 Four-thirds convective heat-transfer law

A high-Rayleigh number closure $\mathrm{Nu}=C{\mathrm{Ra}}^{1/3}$ gives $q=C{k}_T[g\beta /(\nu \kappa ){]}^{1/3}(\Delta T{)}^{4/3}$, independent of layer depth. It assumes boundary-layer-controlled heat transfer, a well-mixed interior, fixed material properties and a fixed Prandtl number regime. It is a model, not a universal asymptotic law for every turbulent convection regime or for an impulsive initial conductive transient.