The results of a numerical investigation of the melting of a PCM occupying an axisymmetric volume in the presence of gravity are presented. The PCM is held between two circular supports maintained at different temperatures. The melting process, which is analyzed for n-octadecane, is affected by a combination of thermocapillary and natural convection. If the PCM is heated from above, the convective motion driven by the thermocapillary force is opposed by the buoyant force, which reduces the heat transfer rate. If the PCM is heated from below, natural convection acts in the same sense as thermocapillary convection and the heat transfer rate is increased. The volume $$\mathcal {V}$$
V
of the PCM relative to an ideal cylinder, which selects the shape of the PCM/air interface, is found to play an important role. The overall effect of natural convection on heat transfer is characterized by the ratio of the melting time in microgravity to that of the same system with gravity. This gain factor is greater (less) than unity when heating from below (above) and depends strongly on $$\mathcal {V}$$
V
, particularly for smaller PCM volumes.
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