Abstract
We prove a new rigorous upper bound on the vertical heat transport for BenardMarangoni convection of a two- or three-dimensional fluid layer with infinite Prandtl number. Precisely, for Marangoni number Ma 1 the Nusselt number Nu is bounded asymptotically by Nu 6 const. Ma2 =7.ln Ma / 1 =7. Key to our proof are a background temperature field with a hyperbolic profile near the fluid's surface and new estimates for the coupling between temperature and vertical velocity.