Bounds on heat transport in Bénard-Marangoni convection.
For Pearson's model of Bénard-Marangoni convection, the Nusselt number Nu is proven to be bounded as a function Marangoni number Ma according to Nu<or=0.838 x Ma(2/7) for infinite Prandtl number and according to Nu <or=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.
Hagstrom
George
G
Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA.
Doering
Charles R
CR