Two-fluid model for blood flow in stenosed arteries under periodic body acceleration: a mathematical model

Abstract

This study analyses the pulsatile flow of blood through narrow arteries with mild asymmetric stenosis. Blood is modeled as a two-fluid model with the suspension of all the erythrocytes in the core region being treated as Casson fluid and the plasma in the peripheral layer being assumed as Newtonian fluid. Perturbation method is used to solve the resulting coupled implicit system of non-linear partial differential equations. The expressions for shear stress, velocity, wall shear stress, plug core radius, flow rate and resistance to flow are obtained. The effects of pulsatility, stenosis shape parameter, stenosis depth, peripheral layer thickness, body acceleration and non-Newtonian behavior of blood on these flow quantities are discussed. It is noted that the plug core radius and resistance to flow decrease with the increase of the body acceleration and pressure gradient. It is observed that the velocity and flow rate increase with the increase of the peripheral layer thickness and they decrease with the increase of the stenosis shape parameter. It is recorded that the estimates of the mean flow rate of the two-fluid blood flow model are considerably higher than that of the single-fluid blood flow model. It is also noticed that the presence of body acceleration and peripheral layer influences the mean flow rate by increasing their magnitude significantly in the arteries with different radii.