A numerical investigation of transient natural convective heat transfer with coupled phase change is presented. The numerical model attempts to capture the solid–fluid interface using a fixed-grid solution and is applied to two pure substance cases found in published literature, one considering the melting of 95% pure Lauric acid and the other involving the freezing of water. The governing equations are solved in a manner such that if the temperature falls below the freezing isotherm then the convection terms in the equations of motion are effectively disengaged. Variations in the specific heat of the material are incorporated in order to account for the phase change. A non-Boussinesq approach is considered which accounts for any density extrema in the flow, particularly for the density inversion found in water. In both of the cases considered the phase change occurs between fixed temperature boundaries and Rayleigh numbers rest well within the laminar flow regime. From the results obtained it is demonstrated that a relatively simple numerical technique can be applied to capture the physics of buoyancy-driven melting and freezing and that the results are in reasonable concurrence with experimental data.