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 $\mathrm{Ra}$, this estimate interpolates between the Whitehead-Doering bound by ${\mathrm{Ra}}^{\frac{5}{12}}$ for free-slip conditions [13] and the classical Doering-Constantin ${\mathrm{Ra}}^{\frac{1}{2}}$ bound [4].

15 pages, 1 figure

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