Numerical solutions for freezing of a phase change medium contained in a sealed vertical tube were carried out using the methodology developed in the preceding paper in this issue of the journal. The solutions took account of natural convection in the unfrozen liquid and heat conduction in the tube wall, as well as heat conduction in the frozen layer. For the investigated problems, the freezing was initiated when the external surface of the tube was exposed to a fluid environment whose temperature was lower than the phase change temperature. The numerical solutions provided information on the response of the freezing process to changes in the tube wall thickness and tube wall material and to changes in the convective heat transfer coefficient at the external surface of the tube. For each case, time-dependent results were obtained for the amount of frozen mass, the profile of the solid-liquid interface, and the temperature distributions at the inner and outer surfaces of the tube. Comparisons were made between the numerical predictions and experimental data, and good agreement was found to prevail.