flow of Herschel–Bulkley fluids in concentric annulus

“…Analytical solutions for power-law and yield-pseudoplastic fluids, but not for Herschel-Bulkley fluids, in concentric annuli have been presented by Gucuyener and Mehmetoglu (1992), David and Filip (1995) and Filip and David (2003). Analytical and numerical codes covering laminar flow of non-Newtonian fluids in both concentric and eccentric annuli have been presented by Haciislamoglu and Langlinais (1990), Walton and Bittleston (1991), Szabo and Hassager (1992), Yang and Chukwu (1995), Hussain and Sharif (1997), Siginer and Bakhtiyarov (1998), Meuric et al (1998), Fang et al (1999 and Hussain and Sharif (2000), while Round and Yu (1993) have studied numerically laminar nonNewtonian flows in the entrance of a concentric annuli. Fordham et al (1991) provided an analysis leading to a numerical code for solving the annulus situation as well as the case of slot approximation for laminar flow, together with some experimental data.…”

Forced convection of non‐Newtonian fluids in porous concentric annuli

“…The natural convection in a porous layer saturated with a non-Newtonian fluid and heated from below was investigated by Rudraiah et al [13]. A simplified couette flow of a non-Newtonian fluid in eccentric annuli has been studied by Yang and Chukwu [14]. An excellent review was introduced by Shenoy [15] in which the reader can notice the different categories of flow and convection heat transfer models, and the achievements in each category.…”