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 ($1\times 1-8\times 8$ $\mathrm{c}{\mathrm{m}}^2$) and heat fluxes ($0.5-2$ $\mathrm{W}/\mathrm{c}{\mathrm{m}}^2$) 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.

这项研究研究了在存在瑞利-贝纳德对流的情况下，在诺伊曼边界条件下从底部加热的相变材料（PCM）的熔化过程。对于一系列域大小，对该问题进行了数值模拟（$\mathrm{1个}\times \mathrm{1个}-8\times 8$ $\mathrm{C}{\mathrm{米}}^2$）和热通量（$0.5-2$ $\mathrm{w\; ^}/\mathrm{C}{\mathrm{米}}^2$）使用焓孔隙率技术，该技术通常适用于电子设备的冷却热交换器。利用定标分析和数值结果来找到Nusselt数和固液界面位置与其他无量纲参数之间的关系，并开发相关性以预测此类熔化问题的Nusselt数和固液界面位置。这项研究的结果可用于更好地了解从底部加热的外壳中融化过程中形成的传热机制，并预测Nusselt数和固液界面位置。发现当瑞利数不大于10 ⁶时，温度和Nusselt数波动是在粗化子区域中引发的。因此对于小型域可能不会发生。可以得出结论，在小型机壳中可能不会出现粗化和湍流子状态，而在大型机壳中，湍流过程主要发生在湍流子过程中。数值结果表明，传热速度最快，因此，当瑞利数为10 ⁴时，在贝纳德细胞形成过程中发生了固液界面。后来使用两个新的数值数据案例验证了本研究中开发的Nusselt数和固液界面位置的相关性。结果表明，这些相关性可以准确地预测Nusselt数和固液界面位置。