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arXiv · 1102.2307

Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection

Richard J. A. M. Stevens·Detlef Lohse·Roberto Verzicco
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Abstract

Results from direct numerical simulation for three-dimensional Rayleigh-Bénard convection in samples of aspect ratio $Γ=0.23$ and $Γ=0.5$ up to Rayleigh number $Ra=2\times10^{12}$ are presented. The broad range of Prandtl numbers $0.5<Pr<10$ is considered. In contrast to some experiments, we do not see any increase in $Nu/Ra^{1/3}$, neither due to $Pr$ number effects, nor due to a constant heat flux boundary condition at the bottom plate instead of constant temperature boundary conditions. Even at these very high $Ra$, both the thermal and kinetic boundary layer thicknesses obey Prandtl-Blasius scaling.

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Richard J. A. M. Stevens, Detlef Lohse, Roberto Verzicco. 2011-05-01. Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection. https://doi.org/10.1017/jfm.2011.354

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