JOINED DISSIMILAR ELASTIC THIN TUBES CONTAINING STEADY VISCOUS-FLOW

THE THEORY of finite deformation of elastic membranes is applied to the problems of the deformation of a single thin tube, and to two and three joined tubes which are extended longitudinally and contain steady viscous flow. Initially the joined circular cylindrical tubes have the same radii but are made from different materials. The viscous flow yields tangential drag stress and normal pressure on the internal surface of the tubes, and the stress and pressure are approximated by various expressions. The resulting governing equations are coupled, highly non-linear ordinary differential equations. A simple step-by-step integration numerical scheme is set up for initial value problems where all the dependent varibles are specified at some section, which is suitable for those who do not have access to standard subroutine packages. Both the simple scheme and the NAG Library subroutine D02BAF are used in the numerical calculations and no distinguishable difference is found. The values of the physical parameters taken in the calculations are very close to those for blood, natural and artificial arteries, so the results may simulate the behaviour of the arterial system. Engineering applications also exist. Validity of the approximation is checked in each case by the momentum theorem for the fluid flow.