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

• We propose an analytical model to estimate the interface temperature $\Theta_{\Gamma}$ and the Nusselt number $Nu$ for an evaporating two-layer Rayleigh-B\'enard configuration in statistically stationary conditions. The model is based on three assumptions: (i) the Grossmann-Lohse theory for thermal convection can be applied on the liquid and gas layers separately, (ii) the vapour content in the gas can be taken as the mean value at the gas-liquid interface and (iii) the bulk gas temperature can be determined neglecting the contributions of the thermal boundary layers. The resulting model can accommodate non-Oberbeck-Boussinesq effects in the liquid and the gas phases, as well as the variation of the liquid height due to evaporation. To obtain a simplified scaling between $Nu$ and the Rayleigh number $Ra$, we specify the model for the case of an Oberbeck-Boussinesq liquid and a gas phase with uniform properties except for the gas density and the vapour diffusion coefficient, which are functions of thermodynamic pressure, local temperature and vapour composition. We validate this simplified setting using direct numerical simulations for $Ra=10^6, 10^7$ and $10^8$ and for four values of the temperature differential $\varepsilon=0.05,0.10,0.15$ and $0.20$, which modulates the change of state variables in the gas layer. The proposed model agrees very well with the numerical simulations in the entire range of $Ra-\varepsilon$ investigated.

Publikations- och innehållstyp

vet (ämneskategori)

art (ämneskategori)