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arXiv · 2109.13205

Bounds on heat flux for Rayleigh-B\'{e}nard convection between Navier-slip fixed-temperature boundaries

Theodore D. Drivas·Huy Q. Nguyen·Camilla Nobili
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Abstract

We study two-dimensional Rayleigh-B\'{e}nard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number $\rm{Ra}$, this estimate interpolates between the Whitehead-Doering bound by $\rm{Ra}^{\frac{5}{12}}$ for free-slip conditions [13] and the classical Doering-Constantin $\rm{Ra}^{\frac{1}{2}}$ bound [4].

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Theodore D. Drivas, Huy Q. Nguyen, Camilla Nobili. 2021-09-27. Bounds on heat flux for Rayleigh-B\'{e}nard convection between Navier-slip fixed-temperature boundaries. https://arxiv.org/abs/2109.13205

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