B.C. on heat flux
 

I am modelling a very simple 2d parallel plates with a fully developed laminar flow through it. The bottom plate is heated uniformly while the top one is adiabatic. What I find strange is when I change the value of the heat flux, the Nusselt number on the bottom plate is changed too, which should be a constant! So would somebody help me to point out where my problem is? Thanks!