Many physical properties of materials, especially the melting point, change when the physical size of the material approaches the micro and nano scales. The problem considered in this paper is the inward melting of nanoparticles with a spherical geometry, and which initially are in a solid state with low temperature. For the nanoparticles, whose melting (freezing) point has been reported to decrease with decreasing particle radius, the numerical enthalpy method is used to solve the melting problem for an idealized two phase Stefan problem. The behaviour of the nanoparticle melting process compared with a particle melting process at the macro scale is also discussed. The numerical results show that the interfacial tension increases the melting rate of the nanoparticle.