In this study, the effect of surface areas of heat transfer fins on the melting and solidification process of phase change material in thermal energy storage was investigated. The melting and solidification process of the PCM in the test domain was investigated by experimental and numerical analysis. Non-melting regions in TES were identified and special heat transfer fins were designed to melt these regions. The designed fins were compared with the heat transfer fins which are highly preferred in the literature. The results showed that the surface area of fins has positive effects on heat transfer, but negative effects on natural convection current. The surface area of Fin 1_C extending throughout the TES is 5 times the surface area of Fin 2 designed in the scope of the study. PCM melted with Fin 2 in 64 min, but it melted with Fin 1_C in 60 min. The best melting process in the melting of PCM (Paraffin wax - RT 55) in the TES was provided with Fin 4 design. The melting time has been improved by 65% with the specially designed Fin 4. In all thermal energy storage designed and considered during the solidification process, no significant difference could be obtained. The main reason for this is thought to be the effect of overcooling.