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- W3147733689 abstract "We prove a new rigorous bound for the mean convective heat transport $langle w T rangle$, where $w$ and $T$ are the nondimensional vertical velocity and temperature, in internally heated convection between an insulating lower boundary and an upper boundary with a fixed heat flux. The quantity $langle wT rangle$ is equal to half the ratio of convective to conductive vertical heat transport, and also to $frac12$ plus the mean temperature difference between the top and bottom boundaries. An analytical application of the background method based on the construction of a quadratic auxiliary function yields $langle w T rangle leq tfrac{1}{2}big(tfrac{1}{2}+ tfrac{1}{sqrt{3}} big) - 1.6552, R^{-frac13}$ uniformly in the Prandtl number, where $R$ is the nondimensional control parameter measuring the strength of the internal heating. Numerical optimisation of the auxiliary function suggests that the asymptotic value of this bound and the $-1/3$ exponent are optimal within our bounding framework. This new result halves the best existing (uniform in $R$) bound (Goluskin 2016, Springer, Table 1.2) and its dependence on $R$ is consistent with previous conjectures and heuristic scaling arguments. Contrary to physical intuition, however, it does not rule out a mean heat transport larger than $frac12$ at high $R$, which corresponds to the top boundary being hotter than the bottom one on average." @default.
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- W3147733689 date "2021-07-05" @default.
- W3147733689 modified "2023-09-27" @default.
- W3147733689 title "Bounds for internally heated convection with fixed boundary heat flux" @default.
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- W3147733689 doi "https://doi.org/10.1017/jfm.2021.527" @default.
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