Navier-Stokes Flow in Cylindrical Elastic Tubes

Abstract

Analytical expressions correlating the volumetric flow rate to the inlet and outlet pressures are derived for the time-independent flow of Newtonian fluids in cylindrically-shaped elastic tubes using a one-dimensional Navier-Stokes flow model with two pressure-area constitutive relations. These expressions for elastic tubes are the equivalent of Poiseuille and Poiseuille-type expressions for rigid tubes which were previously derived for the flow of Newtonian and non-Newtonian fluids under various flow conditions. Formulae and procedures for identifying the pressure field and tube geometric profile are also presented. The results are validated by a finite element method implementation. Sensible trends in the analytical and numerical results are observed and documented.

The flow of Newtonian and power law fluids in elastic tubes

“…The Newtonian formulae can be used as an alternative to the previously derived formulae [17] which are based on the 1D Navier-Stokes flow in distensible tubes.…”

“…In [17] two formulae based on the widely used 1D Navier-Stokes model for the flow of Newtonian fluids in elastic tubes were derived. These formulae, which are based on the first and second p-A relations respectively, are given by…”

Peristaltic Pumping of a Generalized Newtonian Fluid in an Elastic Tube

“…The effect of peristalsis on Herschel -Bulkley fluid flow in an elastic tube was discussed by Vajravelu et al (2014). Sochi (2015) derived analytical expressions for the Newtonian flow characteristics by considering cylindrically shaped elastic tubes. Shen et al (2016) presented an elastic tube model to study the pulsatile flow characteristics of blood by taking arterial wall motion in to consideration.…”

Variational approach for the flow of Ree–Eyring and Casson fluids in pipes

“…where G is a constant, it can be shown that Equation 5 can be reduced to two independent variational forms d dr γ dµ dr = 0 (7) and d dr µ dγ dr = 0 (8)…”