Semi-analytical solution for pressure-driven non-Newtonian flows in concentric annuli

Hemodynamics during cardiac catheterization can be modeled as non-Newtonian fluid flow within concentric annuli. Rapid and precise evaluation of flow rate variations is crucial for understanding the catheter's impact on local hemodynamics. We propose a general semi-analytical solution for flow rates in pressure-driven non-Newtonian flows within concentric annuli. This solution is suitable for commonly used non-Newtonian models. Validation using the Casson and Carreau–Yasuda models across various diameter ratios confirms the accuracy of the proposed solution, with a maximum relative error of 3.55%. It also reliably predicts time-averaged flow rates in pulsatile flows, with a maximum relative error of only 0.53%.