Non-Newtonian rheology of blood in elliptical cross-section artery affected by several stenosis: Prandtl fluid model

A variety of circulatory disorders can be brought on by stenosis, which restricts a bodily passage artery or orifice. It may cause of brain disorders, heart diseases and legs disabilities. With the assistance of the Prandtl fluid model, the present investigation proposes an analytical strategy for monitoring blood flow through a stenosed artery. The artery is depicted as a tube with a cross-sectional view of an ellipse form. The flow-regulating equations are derived in the dimensionless form under the assumption of mild stenosis. The solution of mathematical equations is obtained by employing the perturbation technique via polynomial of degree four. It is analyzed graphically how flow-related parameters such as artery length L, stenosis height \(\delta _l\) ${\delta }_l$ , fluid parameters \(\alpha \) $\alpha$ , and K influence the velocity distribution, wall shear stress, and flow resistance. It is observed that the non-Newtonian effects dominate in the surrounding stenosed wall of the artery along the minor axis. The wall shear stress is found to attain its maximum value at the peak of stenosis. The height of stenosis considerably impacts the flow resistance, and as it increases, so does the opposition, which develops the disorder in the confined area. The streamlines are also plotted to analyze the flow behavior, and it is observed that the contours are produced in the constricted zone.