Bounds on heat transport in Beacutenard-Marangoni convection

For Pearson's model of Beacutenard-Marangoni convection, the Nusselt number Nu is proven to be bounded as a function Marangoni number Ma according to Nu < 0.838xMa(2/7) for infinite Prandtl number and according to Nu less than or similar to Ma(1/2) uniformly for finite Prandtl number. The analysis is also used to raise the lower bound for the critical Marangoni number for energy stability of the conduction solution from 56.77 to 58.36 when the Prandtl number is infinite.