The melting and solidification of nanowires

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.