Perturbation Solutions for Laminar Flow of a Carreau-Yasuda Fluid in Annular Pipes

Laminar flow of viscous non-Newtonian fluids in annular pipes is of considerable practical importance. The Carreau-Yasuda (C-Y) model provides unmatched flexibility to characterize the complex rheology of a broad class of non-Newtonian fluids used in the petroleum and chemical industries, including polymer solutions, drilling fluids, and foams. Despite its extensive applicability, the laminar flow characteristics of C-Y fluids in annular geometries have not been systematically investigated in the literature. We establish a comprehensive analytical-numerical framework for laminar C-Y flow in annuli. A generalized Reynolds number and friction factor correlation are derived via the Rabinowitsch-Mooney (R-M) method for annular C-Y flow, unifying pressure-drop flow-rate prediction. Asymptotic solutions for weak and strong shear-thinning conditions are derived via perturbation. Systematic comparisons with numerical simulations and R-M solutions delineate the valid parameter ranges of each method. Within these ranges, the solutions quantify the effects of key rheological and flow parameters on velocity profiles and flow rate, identifying dominant flow-governing parameters under varying conditions. This framework combines the simplicity of closed-form solutions with numerical accuracy, delivering practical value for hydraulic design and pressure-drop prediction in oil drilling and well-completion operations.