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SUMMARY:Bounds on heat transport for convection driven by internal heating
  - Giovanni Fantuzzi (Imperial College London)
DTSTART:20220311T111500Z
DTEND:20220311T121500Z
UID:TALK170726@talks.cam.ac.uk
DESCRIPTION:Convective flows driven by internal sources of heat present ma
 ny confounding aspects that have attracted increasing attention over the l
 ast few years. One fundamental question that remains largely open is how t
 he mean vertical convective heat flux depends on the non-dimensional contr
 ol parameters of the flow &mdash\; namely\, the Prandtl number Pr and a "f
 lux" Rayleigh number R measuring the strength of internal heating. This ta
 lk presents new parameter-dependent rigorous upper bounds on the mean vert
 ical convective heat flux for a uniformly heated layer of fluid confined b
 etween by two horizontal plates. For fluids with a finite Prandlt number\,
  the upper bound asymptotes to a constant value from below as R is raised\
 , and it does so at an exponential rate that depends on the thermal bounda
 ry conditions (isothermal vs insulating). In the infinite-Pr limit\, inste
 ad\, the bound displays a slower power-law increase. These bounds are prov
 en using a modern formulation of the background method of Doering & Consta
 ntin\, augmented with a minimum principle for the temperature of the fluid
 .
LOCATION:Seminar Room 1\, Newton Institute
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