Pipe Flow for Power-Law and Carreau Fluids

power-law exponent

1

Carreau exponent

0.5

power-law

Carreau

The velocity profile versus radial position is obtained for the steady-state laminar flow of power-law and Carreau fluids in a pipe. The pipe radius is

R=1

and the applied pressure gradient is

ΔP

L

=1

. For both the power-law and Carreau fluids, the green dots represent the solutions obtained using the Chebyshev collocation technique. The velocity profile for a power-law fluid (the blue curve) is obtained from the analytical solution given by

v(r)=

1/n

ΔP

2Lκ

(

1+1/n

R

-

1+1/n

r

)/(1+1/n)

[1, 2]. The velocity profile for a Carreau fluid (the red curve) is obtained using the shooting technique and the built-in Mathematica function NDSolve. For both fluids, you can vary the exponent (see Details section).