The objective of this study is to report on the characterics of convective flow and heat transfer during metling process in order to provide design information for thermal energy storage systems which use phase change material. In present study, flow and heat transfer characteristics of the Phase Change Material in the Open Top Model (O.T.M) and in the Closed Top Model (C.T.M) were studied numerically by the control volume formulation using the algebraic non-orthogonal coordinate transformation. For the calculation procedure, the physical properties of fluid are assumed to be constant except density which is linely dependent on temperature in the bouyancy term of momentum equations. At start of melting process, the thickness of melting layer is assumed from the Stefan Problem assumption. The heat transfer results of Open Top Model and Closed Top Model are compared with the parameters of Grashof number and aspect ratio. It was found that heat transfer phenomena in melted region was greatly affected by buoyancy-driven natural convection and the melting distance of Open Top Model at the upper region is greater than that of Closed Top Model.