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This paper presents a numerical and experimental analysis of the heat transfer process that takes place while melting a solid material, in a rectangular enclosure. Natural convection is present in the melt layer, and the solid phase is assumed to be isothermal. Very detailed and precise experimental results are given that are used to validate a particularly rapid numerical code. Some insights into the kinetics of the melting process lead to a deeper understanding of the coupling between convection and phase change and allow us to propose a simple algebraic correlation that predicts the time evolution of the melting front to within 5 percent.