Critical Prandtl Number for Heat Transfer Enhancement in Rotating Convection

Rotation, which stabilizes flow, can enhance the heat transfer in Rayleigh-Bénard 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 nonrotating 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=2×10^{10} and predict that the enhancement would become even more pronounced at higher Ra, provided Pr is also increased commensurately.