In this study, a numerical analysis is performed to investigate the freezing process of phase change materials (PCM) in a predesigned thermal energy storage (TES) device. This TES device is integrated with a milk storage cooling cycle operating under predefined practical conditions. Using this cooling unit, 100 litres of milk is kept cool at 4 degrees C for 48 hours before it is collected. A 2-D model of the TES device is developed in COMSOL Multiphysics to analyze the phase change performance of water-based PCMs. The variations of thermal properties with temperature during the phase change are considered in the analysis. The model is used for exploring the solidification process of PCMs inside the TES device. Temperature variations with time, ice formation, and the impacts of boundary conditions are investigated in detail. Water PCM shows better characteristics in the solidification process in comparison to eutectic PCMs, which is mainly due to the differences between phase change temperatures of the PCMs.