The melting and solidification of nanowires

Abstract

A mathematical model is developed to describe the melting of nanowires. The first section of the paper deals with a standard theoretical situation, where the wire melts due to a fixed boundary temperature. This analysis allows us to compare with existing results for the phase change of nanospheres. The equivalent solidification problem is also examined. This shows that solidification is a faster process than melting; this is because the energy transfer occurs primarily through the solid rather than the liquid which is a poorer conductor of heat. This effect competes with the energy required to create new solid surface which acts to slow down the process, but overall conduction dominates. In the second section, we consider a more physically realistic boundary condition, where the phase change occurs due to a heat flux from surrounding material. This removes the singularity in initial melt velocity predicted in previous models of nanoparticle melting. It is shown that even with the highest possible flux the melting time is significantly slower than with a fixed boundary temperature condition.

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

“…They investigate an ice-water system and use the standard Gibbs-Thomson relation, a single value for density, a fixed temperature boundary condition and a Stefan condition taken from models of macroscale melting. Growth and melting of nanowires are considered in Florio and Myers (2016). They also employ the standard Gibbs-Thomson relation and a constant density, at the boundary they consider both fixed temperature and cooling conditions.…”

The Stefan problem with variable thermophysical properties and phase change temperature

“…This specifies the liquid velocity in equation (18). At the outer boundary the liquid velocity is simply (24) and integrate then the following relation is obtained…”

The one-dimensional Stefan problem with non-Fourier heat conduction

“…In practice, other forms of boundary conditions should be applied, such as the Newton cooling condition. This has been used in the modelling of melting of nanoparticles [44] and nanowires [45], and leads to a significant increase of the melting times. The cooling condition has also been used in a recent study by Hennessy et al [33], where a thorough asymptotic analysis of the Guyer-Krumhansl-Stefan problem is performed.…”