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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Bounds on heat transport for convection driven by
internal heating - Giovanni Fantuzzi (Imperial Col
lege London)
DTSTART;TZID=Europe/London:20220311T111500
DTEND;TZID=Europe/London:20220311T121500
UID:TALK170726AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170726
DESCRIPTION:Convective flows driven by internal sources of hea
t present many confounding aspects that have attra
cted increasing attention over the last few years.
One fundamental question that remains largely ope
n is how the mean vertical convective heat flux de
pends on the non-dimensional control parameters of
the flow &mdash\; namely\, the Prandtl number Pr
and a "flux" Rayleigh number R measuring the stren
gth of internal heating. This talk presents new pa
rameter-dependent rigorous upper bounds on the mea
n vertical convective heat flux for a uniformly he
ated layer of fluid confined between by two horizo
ntal plates. For fluids with a finite Prandlt numb
er\, the upper bound asymptotes to a constant valu
e from below as R is raised\, and it does so at an
exponential rate that depends on the thermal boun
dary conditions (isothermal vs insulating). In the
infinite-Pr limit\, instead\, the bound displays
a slower power-law increase. These bounds are prov
en using a modern formulation of the background me
thod of Doering & Constantin\, augmented with a mi
nimum principle for the temperature of the fluid.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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