Abstract
This study concerns the problem of blood flow in large elastin arteries in the mammalian circulatory system. The mathematical model is chosen to include the large amplitude forced oscillatory motion of the vessel. The vessel is modeled to be a straight, circular, distensible, thin-walled tube with constant cross-section, and is externally constrained such that longitudinal movement is prohibited. Blood is treated as a Newtonian fluid with constant apparent viscosity. The dynamic oscillatory motion of the axisymmetric vessel is assumed to be represented by a radial oscillation of finite amplitude which decays exponentially along its axis. The dynamic governing equation for the radial motion is derived from the concepts of continuum mechanics. An expression for the finite radial oscillation of the vessel is found. Equations of motion for the blood flow are those given by the continuity and the Navier-Stokes. They are solved by using the linearization techniques under long wave assumption. The solution for the vessel motion is used as the boundary condition for the fluid motion. Results of the propagation speeds for the pressure waves are obtained.
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