Critical Prandtl number for Heat Transfer Enhancement in Rotating Convection

Abstract

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 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 ($P{r}_{cr}$) below which no significant heat transfer enhancement occurs at any rotation rate, and an optimal Prandtl number ($P{r}_{opt}$) at which maximum heat transfer enhancement occurs at an optimal rotation rate ($T{a}_{opt}$). Notably, $P{r}_{cr}$, $P{r}_{opt}$, $T{a}_{opt}$, 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.

Updated texts; Accepted in PRL

References in corpus (3)

• Approaching the Asymptotic Regime of Rapidly Rotating Convection: Boundary Layers vs Interior Dynamics
• What rotation rate maximizes heat transport in rotating Rayleigh-Bénard convection with Prandtl number larger than one?
• Optimal heat transport in rotating Rayleigh-Bénard convection at large Rayleigh numbers

Cited by in corpus (1)

• Gravity drives the flow within the Stewartson layer in centrifugal convection