Nonlinear wave modulation in an inviscid and viscous fluids-filled thin viscoelastic tube - Che Ahmed, Normaisarah (2020)
This research is aimed to study the modulation of nonlinear wave in an artery filled with blood. In recent years, many researchers have carried out studies on arterial wave modulation with different perspectives related to blood flow. Most of the studies focused on wave modulation in the artery by considering the artery as thin elastic tube. The studies of wave modulation in the artery by treating the artery as thin viscoelastic tube are rather limited in the literature. Therefore, in this research, the artery is considered as an incompressible, prestressed, thin walled viscoelastic tube. By considering the blood as an incompressible inviscid fluid and viscous fluid, two mathematical models of nonlinear wave modulation in thin viscoelastic tube are formed through the use of the reductive perturbation method. The equation of fluids used in this research are exact equations where boundary condition of fluid under consideration. It is shown that the governing equation for the model of inviscid fluid flow in viscoelastic tube is nonlinear Schrӧdinger equation (NLSE). The governing equation for the model of viscous fluid flow in viscoelastic tube is dissipative nonlinear Schrӧdinger equation (DNLSE). By seeking the progressive wave solutions to the NLSE and DNLSE, it is observed through the graphical outputs that the solutions of NLSE and DNLSE admit the downward bell-shaped wave with various amplitude. Besides that, based on the solution of NLSE, as the value of space increases, a constant width of wave is obtained with different depths and the resistance pushing through the blood flows in artery is existed. Whereas the solution of DNLSE showed that the solitary wave formed a steep wave profile as it propagates. In addition, the effects of radial velocity, axial velocity, pressure of tube and hydrostatic pressure on the blood flow characteristics are shown graphically.