Investigation of Erying-Powell fluid flow in the elliptical multi-stenosed artery: Application of perturbation method via polynomial solutions

In the current work, we analyzed the non-Newtonian rheology of blood through a multi-stenosed artery with a cross-section of elliptical shape. The blood is regarded as Erying-Powell fluid, and flow is considered to have no slip at the stenotic wall. The mathematical model is processed to a non-dimensional form, and conditions of mild stenosis are utilized to decrease its nonlinearity. The resulting equations are solved by applying the perturbation technique by considering the fluid characteristic parameter K as the perturbation parameter. The solution is completed by using the polynomial of degree four. The solutions of mathematical equations are deeply examined by graphical analysis. The non-Newtonian impacts are predominant in the surrounding of the stenosed wall along the minor axis of the elliptical artery. The height of stenosis affects the pressure rise and flow resistance. The shear stress at the arterial wall is very high in the stenotic region and has more potent effects in the neighboring boundary point on the minor axis. Progressive stenosis causes a reduction in the blood flow velocity surrounding the arterial wall due to higher resistance to the flow. However, the velocity improves near the center line of the artery. Further, the fluid's velocity is very high in the constricted (stenotic zone) region.