Mathematical analysis of Carreau fluid flow and heat transfer within an eccentric catheterized artery

The effect of a catheter on blood flow and heat transfer characteristics of a Carreau fluid model is investigated mathematically using the perturbation method involving appropriate small parameters. Physically, this study relates to the surgical technique when a catheter is injected eccentrically into an artery. The model describes fluid flowing in the gap between eccentric tubes where the inner tube is uniform and rigid representing the moving catheter while the other tube represents an artery with overlapping stenosis. A complete perturbation solution up to the first order is presented whereby a validation exercise carried out shows that previously published solutions involving Newtonian fluids may have some typographical errors. The present results obtained show that the axial velocity, wall shear stress, and temperature in the case of the eccentric catheter are higher than that of the concentric catheter. The average Nusselt number is enhanced with increasing catheter radius and the velocity of the catheter while it decreases with increased Weissenberg number, Prandtl number, and Eckert number. These results agree with physiological observations that the risks and complications associated with catheterization are alleviated when the eccentric position of the catheter is considered. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.