Axisymmetric Motion Of A Second Order Viscous
Fluid In A Circular Straight Tube Under Pressure
Gradients Varying Exponentially With Time
Author(s)
F. Carapau & A. Sequeira
Abstract
The aim of this paper is to analyze the axisymmetric unsteady flow of a non-
Newtonian incompressible second order fluid in a straight rigid and impermeable
tube with circular cross-section of constant radius. To study this problem, we use
the one dimensional (1D) nine-directors Cosserat theory approach which reduces
the exact three-dimensional equations to a system depending only on time and on a
single spatial variable. From this system we obtain the relationship between mean
pressure gradient and volume flow rate over a finite section of the tube. Assuming
that the pressure gradient rises and falls exponentially with time, the 3D exact
solution for unsteady volume flow rate is compared with the corresponding 1D
solution obtained by the Cosserat theory using nine directors.
Keywords: Cosserat theory, nine directors, unsteady rectilinear flow, axisymmetric
motion, pressure gradient, second order fluid.
1 Introduction
A possible simplification to a three-dimensional model for an incompressible viscous
fluid inside a domain is to consider the evolution of average flow quantities
using simpler one-dimensional models. Usually, in the case of flow in a tube, the
classical 1D models are obtained by imposing additional assumptions and integrating
both the equations of conservation of linear momentum and mass over
the cross section of the tube. Here, we introduce a 1D model for non-Newtonian
Rivlin-Ericksen fluids of second order in an axisymmetric tube, based on the nine-
Keywords
Cosserat theory, nine directors, unsteady rectilinear flow, axisymmetric
motion, pressure gradient, second order fluid.
Related Book
Other papers in this volume
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