Heat transfer in turbulent Rayleigh-B\'enard convection within two immiscible fluid layers

TL;DR

This study numerically explores heat transfer in turbulent Rayleigh-Bénard convection within two immiscible fluid layers, revealing how layer thickness and fluid properties influence the Nusselt number and flow regimes.

Contribution

It applies the Grossmann-Lohse theory to two-layer systems without free parameters, accurately predicting heat transfer and interface temperature, validated by simulations and experiments.

Findings

Two flow regimes identified based on layer thickness.

Heat transfer sensitivity varies with flow regime.

Theoretical predictions match numerical and experimental data.

Abstract

We numerically investigate turbulent Rayleigh-B\'enard convection within two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number $Nu$) in two-layer systems. Both two- and three-dimensional simulations are performed at fixed global Rayleigh number $Ra=10^8$, Prandtl number $Pr=4.38$, and Weber number $We=5$. We vary the relative thickness of the upper layer between $0.01 \le \alpha \le 0.99$ and the thermal conductivity coefficient ratio of the two liquids between $0.1 \le \lambda_k \le 10$. Two flow regimes are observed: In the first regime at $0.04\le\alpha\le0.96$, convective flows appear in both layers and $Nu$ is not sensitive to $\alpha$. In the second regime at $\alpha\le0.02$ or $\alpha\ge0.98$, convective flow only exists in the thicker layer, while the thinner one is dominated by pure conduction. In this regime, $Nu$ is sensitive to $\alpha$. To predict $Nu$ in the system in which the two layers are separated by a unique interface, we apply the Grossmann-Lohse theory for both individual layers and impose heat flux conservation at the interface. Without introducing any free parameter, the predictions for $Nu$ and for the temperature at the interface well agree with our numerical results and previous experimental data.