How surface roughness reduces heat transport for small roughness heights in turbulent Rayleigh–Bénard convection

Abstract

Rough surfaces have been widely used as an efficient way to enhance the heat-transfer efficiency in turbulent thermal convection. In this paper, however, we show that roughness does not always mean a heat-transfer enhancement, but in some cases it can also reduce the overall heat transport through the system. To reveal this, we carry out numerical investigations of turbulent Rayleigh–Bénard convection over rough conducting plates. Our study includes two-dimensional (2D) simulations over the Rayleigh number range $10^{7}\leqslant Ra\leqslant 10^{11}$ and three-dimensional (3D) simulations at $Ra=10^{8}$. The Prandtl number is fixed to $Pr=0.7$ for both the 2D and the 3D cases. At a fixed Rayleigh number $Ra$, reduction of the Nusselt number $Nu$ is observed for small roughness height $h$, whereas heat-transport enhancement occurs for large $h$. The crossover between the two regimes yields a critical roughness height $h_{c}$, which is found to decrease with increasing $Ra$ as $h_{c}\sim Ra^{-0.6}$. Through dimensional analysis, we provide a physical explanation for this dependence. The physical reason for the $Nu$ reduction is that the hot/cold fluid is trapped and accumulated inside the cavity regions between the rough elements, leading to a much thicker thermal boundary layer and thus impeding the overall heat flux through the system.