Pulsatile flow of an incompressible, inhomogeneous fluid in a smoothly expanded vascular tube

Abstract

This paper aims to present pulsatile laminar flow of an incompressible, inhomogeneous fluid in an axi-symmetric smoothly expanded tube, modeled as artery, under some specific flow conditions. The flowing blood is an inhomogeneous fluid due to the presence of haematocrit (the percentage of total blood volume occupied by red blood cells (RBCs)). In the present study, the viscosity of flowing blood is assumed to be dependent on radius of the artery with a maximum value at the centerline of the artery. The governing nonlinear equations along with the appropriate boundary conditions are derived and are solved numerically using finite-difference method. The effects of inhomogeneities on flow quantities along with other flow parameters such as Reynolds number (Re), Strouhal number (St), expansion height (d) have been investigated. The numerical values of wall shear stress agree well with the available results of previously published works. It is seen that the value of wall shear stress and the corresponding length of flow separation increases significantly when the viscosity increases about the mean under both steady and pulsatile flow conditions.