An Exact Solution Of The Navier-Stokes
Equations For Swirl Flow Models Through
Porous Pipes
Author(s)
. Vlachakis, A. Fatsis, A. Panoutsopoulou, E. Kioussis,
M. Kouskouti & V. Vlachakis
Abstract
An exact solution of the Navier-Stokes equations for laminar flow inside porous
pipes simulating variable suction and injection of blood flows is proposed in the
present article. To solve these equations analytically, it is assumed that the effect
of the body force by mass transfer phenomena is the ‘porosity’ of the porous
pipe in which the fluid moves. The resultant of the forces in the pores can be
expressed as filtration resistance. The developed solutions are of general
application and can be applied to any swirling flow in porous pipes.
The effect of porous boundaries on steady laminar flow as well as on species
concentration profiles has been considered for several different shapes and
systems. In certain physical and physiological processes filtration and mass
transfer occurs as a fluid flows through a permeable tube. The velocity and
pressure fields in these situations differ from simple Poiseuille flow in an
impermeable tube since the fluid in contact with the wall has a normal velocity
component. In the new flow model, a variation of the solutions with Bessel
functions based on Terrill’s theoretical flow model is adopted.
Keywords: exact solution, Navier-Stokes equations, pipe flow, laminar flow,
porous media, blood flow characteristics.
Keywords
exact solution, Navier-Stokes equations, pipe flow, laminar flow,
porous media, blood flow characteristics.
Related Book
Other papers in this volume
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