Forced Korteweg-de Vries–Burgers equation in an elastic tube filled with a variable viscosity fluid

Abstract

In the present work, treating the arteries as a prestressed thin walled elastic tube with a stenosis and the blood as a Newtonian fluid with variable viscosity, we have studied the propagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method [Jeffrey A, Kawahara T. Asymptotic methods in nonlinear wave theory. Boston: Pitman; 1981]. We obtained the forced Korteweg-de Vries–Burgers (FKdVB) equation with variable coefficients as the evolution equation. By use of the coordinate transformation, it is shown that this type of evolution equation admits a progressive wave solution with variable wave speed. As might be expected from physical consideration, the wave speed reaches its maximum value at the center of stenosis and gets smaller and smaller as we go away from the center of the stenosis. The variations of radial displacement and the fluid pressure with the distance parameter are also examined numerically. The results seem to be consistent with physical intuition.