Nonlinear Waves Propagation in an Elastic Tube with Stenosis Filled with Newtonian Fluid

Abstract

First and foremost, the goal of this study is to investigate the nonlinear wave propagation in an elastic tube with stenosis filled with Newtonian fluid. In the present work, the artery is considered as an incompressible, pre-stressed, thin walled stenosed elastic tube and the blood is treated as Newtonian fluid. The dimensional equations of tube and fluid are converted into dimensionless equation by applying non-dimensional quantities. The reductive perturbation method is implemented in this study in order to obtain the various orders of nonlinear differential equations. Next, the forced Korteweg-de Vries (FpKdV) equation with variable coefficient is obtained by solving the various orders of differential equations. Then, the progressive wave solution of forced perturbed Korteweg-de Vries equation with variable coefficients is carried out and discussed. From the graphical output obtained, it shows that the increase of fluid viscosity will cause the radial displacement decreases. Thus, the higher the viscosity of fluid, the fluid is not easy to pass through the stenosis along the tube. Besides, there is resistance on blood flows in the artery due to the presence of viscosity.  It is because the radial displacement is decreasing when the time is increasing. Last but not least, the trajectory of the wave is not a straight line while a curve in the plane.