https://doi.org/10.1007/s100510051136
Convective heat transport in a fluid layer of infinite Prandtl number: upper bounds for the case of rigid lower boundary and stress-free upper boundary
Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden,
Germany
Received:
29
September
1999
Published online: 15 May 2000
We present the theory of the multi-α-solutions of the variational
problem for the upper bounds on the convective heat transport in a heated
from below horizontal fluid layer with rigid lower boundary and stress-free
upper boundary. A sequence of upper bounds on the convective
heat transport is obtained. The highest bound 
is
between the bounds 
for the case of a fluid layer
with two rigid boundaries and 
for the case of a
fluid layer with two stress-free boundaries. As an additional result of
the presented theory we obtain small corrections of the boundary layer
thicknesses of the optimum fields for the case of fluid layer with two
rigid boundaries. These corrections lead to systematically lower
upper bounds on the convective heat transport in comparison to the bounds
obtained in [5].
PACS: 47.27.Te – Convection and heat transfer / 47.27.Cn – Transition to turbulence
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000
