Experiments were performed to investigate the melting of a phase-change medium contained in a circular tube when the heating at the tube wall is nonuniform around the circumference. Melting experiments for uniform heating conditions were also carried out to provide baseline information. For a vertically oriented tube with heating confined to half the circumference, the amount of melting, relative to that for uniform heating, was reduced by 45% in the early stages of melting and by 35% in the later stages. When the containment tube was inclined to the vertical, the decreased melting associated with the nonuniform heating was recouped at inclinations large enough to cause the solid to be pressed by gravity against the heated portion of the tube wall. This direct contact mode of melting was achieved consistently at an inclination of 30° and intermittently at an inclination of 15°. The use of a low-friction base surface for supporting the melting solid was shown to favor the direct contact mode. Timewise measurements of the shape of the melting solid enabled identification of the pattern of melting for the different types of heating and the various inclinations. Results are also presented for the timewise variation of the stored energy.