Experiments and supplementary numerical solutions have been performed to study the melting of a solid encapsulated in a horizontal tube. In one set of experiments, the solid was constrained not to move, while in a second set of experiments the solid was able to fall freely under gravity. In the latter (i.e. unconstrained) case, the lower portion of the solid was separated from the tube wall by a narrow, liquidfilled gap. The numerical solutions enabled the rates of melting at the lower and upper portions of the unconstrained solid to be determined. At a given duration of the melting period, the amount of mass melted in the unconstrained mode exceeded that melted in the constrained mode by 50-100%, with a similar gain in energy transfer. For the unconstrained mode, about 90% of the melting occurred at the lower portion of the solid. Photographic evidence demonstrated that the melting process in the constrained mode is intrinsically three-dimensional, while in the absence of end effects the unconstrained-mode melting is two-dimensional.