Mathematical Analysis of Carreau Fluid model for Blood Flow in Tapered Constricted Arteries

The pulsatile flow of blood through a tapered constricted narrow artery is investigated in this study, treating the blood as Carreau fluid model. The constriction in the artery is due to the formation of asymmetric stenosis in the lumen of the artery. The expressions obtained by Sankar (2016) for the various flow quantities are used to analyze the flow with different arterial geometry. The influence of various flow parameters on the velocity distribution, wall shear stress and longitudinal impedance to flow is discussed. The velocity of blood increases with the increase of the power law index and stenosis shape parameter and it decreases considerably with the increase of the maximum depth of the stenosis. The wall shear stress and longitudinal impedance to flow decrease with the increase stenosis shape parameter, amplitude of the pulsatile pressure gradient, flow rate, power law index and Weissenberg number. The estimates of the percentage of increase in the wall shear stress and longitudinal impedance to flow increase with the increase of the angle tapering and these increase significantly with the increase of the maximum depth of the stenosis. The mean velocity of blood decreases considerably with the increase of the artery radius (except in arteriole), maximum depth of the stenosis and angle of tapering and it is considerably higher in pulsatile flow of blood than in the steady flow of blood