Impact of unsteadiness on the non-Newtonian flow of blood in a vascular tube with stenosis and aneurysm: analytical solution

Abstract

A theoretical analysis is conducted to explore the time-dependent problem of blood flow streaming in a tapered vascular tube having post-stenotic dilatation followed by symmetric arterial stenosis. Blood is considered a homogeneous incompressible fluid whose rheological behavior is estimated by Herschel–Bulkley fluid model. By exploiting the prescribed boundary conditions, unique expressions of velocity, flow rate, plug core radius and resistance to the flow have been made by handling the complexity of the governing equations with the standard perturbation technique. The steady-state component of the pressure gradient originating due to the functioning of the heart is computed numerically. The effects of various parameters involved in the problem in accordance with the stenosis and aneurysm on the different flow variables are elaborated with the help of graphs. It has been investigated that the rheological parameters have considerable effects on the dynamic of the flow throughout the constricted region of the vascular tube.

KEYWORDS:

• Unsteady flow
• Herschel–Bulkley fluid
• stenosis and aneurysm
• perturbation method
• plug core radius
• impedance

Disclosure statement

No potential conflict of interest was reported by the author(s).