Oscillatory flow of a viscous fluid through converging-diverging orthotropic tethered tubes

AbstractA theoretical investigation of the propagation of pressure waves through uniformly converging and diverging thin-walled orthotropic elastic tubes filled with a Newtonian fluid is made in this paper, by considering the flow to be laminar and unsteady. Axisymmetric solutions of the differential equations that govern the motion of the fluid and the solid elastic wall are obtained. The outer surface of the wall is taken to be free of tractions. By using the solutions, a complicated form of transcendental equation is derived, that serves as a dispersion equation and puts forth a relation between the frequency and the wave number. This equation is solved by employing both analytical and numerical techniques. Numerical values of the pressure gradient, mean axial velocity, radial velocity, flow rate, amplitude ratio, phase velocity, and wave length have been computed for different angles of taper for a particular situation. It is felt that the results presented in the paper will find adequate applications in the study of blood flow through certain arterial segments, particularly in investigating the propagation of small amplitude harmonic waves, generated due to the flow of blood when the wave length is large compared to the radius of the arterial segment