Flow in a duct

[Dieter Britz]

I want to determine the flow profile across a closed rectangular duct
for laminar flow. The aspect ratio is small enough that the parallel
plate model will not do.

Is there an analytical solution to this? If so, a reference please.
I find it hard to believe that this must be simulated.
--
Dieter Britz (britz<at>chem.au.dk)

[Jan Gerrit Kootstra]

Dieter Britz wrote:
> I want to determine the flow profile across a closed rectangular duct
> for laminar flow. The aspect ratio is small enough that the parallel
> plate model will not do.
>
> Is there an analytical solution to this? If so, a reference please.
> I find it hard to believe that this must be simulated.

Dieter,

Have a look at this.

http://galileo.phys.virginia.edu/classes/311/notes/fluids2/node6.html

You are right about the analytical solution of the velocity field. It is
given on that website.

Kind regards,

Jan Gerrit Kootstra

[lcaretto]

Dieter -- I just started this newsgroup, so you may have already found
a solution. I think that it would be difficult to find a solution
since the usual approximations (steady, constant properties, fully-
developed flow so that v = w = 0 and partial_u/partial_x = 0) give a
constant pressure gradient, dp/dx. The equation that you have to
solve then becomes Poisson's equation: partial^2_u/partial_y^2 +
partial^2_u/partial_z^2 = (1/mu) dp/dx = C. The usual separation of
variables technique for solving PDEs will not work on this equation.

Larry