The role of natural convection on solid-liquid interface motion during constrained melting within a horizontal cylindrical capsule was investigated. A numerical code is developed using an unstructured finite-volume method and an enthalpy porosity technique to solve for natural convection coupled to solid-liquid phase change. Flow patterns for different Rayleigh numbers are presented. The resulting melt shapes and the temperature in the PCM provide conclusive evidence of the importance of natural convection on heat transfer in the melt region.