The present study deals with melting in a geometry suitable for Latent-Heat Thermal Energy Storage (LHTES) systems, which are of importance for future industrial installations utilizing solar energy or waste heat. The intrinsically high thermal resistance of phase-change materials (PCM) can be remedied by taking advantage of close contact melting (CCM), where the solid phase is separated from a hot surface by only a thin liquid layer. The basic CCM takes place on a horizontal flat surface, but during the last decade its application in various finned LHTES units has been demonstrated experimentally and analyzed numerically.Specifically, the configuration studied in the present work is relevant to a horizontal double-pipe concentric storage unit with a longitudinally finned inner tube. While this rather simple geometry has been extensively studied in the past, the present work is completely novel in its demonstration and analysis of simultaneous close-contact melting on two generally asymmetric surfaces created by the longitudinal fins. A unique experimental apparatus is introduced, based on the so-called 'Mercedes' configuration of the fins. It is designed transparent, allowing for real-time observation of melting sequences. Close-contact melting is achieved by supplying heat to the outer shell of the unit: the solid phase is detached from the shell and moves, by translation and rotation, in the liquid phase. The results from these experiments demonstrate the feasibility of CCM on two asymmetric walls within this system, hinting at the potential for optimizing the melting rate by utilizing a larger portion of the extended surface for CCM.A key component of this study is the development of a reliable numerical approach, which goes beyond the limitations of widely-applied enthalpy-porosity method and combines the general enthalpy formulation, convective heat transfer and general rigid body motion that includes rotation. Therefore, a new numerical model has been devised, using an in-house code realized in MATLAB. A full set of the governing conservation equations is solved using a finite-difference framework, integrated with advanced numerical methods for the fluid-solid interaction and an enthalpy formulation for the phase change process. The model is validated carefully, and then numerical studies are conducted to elucidate the melting process.The present paper presents a further proof of the special role that close-contact melting (CCM) can play in properly designed thermal energy storage units and finned systems in general. It is demonstrated that the fins, when properly designed and oriented, can induce CCM in their vicinity, contributing to a very significant increase in the melting rate, which reflects charging of the unit.