A Study for Analyzing the Effect of Overlapping Stenosis and Dilatation on Non-Newtonian Blood Flow in an Inclined Artery

Abstract

The stenosis in the artery, which reduces the flow passage to blood, is a common cardiovascular disease that is responsible even for cardiac arrest sometimes. The hemodynaics reveals that the severe blockage in an artery due to stenosis generates pressure tangential stress that impacts adversely on the arterial wall downstream to stenosis and weakens the arterial wall. The site of weakened wall in the artery generates post stenotic dilatation. The objective of this paper is to study flow of blood, of non-Newtonian in nature described by Herschel-Bulkley model, in a diseased artery suffering with partly overlapped two stenoses and a dilatation distal to the stenoses. A mathematical model, describing the blood flow, has been derived using Navier-Stokes equations along with the prescribed geometry of the diseased artery. The expressions of velocity profile, resistive impedance to flow and wall shear stress (skin-friction) are derived. The effect of inclination of the vessel on the resistive impedance to flow is discussed along with the effect of rheological and geometrical parameters on the resistive impedance to flow and skin friction.