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We investigate the fluid flow through a finite length, axisymmetric tube when the elastic wall is subject to either a prescribed external pressure or a prescribed motion. The prescribed wall forcing is assumed to consist of a forward travelling wave together with a reflected travelling wave. The dimensionless diameter variation of the tube is taken to be small and perturbation techniques are used to solve the weakly non-linear problem. Particular attention is given to the steady streaming flow that is induced through the non-linear convective acceleration terms. The results are applied to the flow of blood in the umbilical vein (UV), which has important physiological implications.

Original publication




Journal article


Journal of Theoretical Medicine

Publication Date





287 - 298