A Non-local Formulation of the One-Phase Stefan Problem Based on Extended Irreversible Thermodynamics

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

“…Sobolev [34,35] solved different non-Fourier formulations under the assumption of constant interface velocity. To account for non-local effects, some authors [36][37][38] recently proposed a formulation of the Stefan problem based on Fourier's law with an effective thermal conductivity dependent on the size of the solid. From a microscopic point of view, Font and Bresme [39] published a work where non-classical effects in a melting process were observed using molecular dynamics.…”