One of the main challenges for latent thermal energy storage (LTES) systems is low heat transfer rates due to the low thermal conductivity of most phase change materials (PCM). Close-contact melting (CCM) can accelerate melting times in LTES systems but the current numerical techniques for solid liquid phase change have difficulties with accurately predicting this process. In this study, close-contact melting of PCM on an inclined surface is simulated using the enthalpy-porosity method in ANSYS Fluent. All PCM properties, including density, are temperature-dependent. In this way, phenomena such as natural convection, volume change and buoyancy between the solid and liquid are taken into account. The volume change is compensated by a gaseous expansion volume. Both 2D and 3D simulations are used to show discrepancy between state-of-the-art enthalpy porosity modelling and experimentally observed phenomena in the case of CCM. The mushy zone constant, which is set to 105 to allow motion of the solid bulk, causes the solid phase to deform as a highly viscous fluid instead of moving as a rigid body. The velocity differences inside the solid are more than 50 % of its sinking velocity. As a result, the movement of the solid resembles creep behaviour and the obtained CCM patterns are not physically accurate. Furthermore, the density difference between the solid and liquid phases causes an avalanching effect in the mushy zone, which artificially strengthens convection. In conclusion, the enthalpy porosity method exhibits significant limitations in accurately capturing close-contact melting phenomena.