3. Determination of the critical Rayleigh Number
Ra is the Rayleigh number. Rac, the critical Rayleigh number is a criterion of stability. In theory, Rac=1708. When Ra>Rac, there is instability.
3.1 With the Nusselt numberThe Nusselt number is the ratio of the actual heat transfert to what it would be is there were conduction but no convection. Thus Nu=1 in stable conditions. In general, Nu varies with Ra.
Nu=1 if Ra<Rac.
Nu-1=(Ra-Rac)^(1/2) if Ra>Rac.
In this case, the critical Rayleigh number is 1772.
3.2 With the velocity maximum
In steady cases, the velocity fields are:
Thus, we can trace Vx_max in function of Ra to find Rac:
We find also that Rac=1772.