A bound on the vertical transport of heat in the ultimate state of slippery convection at large Prandtl numbers

Xiaoming Wang, Jared P. Whitehead

A new upper bound on the rate of vertical heat transport is established in 3 dimensions for stress-free velocity boundary conditions on horizontally periodic plates. For large (but finite) Prandtl numbers this bound is an improvement over the `ultimate' Ra^{1/2} scaling and in the limit of infinite Pr, agrees with the bound of Ra^{5/12} recently derived in that limit.