Heat transfer in turbulent Rayleigh–Bénard convection through two immiscible fluid layers

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