Mathematical Modelling of Inviscid Fluid Flows in Thin Stenosed Elastic Tube Using Reductive Perturbation Method

Abstract

Mathematical modelling of the wave propagation blood flow gives useful information to medicine. This paper presents an analytical study on the wave propagation flow in the stenosed artery. First, the artery is treated as a thin-walled prestressed elastic tube with stenosis. By considering blood as an incompressible inviscid fluid, a mathematical model of nonlinear wave propagation in the thin-walled elastic tube with stenosis is proposed. Then, by applying the reductive perturbation method to the nondimensional equations of tube and fluid, a set of various orders of differential equations is obtained. As a result, the partial differential equation for the incompressible inviscid fluid flow in the stenosed tube is proved to be the Korteweg-de Vries (KdV) equation with variable coefficients, and its analytical solution is determined. From graphical outputs, the fluid passes through the stenosis, and the amplitude of the wave and fluid pressure decreases as time increases, but the amplitude of the wave and fluid pressure increases as time increases after the fluid passes through the stenosis. In addition to this, when the height of stenosis is higher, the wave speed is lower. Finally, the increase in circumferential stretch causes the wave speed to decrease, and the peak-to-peak of the wave also becomes wider.