Quasi‐Newtonian Approach determination of velocity profile for the fully developed axial power law fluid flow in concentric annuli

Abstract

The Quasi-Newtonian Approach has been developed for the closed-form analytical solution of isothermic, inelastic, and steady-state fully developed axial power law fluid flow in a concentric annuli. This approach is developed to eliminate the need to solve the two flow regions separately in the rheological flow problems. Using the approximate definition shear deformation distribution of power law rheological model, an analytical expression, which permits direct evaluation of the velocity distribution profiles, volumetric flow rate, and pressure drop in concentric annuli is derived. It is shown that all developed equations are applicable for both Newtonian and non-Newtonian flows in concentric annuli, and these can be applied for a wider range of rheological parameters of the power law rheological model. Final analytical equations can easily be used in all theoretical and practical applications of the power law flow problems in annuli that are encountered in several interdisciplinary fields without using tables, graphs, and tedious numerical calculations. Theoretically obtained, fully developed velocity profiles are compared with the experimental results taken from the relevant literature.