Friction factor of shear thinning fluids in non-circular ducts—a simplified approach for rapid engineering calculation

Abstract

This work reports on an investigation of the relationship between the Reynolds number and the friction factor of the fully developed laminar flow of power-law fluids through non-circular cross-sections (elliptical, concentric annuli, symmetrical L-shape, isosceles triangle, eccentric annuli, and square duct with a central cylindrical core), with the aim of providing a simple method for rapid and simplified engineering calculations. The friction factor—Reynolds number relation has been derived for non-circular ducts on the basis of the modified Reynolds number proposed by Metzner and Reed. It has been shown that the proposed correlation enables a prediction of the friction factor for the fully developed laminar flow of shear thinning fluids in non-circular cross-sections by using a calculation method similar to the method used for laminar flow of a Newtonian fluid. The correlation that is provided has been validated by analytical and numerical methods. It has been found that the proposed method can be used to determine the friction factor with high accuracy. This method yields a friction factor with a deviation of less than 5% in comparison with the conventional method.