Rheological properties of Carreau liquid model for blood flow through an elliptical heated multi-stenosed artery

The study of blood flow through stenotic arteries is crucial, as the presence and progression of stenosis can lead to severe cardiovascular complications. This work investigates the non-Newtonian characteristics of blood flow through a multi-stenosed artery with an elliptical cross-section, modeled using the Carreau fluid model. The effects of heat transfer, incorporating viscous dissipation, are also examined. The governing equations are non-dimensionalized, and the assumption of mild stenosis is applied to simplify the model. A perturbation technique based on a polynomial approach is employed, using the square of the Weissenberg number ${\left(W_2\right)}^2$ as the perturbation parameter. The impact of key parameters on velocity, temperature, pressure gradient, and wall shear stress (WSS) is illustrated graphically. Additionally, Nusselt number analysis provides insights into the thermal behavior in the stenotic segments. Results reveal that increased stenosis severity notably reduces flow velocity and elevates WSS in narrowed regions. Internal heat generation and the Brinkman number significantly influence the temperature distribution, particularly along the artery's minor axis, where thermal sensitivity and dissipative effects are more pronounced. Non-Newtonian effects are dominant along the minor axis, highlighting the role of geometric confinement in enhancing shear-thinning behavior. Compared to Newtonian fluids, the Carreau model predicts lower velocities and anisotropic flow characteristics along the elliptical axes. These findings offer valuable insights into hemodynamic behavior in stenotic arteries and may aid in improving diagnostic and therapeutic strategies for vascular diseases.