We carry out direct numerical simulations of turbulent Rayleigh–Bénard convection in a square box with rough conducting plates over the Rayleigh number range
$10^7\leqslant Ra\leqslant 10^9$ and the Prandtl number range
$0.01\leqslant Pr\leqslant 100$. In Zhang et al. (J. Fluid Mech., vol. 836, 2018, R2), it was reported that while the measured Nusselt number
$Nu$ is enhanced at large roughness height
$h$, the global heat transport is reduced at small
$h$. The division between the two regimes yields a critical roughness height
$h_c$, and we now focus on the effects of the Prandtl number (
$Pr$) on
$h_c$. Based on the variations of
$h_c$, we identify three regimes for
$h_c(Pr)$. For low
$Pr$, thermal boundary layers become thinner with increasing
$Pr$. This makes the boundary layers easier to be disrupted by rough elements, leading to the decrease of
$h_c$ with increasing
$Pr$. For moderate
$Pr$, the corner-flow rolls become much more pronounced and suppress the global heat transport via the competition between the corner-flow rolls and the large-scale circulation (LSC). As a consequence,
$h_c$ increases with increasing
$Pr$ due to the intensification of the corner–LSC competition. For high
$Pr$, the convective flow transitions to the plume-controlled regime. As the rough elements trigger much stronger and more frequent plume emissions,
$h_c$ again decreases with increasing
$Pr$.