Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries
Abstract
We study two-dimensional Rayleigh-Bénard 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].
- Publication:
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arXiv e-prints
- Pub Date:
- September 2021
- DOI:
- 10.48550/arXiv.2109.13205
- arXiv:
- arXiv:2109.13205
- Bibcode:
- 2021arXiv210913205D
- Keywords:
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- Mathematics - Analysis of PDEs;
- Physics - Fluid Dynamics
- E-Print:
- 15 pages, 1 figure