Experiments on the melting of a phase-change medium in a vertical tube yielded quantitative results both for the heat transfer and the timewise evolution of the melting front. The upper surface of the phase-change medium was bounded by an insulated air space, which accommodated the volume changes which accompany the melting process. Numerical solutions based on a pure conduction model were also performed for comparison purposes. It was found that the rate of melting and the heat transfer are significantly affected by fluid motions in the liquid melt induced by the volume change and by natural convection, with the former being significant only at early times. For melting initiated with the solid at the phase-change temperature, the experimentally determined values of the energy transfer associated with the melting process were about 50 percent higher than those predicted by the conduction model. Furthermore, the measured values of the energy stored in the liquid melt were about twice the conduction prediction. A compact dimensionless correlation of the experimental results was achieved using the Fourier, Stefan, and Grashof numbers. Initial subcooling of the solid substantially decreased the rate of melting, with corresponding decreases in the energy transfers for melting and sensible heat storage.