Critical Prandtl Number for Heat Transfer Enhancement in Rotating Convection

Rotation, which stabilizes flow, can enhance the heat transfer in Rayleigh-Benard 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 show that for a given Ra, there exists a critical Prandtl number (Prcr) below which no significant heat transfer enhancement occurs at any rotation rate, and an optimal Prandtl number (Propt) at which maximum heat transfer enhancement occurs at an optimal rotation rate (Taopt). Notably, Prcr, Propt, Taopt, and the maximum heat transfer enhancement all increase with increasing Ra. We also demonstrate a significant heat transfer enhancement up to Ra = 2 x 1010 and predict that the enhancement would become even more pronounced at higher Ra, provided Pr is also increased commensurately.