An Analytical Approach to Study the Blood Flow over a Nonlinear Tapering Stenosed Artery in Flow of Carreau Fluid Model

Abstract

The current study provides an analytical approach to analyze the blood flow through a stenosed artery by using the Carreau fluid model. The flow governing equations are derived under the consideration of mild stenosis. Mathematical analysis has been carried out by considering the blood as non-Newtonian nature. Then, the analytical solution has been investigated by using the regular perturbation technique. The solutions obtained by this perturbation are up to the second-order in dimensionless Weissenberg number $\left(\text{We}\right)$ . The performed computations of various parameter values such as velocity, wall shear stress, shear stress, and resistance impedance at the stenotic throat are discussed in detail for different values of Weissenberg number $\left(\text{We}\right)$ . The obtained results demonstrate that for shear-thinning fluid, the fluid velocity increases with the increasing parameter m while opposite behavior is observed with the increase in $\text{We}$ . Hence, the presented numerical analysis reveals many aspects of the flow by considering the blood as a non-Newtonian Carreau fluid model, and the presented model can be equally applicable to other bio-mathematical studies.