Results from direct numerical simulation for three-dimensional Rayleigh–Bénard convection in samples of aspect ratio $\Gamma = 0. 23$ and $\Gamma = 1/ 2$ up to Rayleigh number $\mathit{Ra}= 2\ensuremath{\times} 1{0}^{12} $ are presented. The broad range of Prandtl numbers $0. 5\lt \mathit{Pr}\lt 10$ is considered. In contrast to some experiments, we do not see any increase in $\mathit{Nu}/ {\mathit{Ra}}^{1/ 3} $ with increasing $\mathit{Ra}$, neither due to an increasing $\mathit{Pr}$, nor due to constant heat flux boundary conditions at the bottom plate instead of constant temperature boundary conditions. Even at these very high $\mathit{Ra}$, both the thermal and kinetic boundary layer thicknesses obey Prandtl–Blasius scaling.
Stevens, R., Lohse, D., Verzicco, R. (2011). Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection. JOURNAL OF FLUID MECHANICS, 688, 31-43 [DOI: 10.1017/jfm.2011.354].
Prandtl and Rayleigh number dependence of heat transport in high Rayleigh number thermal convection
VERZICCO, ROBERTO
2011-01-01
Abstract
Results from direct numerical simulation for three-dimensional Rayleigh–Bénard convection in samples of aspect ratio $\Gamma = 0. 23$ and $\Gamma = 1/ 2$ up to Rayleigh number $\mathit{Ra}= 2\ensuremath{\times} 1{0}^{12} $ are presented. The broad range of Prandtl numbers $0. 5\lt \mathit{Pr}\lt 10$ is considered. In contrast to some experiments, we do not see any increase in $\mathit{Nu}/ {\mathit{Ra}}^{1/ 3} $ with increasing $\mathit{Ra}$, neither due to an increasing $\mathit{Pr}$, nor due to constant heat flux boundary conditions at the bottom plate instead of constant temperature boundary conditions. Even at these very high $\mathit{Ra}$, both the thermal and kinetic boundary layer thicknesses obey Prandtl–Blasius scaling.File | Dimensione | Formato | |
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