Mathematical modeling of melting of nano-sized metal particles

A physicomathematical model is developed to describe melting of nano-sized aluminum and gold particles within the framework of a single-phase Stefan problem with allowance for the experimentally established fact of melting temperature reduction with decreasing particle radius. The time of melting of aluminum and gold nanoparticles is determined as a function of the particle radius and ambient temperature. At identical ratios of the ambient temperature to the melting temperature, the ratio of the time of melting of aluminum particles to the time of melting of gold particles is found to remain approximately constant and equal to 4.