FDM Analysis for Blood Flow through Stenosed Tapered Arteries

Abstract

A computational model is developed to analyze the unsteady flow of blood through stenosed tapered narrow arteries, treating blood as a two-fluid model with the suspension of all the erythrocytes in the core region as Herschel-Bulkley fluid and the plasma in the peripheral layer as Newtonian fluid. The finite difference method is employed to solve the resulting system of nonlinear partial differential equations. The effects of stenosis height, peripheral layer thickness, yield stress, viscosity ratio, angle of tapering and power law index on the velocity, wall shear stress, flow rate and the longitudinal impedance are analyzed. It is found that the velocity and flow rate increase with the increase of the peripheral layer thickness and decrease with the increase of the angle of tapering and depth of the stenosis. It is observed that the flow rate decreases nonlinearly with the increase of the viscosity ratio and yield stress. The estimates of the increase in the longitudinal impedance to flow are considerably lower for the two-fluid Herschel-Bulkley model compared with those of the single-fluid Herschel-Bulkley model. Hence, it is concluded that the presence of the peripheral layer helps in the functioning of the diseased arterial system.

Mathematical Analysis of Blood Flow in Porous Tubes: A Comparative Study

“…Two types of permeability considered in this study are (i) constant permeability with ( ) = 0 , where 0 is a constant (permeability factor) and (ii) variable (in the radial direction) permeability with ( ) = 0 [(1 − )/ ]. For Herschel-Bulkley fluid, the typical value of power law index is generally taken as 0.95 [22]. It is noted that in the case of constant permeability with lower values of the permeability factor ( 0 = 0.05, 0.1, 0.25), the shear stress increases slowly in the radial direction when increases from 0 to 0.6 and then it increases rapidly when increases further from 0.6 to 1.…”