Tailoring boundary geometry to optimize heat transport in turbulent convection

TL;DR

This study investigates how tailoring the upper boundary geometry in turbulent Rayleigh-Bénard convection affects heat transport, revealing an optimal boundary wavelength that maximizes the heat transfer efficiency.

Contribution

The paper introduces a novel approach of boundary geometry tailoring to optimize heat transport in turbulent convection, supported by a simple scaling model.

Findings

Maximum heat transport occurs at a specific boundary wavelength.

Heat transfer efficiency decreases outside the optimal wavelength range.

The coupling between boundary layer and interior flow explains the observed behavior.

Abstract

By tailoring the geometry of the upper boundary in turbulent Rayleigh-B\'enard 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, $Nu-1 \propto Ra^\beta$, 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.