New bounds on the vertical heat transport for Bénard-Marangoni convection at infinite Prandtl number - Fantuzzi, Giovanni; Nobili, Camilla; Wynn, Andrew (Journal of Fluid Mechanics, 2019)
We prove a new rigorous upper bound on the vertical heat transport for Bénard-Marangoni Â convection of a two-or three-dimensional fluid layer with infinite Prandtl number. Precisely, for Marangoni number the Nusselt number is bounded asymptotically by. 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.
CRIS-Team Scopus Importer:2022-09-26
Keywords: Marangoni convection; variational methods