Mathematical modelling of time dependent flow of non-Newtonian fluid through unsymmetric stenotic tapered artery: Effects of catheter and slip velocity

Abstract

In this article pulsatile nature of blood flow through unsymmetric stenosed tapered artery in the presence of catheter has been modelled. Blood is represented by micropolar fluid. The analytical solutions for velocity and microrotation components are obtained in terms of Bessel functions of the first and second kind. Flow parameters such as the resistance to flow (impedance) in the artery and wall shear stress at the maximum height of the stenosis have been calculated and the effects of various parameters such as shape parameter ($n$), tapered parameter ($\zeta$), slip velocity ($u_{1}$, $u_{2}$), radius of the catheter ($r_{c}$), Reynolds number ($Re$), Strouhal number ($\sigma$), micropolar parameter ($m$), coupling number ($N$) and height of the stenosis ($\epsilon$) on impedance and wall shear stress are discussed. The locations of the maximum height of the stenosis and the annular radius which are dependent on both tapered parameter ($\zeta$) and shape parameter ($n$) are computed. It is observed that impedance is increasing while catheter radius, height of the stenosis, coupling number are increasing, while it is decreasing in case of shape parameter and micropolar parameter. Shape parameter has no effect on wall shear stress at the maximum height of the stenosis in case of non-tapered artery. However it is dependent on $n$ in case of tapered artery. In particular wall shear stress decreases as stenosis is becoming more and more asymmetric in case of diverging tapered artery and the behaviour is exactly reverse in case of converging tapered artery. Also a comparison of the results for impedance of the present model with the experimental results of Back [4] have been carried out, it is observed that impedance increases significantly for higher values of the ratio of the radius of the catheter to that of the annular region is high.