Critical Prandtl number for Heat Transfer Enhancement in Rotating Convection

Abstract: Rotation, which stabilizes flow, can enhance the heat transfer in Rayleigh-B\'enard convection (RBC) through Ekman pumping. In this Letter, we present the results of our direct numerical simulations of rotating RBC, providing a comprehensive analysis of this heat transfer enhancement relative to non-rotating RBC in the parameter space of Rayleigh number ($Ra$), Prandtl number ($Pr$), and Taylor number ($Ta$). We show that for a given $Ra$, there exists a critical Prandtl number ($Pr_{cr}$) below which no significant heat transfer enhancement occurs at any rotation rate, and an optimal Prandtl number ($Pr_{opt}$) at which maximum heat transfer enhancement occurs at an optimal rotation rate ($Ta_{opt}$). Notably, $Pr_{cr}$, $Pr_{opt}$, $Ta_{opt}$, and the maximum heat transfer enhancement all increase with increasing $Ra$. We also demonstrate a significant heat transfer enhancement up to $Ra=2\times 10^{10}$ and predict that the enhancement would become even more pronounced at higher $Ra$, provided $Pr$ is also increased commensurately.