The Nonlinear Wave Modulation In Prestressed Elastic Tube Filled With Viscous Fluid

Abstract

The aim of this study is to investigate nonlinear wave modulation in a prestressed elastic tube filled with the viscous fluid. In this research, the artery is assumed as thin-walled, long, and circularly cylindrical, the prestressed elastic tube with variable cross-section. The blood is considered as an incompressible viscous fluid. For reductive perturbation method (RPM), the stretched coordinates and asymptotic series were introduced in the dimesionless equations of tube and fluid .The RPM is applied to obtain a set of various orders of differential equations. The nonlinear Schrodinger (NLS) equation with variable coefficients is obtained by solving these differential equations as the nonlinear evolution equation in the corresponding mathematical model. The NLS equation with variable coefficients will be solved analytically. The MATLAB’s graphical output shows that the wave speed increases when the viscosity of fluid increasing. This happened due to the resistance of the blood flow indicates which results in the reaction of the wave speed. Increasing in wave number leads to decreasing in wavelength. Other than that, wave travels further in the expanding tube than narrowing tube. Furthermore, the wave amplitude effected by cross-section area of tube. Waves with greater amplitude comes from high disturbance of energy.