A quasi-analytical solution for Carreau–Yasuda-type shear-thinning flows in slightly tapered pipes using a truncated power-law model

This paper presents a quasi-analytical framework for shear-thinning generalized Newtonian fluids flowing in slightly tapered conical pipes. The nonlinear rheology is approximated through a Truncated Power-Law (TPL) formulation, characterized by Newtonian plateaus at low and high shear rates connected by a finite power-law region. Relying on lubrication theory and the slender approximation, a quasi-analytical solution is derived for velocity, pressure gradient, and shear stress distributions. The solution strategy is validated against dedicated numerical simulations, showing excellent agreement and confirming both consistency and predictive accuracy. An application to extrusion-based bioprinting illustrates how the framework can be employed to evaluate shear stresses in conical nozzles, identify critical operating conditions, and support process optimization, thus reducing reliance on costly simulations and trial-and-error experiments. The MATLAB scripts used for the flow solutions have been made available for the community use.