Biorheological Model on Pulsatile Flow of Blood (K–L Fluid) Through Flexible Stenotic Tapered Blood Vessels

In the present article, we investigate the pulsatile flow of blood through a tapered constricted blood vessel with a flexible nature of the wall and no-slip condition on the wall in view of analyzing the role of rheological behavior of blood, flow amplitude, the flexibility of wall, tapering, stenotic shape, and height in the origination and proliferation of cardiovascular disorders. The rheology of blood is treated as viscous incompressible non-Newtonian Luo and Kuang (K–L) model fluid by taking into account that the influence of non-Newtonian nature of blood with a finite yield stress and shear thinning character when it flows in small-diameter blood vessels. The pressure gradient has been taken as a periodic function of time, which accounts for the effects of systole and diastole of the heart. The equations governing the flow of K–L fluid when the stenotic vessel is slightly tapered are coupled and highly non-linear. A standard perturbation technique is adopted to solve the equations subject to the suitable boundary conditions assuming that the pulsatile Reynolds number is small, which is valid for physiological conditions in small blood vessels. The analytical expressions for flow characteristics, namely, the blood velocity distribution, the plug-core radius, the volumetric flow flux, the wall shear stress, and the impedance have been obtained by considering three terms (the coefficients of $$\alpha ^0, \alpha ^2,$$ and $$\alpha ^4$$ ) in the flow characteristics for the first time. The influence of physiologically vital parameters such as pulsatile Reynolds number, the amplitude of the flow, yield stress, K–L fluid parameters, time, amplitude constant, shape parameter of the constriction, maximum height of the constriction, and the tapering parameter on the flow variables are investigated, and the results are depicted graphically using MATLAB software. From the analysis, it is noticed that the yield stress, K–L fluid parameters, tapering angle, and the flexibility of the vessel wall have a substantial impact on examining the blood flow through tapered blood vessels with time-dependent constriction. The wall shear stress and resistive impedance increase as the K–L fluid parameters, yield stress, stenotic height increase, and decrease with the increase in Womersley frequency parameter, flow amplitude, and time-variant parameter.