Modulation of non-linear wave in a fluid-filled thick elastic tube - Ahmad, Nur Fara Adila (2020)
This research presents an analytical study on the wave modulation flow in an artery. The artery is simulated as an incompressible, isotropic, and thick walled elastic tube. By considering blood as an incompressible inviscid fluid or incompressible viscous fluid, two mathematical models of non-linear wave modulation in a thick elastic tube were developed. The modulation of the non-linear wave in the long wave approximation was investigated using the reductive perturbation method. The governing equation for the incompressible inviscid fluid model was shown to be the non-linear Schrodinger equation (NLSE). As the dissipative non-linear Schrodinger equation (DNLSE), the control equation of the incompressible viscous fluid model was derived. These governing equations have been sought progressive wave-type solutions. It is observed that solitary wave type solutions with variable amplitude are admitted by these two equations. The effects on the blood flow characteristics have been extracted graphically by radial displacement, radial speed, axial speed, tube pressure, and hydrostatic pressure. Graphical analysis on wave amplitude variation, wave width, and wave travel was performed to illustrate the clarification of these two models towards wave modulation. Results showed that wave propagated smoothly for the first model, while the second model displayed the wave propagated with decreasing of wave amplitude. It was found that as the fluid viscosity increased, the resistance for blood to flow also increased.