Due to the low thermal conductivity of phase change materials (PCMs), increasing efforts are dedicated to exploring methods of enhancing the thermal performance of PCM melting processes, among which is the appropriate geometric design of PCM enclosure to passively augment natural convection. This numerical study first confirmed and explained the fact that for PCM melting from an isothermal vertical wall, the vertical adiabatic wall opposite of the heating wall has a detrimental effect on the thermal performance. Alternatively, the optimal shape of the opposing wall is the one which strictly matches that of the free-forming melting front. The effect of the other constraints of the enclosure which are the top and bottom walls was then studied. We found that by tilting the top wall outwards generally accelerates heat transfer and latent heat storage due to beneficial alterations to natural convection within the molten PCM; whereas tilting the bottom wall has negligible effect. This study covers the parameter ranges of Prandtl number Pr = 40, Stefan number Ste = 0.33 and Rayleigh numbers Ra = 0 (pure conduction), 10(5) and 10(7). The shapes of the melting fronts computed here for the configurations of tilted top wall provide a useful reference and groundwork for the future geometric optimization of PCM enclosure. (C) 2018 Elsevier Ltd. All rights reserved.