Rayleigh-Bénard question

Alej

Hello. I`m a bit confused. If you have the typical Rayleigh-Bénard problem configuration, that`s, a bidimensional cavity, with lateral walls insulated, and a constant temperature difference between vertical walls, and using Boussinesq approximation. Now, if you see how the nusselt numeber develps, on the bottom wall, and on the upper wall (by means of a numeric method), you will see that both numbers (well...the number in both locations) converge, showing the existence of a steady state. Now my question: Does it means that enters the same heat flux that leaves the cavity (because the Nu are equal)? And if the heat flux are equal, where does the energy to keep the flux moving come from? I don´t know where is the bad thing of this way of think. Maybe in the fact that`s a net heat flux, but then, why did I had two different Nusselt numbers in the unsteady stage?

Thanks for your time Alej