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

## TL;DR

This paper models one-dimensional solidification using non-Fourier heat conduction theories, revealing that heat flux measurements better indicate non-classical heat transport during phase change.

## Contribution

It introduces a reduced ODE system for non-Fourier solidification, linking heat flux to non-classical heat conduction effects during phase change.

## Key findings

- Good agreement between reduced model and simulations
- Small differences in silicon solidification kinetics
- Significant deviations in heat flux evolution

## Abstract

We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time regimes we are able to reduce the problem to a system of two coupled ordinary differential equations describing the evolution of the solid-liquid interface and the heat flux. The reduced formulation is in good agreement with numerical simulations. In the case of silicon, differences between classical and non-classical solidification kinetics are relatively small, but larger deviations can be observed in the evolution in time of the heat flux through the growing solid. From this study we conclude that the heat flux provides more information about the presence of non-classical modes of heat transport during phase-change processes.