On Oct 3, 1:21 am, Dieter Britz <br...
> 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)
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.