Heat transfer in turbulent Rayleigh-Bénard convection with two immiscible fluid layers

We numerically investigate turbulent Rayleigh-Bénard convection with two immiscible fluid layers, aiming to understand how the layer height 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 = 10⁸, Prandtl number Pr = 4.38 and Weber number We = 5. We vary the thickness of the upper layer 0.01 < α <  0.99 and the thermal conduction coefficient ratio 0.1 < λ_k < 10 of the two layers. Two flow regimes are observed: In the first regime at 0.02 < α < 0.98, convective flows appear in both layers and Nu is not sensitive to α. In another regime at α < 0.02 or α > 0.98, convective flow only exists in the thicker layer, while the thinner layer is dominated by pure conduction. In this regime, Nu is sensitive to α. To predict Nu in the two-layer system with the interface between the two layers does not break up, we apply the Grossmann-Lohse theory in the individual layers, imposing heat flux conservation at the interface. The predictions for Nu and for the temperature at the interface well agree with our numerical results and previous experimental data.