Phase Change Materials (PCMs) are one of the most promising materials to develop thermal energy storages in Heating, Ventilation, and Air-Conditioning (HVAC) systems to supply alternative energy during peak demand hours. In this work, a three-dimensional Computational Fluid Dynamics model was created with ANSYS Fluent to determine an optimum thickness for a PCM evaporator in a proposed high-efficiency refrigerator to supply a suitable amount of cold thermal energy during compressor off time while using refrigerator cabin space efficiently. Refrigerator geometries were created with varying PCM thicknesses of 2-6 cm, with 1 cm increments. Simulations to determine the time taken for each PCM material to completely discharge/melt were conducted. The concept of the simulation was of the onset of compressor off time and the onset of the introduction of heat into the refrigerator system. The discharging time per unit mass of PCM (τ_disch), thermal power discharged, and volume coverage of each configuration were factors used to determine the most efficient PCM thickness. It was observed from the results that with increasing PCM thickness, there was a corresponding increase in total heat transferred from the thermal energy storage systems to the refrigerator cabins resulting in lower air temperatures and longer hours of temperature stability. The 2 cm geometry emerged as the best choice since it had the lowest volume coverage of 9.5% and a comparable cold thermal power supply of 230.4 W versus the 233.3 W of the 5 cm geometry which had the highest τ_disch value.