Optimal Prandtl number for heat transfer in rotating Rayleigh-Benard convection

TL;DR

This study investigates how the Prandtl number influences heat transfer efficiency in turbulent rotating Rayleigh-Benard convection at a fixed Rayleigh number, revealing an optimal Prandtl number for maximum heat transfer enhancement.

Contribution

It identifies the optimal Prandtl number for heat transfer in rotating convection and explains the underlying mechanisms involving Ekman pumping and boundary layer interactions.

Findings

Maximum heat transfer occurs at an intermediate Prandtl number.

Heat transfer efficiency decreases when Pr is too low or too high due to boundary layer effects.

The study clarifies the role of thermal and kinetic boundary layers in heat transfer.

Abstract

Numerical data for the heat transfer as a function of the Prandtl (Pr) and Rossby (Ro) numbers in turbulent rotating Rayleigh-Benard convection are presented for Rayleigh number Ra = 10^8. When Ro is fixed the heat transfer enhancement with respect to the non-rotating value shows a maximum as function of Pr. This maximum is due to the reduced efficiency of Ekman pumping when Pr becomes too small or too large. When Pr becomes small, i.e. for large thermal diffusivity, the heat that is carried by the vertical vortices spreads out in the middle of the cell, and Ekman pumping thus becomes less efficient. For higher Pr the thermal boundary layers (BLs) are thinner than the kinetic BLs and therefore the Ekman vortices do not reach the thermal BL. This means that the fluid that is sucked into the vertical vortices is colder than for lower Pr which limits the efficiency of the upwards heat transfer.