Non-Newtonian characteristics of blood flow in a multi-stenosed elliptical artery: A case of sensitivity analysis

The occurrence and growth of stenosis effectively interrupt the blood flow in the artery, which may result in vascular disease. It makes the study of blood flow in the artery narrowed with crucial stenosis. This work studies the non-Newtonian nature of blood flow in a diseased artery with an elliptic cross-section. The artery is harmed due to several stenosis, which diminishes its lumen. The Phan-Thein–Tanner fluid is considered to analyze the non-Newtonian characteristics of blood. The Phan-Thein–Tanner fluid model is much suitable for blood flow analysis because of its viscoelastic and shear thinning properties. The governing equations are processed to dimensionless form by employing dimensionless variables and assumptions for a mild stenosis case. The solutions of the nondimensional equations are acquired analytically. The visual examination of the exact solutions is discussed in detail. The fluid velocity is strongly affected by stenosis height, and a more significant disorder is generated in the constricted region with the growing size of stenosis. The flow velocity is found as a decreasing function of the Weissenberg number. The velocity profile is parabolic and axisymmetric as well. The most significant and least influential physical constraints are identified by completing the local sensitivity analysis.