3D fully-developed parabolic velocity profile

Hi everyone,

I have a short question, I am trying to impose fully-developed flow as inlet condition but in 3D, does anyone know whether there is a analytical solution (equation) for such 3D profile.
I am looking for the solution of equation:

1/rho dp/dx = nu (d^2 u /dy^2 + d^2 u/dz^2) where

BC’s u(0,z)=0 u(H,z)=0
u(y,0)=0 u(y,W)=0

the flow direction is in x.

thanks a lot.


Hello, yes there are solutions available. Have a look at those articles:
Latt et al.
Krüger et al.


Thanks Timm