Carreau fluid model for blood flow through a tapered artery with a stenosis

Abstract

In present article, we have studied the blood flow through tapered artery with stenosis. The non-Newtonian nature of blood in small arteries is analyzed mathematically by considering the blood as Carreau fluid. Carreau fluid is a type of generalized Newtonian fluid. At low shear rate Carreau fluids behaves as a Newtonian fluid n=1 and at high shear rate as power law fluid. For n<1 Carreau fluid gives pseudoplastic(non-Newtonian), or shear-thinning fluids have a lower apparent viscosity at higher shear rates and for n>1 Carreau fluid behaves as Dilatant(non-Newtonian), or shear-thickening fluids increase in apparent viscosity at higher shear rates. All three cases are appropriate for blood flow in arteries because the assumption of Newtonian behavior of blood is acceptable for high shear rate flow, i.e. the case of flow through larger arteries. It is not, however, valid when the shear rate is low as is the flow in smaller arteries and in the downstream of the stenosis. It has been pointed out that in some diseased conditions, blood exhibits remarkable non-Newtonian properties. The representation for the blood flow is through an axially non-symmetrical but radially symmetric stenosis. Symmetry of the distribution of the wall shear stress and resistive impedance and their growth with the developing stenosis is another important feature of our analysis. Analytical solutions has been evaluated for velocity, resistance impedance, wall shear stress and shear stress at the stenosis throat. The graphical results of different types of tapered arteries (i.e converging tapering, diverging tapering, non-tapered artery) have been examined for different parameters of interest.