Author:
Whitehead Jared P.,Doering Charles R.
Abstract
AbstractRigorous bounds on heat transport are derived for thermal convection between stress-free horizontal plates. For three-dimensional Rayleigh–Bénard convection at infinite Prandtl number ($\mathit{Pr}$), the Nusselt number ($\mathit{Nu}$) is bounded according to $\mathit{Nu}\leq 0. 28764{\mathit{Ra}}^{5/ 12} $ where $\mathit{Ra}$ is the standard Rayleigh number. For convection driven by a uniform steady internal heat source between isothermal boundaries, the spatially and temporally averaged (non-dimensional) temperature is bounded from below by $\langle T\rangle \geq 0. 6910{\mathit{R}}^{\ensuremath{-} 5/ 17} $ in three dimensions at infinite $\mathit{Pr}$ and by $\langle T\rangle \geq 0. 8473{\mathit{R}}^{\ensuremath{-} 5/ 17} $ in two dimensions at arbitrary $\mathit{Pr}$, where $\mathit{R}$ is the heat Rayleigh number proportional to the injected flux.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
28 articles.
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