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Bounds for the heat transport in convection with fixed heat flux through the layer
Optimization| Speaker: | Dr. Jesse Otero, Univerisity of Michigan |
| Location: | 693 Kerr |
| Start time: | Thu, May 30 2002, 4:10PM |
Description
We discuss the problem of formulating an upper bound principle for
the heat transport in a convecting fluid with fixed heat flux
through the layer. The heat transport is shown to be inversely
proportional to the temperature drop across the plates, and is
bounded above according to Nu< c R^(1/3), where
c is an absolute constant and R a non-dimensional forcing
scale. The relation between the parameter R and the Rayleigh
number of the flow, Ra, is discussed and this relation is used
to recast the bound in terms of Ra, yielding Nu< c Ra^(1/2).
The `full' convection problem, consisting of
a fluid bound by two plates with some thickness and finite conductivity,
is also discussed.