Correlations for friction factor of Carreau fluids in a laminar tube flow

This study presents an improved approach to correlating the Darcy friction factor for a fully developed laminar flow of Carreau fluids in circular pipes. The Carreau model stands as an essential representation of viscosity behavior and captures the complex rheological characteristics of polymeric fluids. By deriving a semi-analytical form of the Darcy friction factor, the study enables rapid and repeated evaluations across diverse flow conditions, facilitating the development of an explicit correlation. This improved correlation, built upon extensive data analysis, offers enhanced accuracy and broader applicability in predicting fluid behavior. The practical significance of this advancement is demonstrated through its successful application in calculating pressure drops for polymer melt and blood flows, highlighting its potential impact on industries ranging from materials processing to biomedical engineering. This work not only contributes to the theoretical understanding of non-Newtonian fluid dynamics but also provides a valuable tool for engineers dealing with complex fluid systems in circular pipes.