Harmonic waves in a prestressed thin elastic tube filled with a viscous fluid

In this work a theoretical analysis is presented for wave propagation in a thin-walled prestressed elastic tube filled with a viscous fluid. The fluid is assumed to be incompressible and Newtonian, whereas the tube material is considered to be incompressible, isotropic and elastic. Considering the physiological conditions that the arteries experience, such a tube is initially subjected to a mean pressure P_i and an axial stretch λ_z. If it is assumed that in the course of blood flow small incremental disturbances are superimposed on this initial field, then the governing equations of this incremental motion are obtained for the fluid and the elastic tube. A harmonic-wave type of solution is sought for these field equations and the dispersion relation is obtained. Some special cases, as well as the general case, are discussed and the present formulation is compared with some previous works on the same subject.