Due to the poor thermal conductivity of the Phase Change Materials (PCMs), heat transfer performance of Latent Thermal Energy Storage (LTES) systems is usually unsatisfactory. In this work, a detailed numerical study is carried out to analyze the impact of fin geometry (including fin-length, fin-ratio and the angle between neighbor fins) and outer tube conductivity on PCM melting process; the influence of the natural convection in the horizontal sleeve-tube unit within the longitudinal fins is further examined. Results shows that small fin-ratio can reduce melting time, but not remarkably; the angle between neighbor fins has little impact on melting process, however, there is an optimization of the angle between neighbor fins to reduce melting time in the full-scale unit. The outer tube conductivity has great impact on melting process whether considering the natural convection or not. (C) 2015 Elsevier Ltd. All rights reserved.