Solitary Waves in Stenosed Thin Elastic Tube with Variable Viscosity Newtonian Fluid

Abstract

Researchers found that nonlinear waves propagate in a stenosed artery have more valuable in medical science for detecting the blood flows characteristic in the abnormal arteries [16]. Therefore, for this study, the artery is considered as a prestressed thin-walled elastic stenosed tube, moreover the blood is treated as an incompressible Newtonian fluid with variable viscosity. Here, the solitary wave propagation in this composite medium has been investigated by using the reductive perturbation method. A set of various orders of nonlinear differential equations are obtained by introducing the reductive perturbation method into the dimensionless equations (tube and fluid). Then, solve the various orders of differential equations to get the forced Korteweg-de Vries-Burgers (FKdVB) equation with variable coefficient. The evolution equation is solved analytically. The result revealed that when the blood flows in a stenosed tube, the wave amplitude decreases over time corresponding to the viscous effect of fluid and the stenosis. Conversely, when blood flows in a tube without stenosis, the wave structure is an increasing shock wave profile propagates to the right. In addition, by discarding the stenotic effect, the solution of fluid pressure shows an increasing shock wave profile propagates to the right when the time increases. The fluid pressure function reached minimum value in the center of stenosis due to the existence of stenosis. The wave speed variation is presented when different value of stenotic effects is under consideration.