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

## Authors

• Zoey Loh Universiti Tun Hussein Onn Malaysia
• Yaan Yee Choy School of Mathematics and Science, Singapore Polytechnic, 500 Dover Road, Singapore 139651
• Sie Long Kek Department of Mathematics and Statistics, Faculty of Applied Sciences and Technology, Pagoh Campus, Universiti Tun Hussein Onn Malaysia, 84600 Pagoh, Johor, MALAYSIA

## Keywords:

Inviscid Fluid, Thin-Walled Elastic Tube, Stenosis, Reductive Perturbation Method, Korteweg-de Vries Equation

## 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.

07-08-2023

Mathematics

## How to Cite

Loh, Z., Choy, Y. Y. ., & Kek, S. L. (2023). Mathematical Modelling of Inviscid Fluid Flows in Thin Stenosed Elastic Tube Using Reductive Perturbation Method. Enhanced Knowledge in Sciences and Technology, 3(1), 037-046. https://publisher.uthm.edu.my/periodicals/index.php/ekst/article/view/10566