The classical formulation for the Stefan problem at the nanoscale does not work because the melting temperature and the effective latent heat decrease with the nanoparticle size. In this work, a model for the effective latent heat is corrected because it does not correspond to the definition of latent heat. This model is used to see the consequences of imposing a Dirichlet boundary condition instead of a convective boundary condition. To do it, the liquid and the solid problem are simplified using a perturbed solution to reduce the Stefan problem into a first order ODE.