Numerical study on melting of phase change material in an enclosure subject to Neumann boundary condition in the presence of Rayleigh-Bénard convection

Abstract

This research study investigated the melting process of a phase change material (PCM), heated from the bottom, under Neumann boundary conditions, in the presence of Rayleigh-Bénard convection. The problem was numerically simulated for a range of domain sizes (1×1−8×8cm2) and heat fluxes (0.5−2W/cm2) using the enthalpy porosity technique, which is mostly applicable in cooling heat exchangers of electronic devices. Scaling analysis and the numerical results were employed to find the relationship between the Nusselt number and the solid-liquid interface location with other dimensionless parameters and develop correlations to predict the Nusselt number and the solid-liquid interface location for this type of melting problem. The results of this research could be used to better understand the heat transfer regimes formed during melting in an enclosure heated from the bottom and predict the Nusselt number and the solid-liquid interface location. It was found that the temperature and Nusselt number fluctuations are initiated in the coarsening subregime when the Rayleigh number was not larger than 106 and thus may not occur for small-sized domains. It can be concluded the coarsening and turbulent subregimes may not occur in small enclosures, while the melting process mostly occurs during turbulent subregiem in large enclosures. The numerical results revealed the fastest advance of heat transfer rate and consequently, solid-liquid interface occur during the formation of Bénard cells when the Rayleigh number was on the order of 104. The Nusselt number and solid-liquid interface location correlations developed in this study were later validated using two new cases of numerical data. The results revealed that these correlations could accurately predict the Nusselt number and solid-liquid interface location.