A mathematical model for nanoparticle melting with size-dependent latent heat and melt temperature

Abstract

In this paper, we study the melting of a spherical nanoparticle. The model differs from previous ones in that a number of features have been incorporated to match experimental observations. These include the size dependence of the latent heat and a cooling condition at the boundary (as opposed to the fixed temperature condition used in previous studies). Melt temperature variation and density change are also included. The density variation drives the flow of the outer fluid layer. The latent heat variation is modelled by a new relation, which matches experimental data better than previous models. A novel form of Stefan condition is used to determine the position of the melt front. This condition takes into account the latent heat variation, the energy required to create new surface and the kinetic energy of the displaced fluid layer. Results show that melting times can be significantly faster than predicted by previous theoretical models; for smaller particles, this can be around a factor 3. This is primarily due to the latent heat variation. The previously used fixed temperature boundary condition had two opposing effects on melt times: the implied infinite heat transfer led to faster melting but also artificially magnified the effect of kinetic energy, which slowed down the process. We conclude that any future models of nanoparticle melting must be based on the new Stefan condition and account for latent heat variation.