The Stability of Planar Melting Fronts in Two-Phase Thermal Stefan Problems

The local stability of a plane horizontal melting front against small amplitude spatial perturbations is analysed when the front between the solid phase and the incompressible inviscid liquid phase is stationary or is advancing steadily into the solid phase. Both semi-infinite media and layers of finite depth are considered. It is found that all local perturbations are stable. The result holds whether the solid is at its melting point or not.