Background: A mathematical model of blood flow is a way to study the blood flow
behavior. In this research work, a mathematical model of non-Newtonian blood flow through
different stenosis, namely bell shape and cosine shape, is considered. The physiologically important
flow quantities of blood flow behavior to describe the blood flow phenomena are obtained such as
resistance to flow, skin friction and blood flow rate.
Methods: Mathematical methods are used to analyze a mathematical model of blood flow through
stenosed artery. The resistance to flow, skin friction and blood flow rate were obtained to describe
the blood flow in stenosis. The resistance to flow is a relation between pressure and blood flow rate
while the skin friction is the friction at the artery membrane.
Resutls: The blood flow in cosine geometry exhibits higher resistance to flow and flow rate than in
the bell geometry, while the blood flow in bell geometry gives a higher skin friction than in cosine
geometry. Not only the effect of stenotic geometry was studied but also the effect of stenosis depth
and stenosis height on the flow quantities Moreover, the power law index was adjusted to explore
the non-Newtonian behavior. When blood exhibits Newtonian behavior, the resistance to flow and
skin friction decrease but the blood flow rate increases.
Conclusion: The stenosed artery geometry, the stenosis length, stenosis depth and the power law
index (non-Newtonian behavior) are important factors affecting the blood flow through the stenosed
artery. This work provides some potential aspects to further study the causes and development of