Evolution of melting boundary in the solid–liquid phase-change problem involves nonplanar geometry due to the presence of Rayleigh–Benard convective cells in the melted region. The transition of flow behavior from steady to oscillatory in the melt zone is particularly an interesting phenomenon to study. In this work, numerical investigation of melting of low Prandtl number materials in a square cavity with two adjacent heated walls has been carried out using total enthalpy-based lattice Boltzmann method. The local thermal and fluid flow behavior within a moving melting front has been investigated. The influence of natural convection in the melt zone has been observed for two different cases: (1) heating from a corner formed by the left and the bottom walls and (2) heating from a corner formed by the top and the right walls. The effect of Rayleigh number in the range of Ra = 102–5 × 107 on the convective flow field is evaluated for a typical parametric value of Stefan number of 0.01 and Prandtl number of 0.025. Results show distinct convection rolls at the melt zone for the cases under investigations. Evolution of flow fields in the melt zone has been described by a set of isotherms and streamlines for both the cases. The interface fronts for both the cases are initially of convex shape, and around Fourier number of 0.5 turn into concave shape, as viewed from the direction of the movement of melting front. At higher Ra, the rates of melting for top-right side and left-bottom side heated cavities are nearly the same above Fourier number of about 1.2. The average heat flux from the walls scales with Ran , where n is a constant which varies between 0.98 and 1.11. In the melt region, the instability pattern of flow and thermal field changes with the change of effective melt area. Transition to periodic flow is observed at Ra of 7.5 × 106 for case 1 and 2.2 × 107 for case 2, respectively.