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We propose an analytical model to estimate the interface temperature$\Theta_{\Gamma}$ and the Nusselt number $Nu$ for an evaporating two-layerRayleigh-B\'enard configuration in statistically stationary conditions. Themodel is based on three assumptions: (i) the Oberbeck-Boussinesq approximationcan be applied to the liquid phase, while the gas thermophysical properties aregeneric functions of thermodynamic pressure, local temperature, and vapourcomposition, (ii) the Grossmann-Lohse theory for thermal convection can beapplied to the liquid and gas layers separately, (iii) the vapour content inthe gas can be taken as the mean value at the gas-liquid interface. We validatethis setting using direct numerical simulations (DNS) in a parameter spacecomposed of the Rayleigh number ($10^6\leq Ra\leq 10^8$) and the temperaturedifferential ($0.05\leq\varepsilon\leq 0.20$), which modulates the variation ofstate variables in the gas layer. To better disentangle the variable propertyeffects on $\Theta_\Gamma$ and $Nu$, simulations are performed in twoconditions. First, we consider the case of uniform gas properties except forthe gas density and gas-liquid diffusion coefficient. Second, we include thevariation of specific heat capacity, dynamic viscosity, and thermalconductivity using realistic equations of state. Irrespective of the employedsetting, the proposed model agrees very well with the numerical simulationsover the entire range of $Ra-\varepsilon$ investigated.

Evaporating Rayleigh-B\'enard convection: prediction of interface temperature and global heat transfer modulation