Scale Analysis of Convective Melting With Internal Heat Generation

Using a scale analysis approach, we model phase change (melting) for pure materials which generate internal heat for small Stefan numbers (approximately one). The analysis considers conduction in the solid phase and natural convection, driven by internal heat generation, in the liquid regime. The model is applied for a constant surface temperature boundary condition where the melting temperature is greater than the surface temperature in a cylindrical geometry. We show the time scales in which conduction and convection heat transfer dominate.