Numerical treatment of slip velocity and catheterization on the gravity flow of non-Newtonian fluid model through a uniform blood vessel

The aim of the present article is to investigate the influence of gravity and slip velocity on the steady flow of blood through an inclined catheterized blood vessel. The constitutive relation of Herschel-Bulkley fluid is utilized to capture the non-Newtonian characteristics of the blood. The effects of catheter radius, yield stress, slip velocity and the inclination angle on the velocity, flow rate, wall shear stress and resistance to the flow are analyzed in detail. The expression of velocity is evaluated numerically by using Regula falsi method. The variation of different flow variables corresponding to the involved geometric and rheologic parameters is shown through graphs. It is shown that the velocity decreases as the yield stress attains higher values. The yield stress enhances the impedance and wall shear stress. Increase in the catheter radius reduces the wall shear stress and resistive impedance. The study also reveals that the impedance for horizontal blood vessel is higher as compared to the vertical blood vessel.