Critical Prandtl number for Heat Transfer Enhancement in Rotating Convection

TL;DR

This study uses direct numerical simulations to identify critical and optimal Prandtl numbers for heat transfer enhancement in rotating Rayleigh-Bénard convection, revealing how these parameters influence heat transfer at high Rayleigh numbers.

Contribution

It introduces a comprehensive analysis of heat transfer enhancement in rotating RBC, identifying critical and optimal Prandtl numbers and their dependence on Rayleigh and Taylor numbers.

Findings

Existence of a critical Prandtl number below which no enhancement occurs

Identification of an optimal Prandtl number for maximum heat transfer

Heat transfer enhancement increases with Rayleigh number and Prandtl number

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.