nusselt number calculation
 

I'm stuck calculating nusselt number and I don't know what I'm doing wrong.
I have a fully developed flow passing between infinite parallel plates. The flow is then heated by constant temperature plates. I have calculated a nondimensional temperature field theta.

Theta = (T-T_w)/(T_in-T_w) where T_w is the wall temperature and T_in is the inlet temp.

To find nusselt number I am using the equation Nu=(dtheta/dy)/theta_avg

dtheta/dy is (theta(boundary)-theta(interior))/dy
thetavg = theta u* dy

this is giving me all sorts of strange results even for the graetz problem. any ideas

Where have you found this equation?

I used to equation provided in this paper whose results I am trying to reproduce. The equation for nusselt number is equation 21.


http://enstrophy.mae.ufl.edu/~mohsen...008DHTcfd1.pdf

have you tried different values for dy to see how that affects your answer? You might have to use a small value

How are you calculating T?

I have tried smaller dy and it hasn't really changed my results

I'm not really calculating T, but I'm calculating theta on a staggered grid and trying to keep everything non dimensional.

Here is a code I have been using in matlab to test a basic hagen poiseuille flow between two plates and a slug flow between two plates. The Nu number plots show some of the correct behaviors but asymptote to the wrong values.