The use of thermal energy storage systems is necessary in order to balance energy supply and demand, thus increasing the reliability of the energy systems as well as offering potential improvement in overall efficiency. Latent heat thermal energy storages have huge potential since they offer higher energy density than sensible heat storages and can provide a significant amount of heat over a small temperature difference. In this study, a two-dimensional axisymmetric computational fluid dynamics (CFD) model of an experimental shell-and-tube laboratory device for latent heat energy storage is developed. Stearic acid with a peak melting temperature of 69.95 °C is used as a phase change material (PCM). The enthalpy-porosity technique is used to model the melting and solidification processes of the PCM. The model takes into account the natural convection in the melted PCM as well as its thermal expansion using the volume of fluid multiphase model. The initial results show a mismatch between the numerical and experimental data caused by inaccuracy in PCM properties and unaccounted heat losses. Different approaches for model improvement via adjusting the PCM properties are considered based on the measurement data. The comparison of the results with the conduction-only simulations confirmed the importance of including the computationally demanding natural convection in the modelling of melting.