Comparative assessment of classical and fractional Casson models for hemodynamic flow in inclined vessels

Abstract

Mathematical modelling in hemodynamic applications is essential for rapidly developing hypotheses and predicting experimental results within vascular systems. For such models to be reliable, they must closely replicate real-world physiological conditions. This study aims to analytically compare classical and fractional Casson fluid models for blood flow in inclined cylinders, incorporating slip velocity effects, magnetohydrodynamics (MHD), and porous media. Recent studies suggest that fractional fluid models offer advantages by capturing memory effects and non-local behaviour in blood flow. The Caputo-Fabrizio fractional derivative is employed to resolve singularities inherent in classical approaches, facilitating improved modelling of viscoelastic blood behaviour under pulsatile conditions. Analytical solutions for both models are attained using Laplace and finite Hankel transforms. Graphical results illustrate velocity and temperature profiles, highlighting key parameters such as magnetic influence, Casson fluid properties, Darcy's law, fractional derivatives, slip velocity, Grashof number, and inclination angle. Findings show that increased slip velocity augments fluid flow near the cylinder wall, with greater blood flow observed when the artery is oriented vertically upward. Results reveal that the fractional model can mitigate unphysical velocity spikes (common in classical models). The analytical results provide a benchmark for validating numerical models and demonstrate the fractional model's ability to address mathematical limitations of classical approaches. Although the study is theoretical, it provides a foundation for future mapping of physiological parameters and experimental validation.