Tailoring boundary geometry to optimize heat transport in turbulent convection

Abstract

By tailoring the geometry of the upper boundary in turbulent Rayleigh-Bénard convection we manipulate the boundary layer -- interior flow interaction, and examine the heat transport using the Lattice Boltzmann method. For fixed amplitude and varying boundary wavelength $\lambda$, we find that the exponent $\beta$ in the Nusselt-Rayleigh scaling relation, $Nu-1\propto R{a}^{\beta }$, is maximized at $\lambda \equiv {\lambda }_{\text{max}}\approx (2\pi {)}^{-1}$, but decays to the planar value in both the large ($\lambda \gg {\lambda }_{\text{max}}$) and small ($\lambda \ll {\lambda }_{\text{max}}$) wavelength limits. The changes in the exponent originate in the nature of the coupling between the boundary layer and the interior flow. We present a simple scaling argument embodying this coupling, which describes the maximal convective heat flux.

6 pages, 6 figures

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