Pulsatile flow of blood with shear-dependent viscosity through a flexible stenosed artery in the presence of body acceleration

Abstract

A mathematical model of physiological pulsatile flow of blood through a stenotic flexible artery in the presence of body acceleration is presented in this paper. Streaming blood is considered as a shear-thinning non-Newtonian fluid as proposed by Yeleswarapu (Evaluation of continuum models for characterizing the constitutive behaviour of blood, Ph.D. thesis, Dept. Mech. Eng., University of Pittsburgh, 1996), and a physiological pulsatile flow rate proposed by Pedrizzetti (J Fluid Mech 310:89–111, 1996) has been taken through the tube. Deformation of vessel wall is modelled as a function of flow rate. This computational study of an idealized model may bring some insights for realistic blood flow through a stenotic artery. The novelty of this work lies in the fact that realistic flow of blood through a stenosed artery has been studied as far as possible and a new idea has been provided to describe the arterial wall motion. Governing equations in cylindrical polar coordinates are solved using stream function–vorticity method. Behaviour of various flow quantities is investigated through a parametric study. It is noted that the degree of constriction and body acceleration have important impacts on the haemodynamic parameters such as wall shear stress, oscillatory shear index, and relative residence time. Increasing body acceleration enhances the peak value of wall shear stress, but reduces the oscillatory shear index and relative residence time. Almost 1/4th increase in length of flow separation is found when Froude number raises its value from 0.1 to 0.5, other parametric values remaining fixed. On the other hand, almost 50% increase in the magnitude of the peak value of wall pressure is found when the amplitude of body acceleration takes a value 0.4 (A = 0.4) compared to the without body acceleration case (A = 0). These results have a significant role.