Constant mass model for the liquid-solid phase transition on a one-dimensional Stefan problem: Transient and steady state regimes

As a consequence of mass conservation, a subtle change in the thermal balance at the interface (Stefan's condition), is needed. The numerical and semi-analytical solutions for the improved model and the asymptotic values for the interface position, system length, temperature profile and liquid and solid masses, are compared. In the case of isothermal boundary conditions, due to mass conservation, more general asymptotic values are found. A good agreement between the numerical and semi-analytical solutions and the asymptotic time values is observed. In the case of adiabatic boundary conditions, the interface position at thermodynamic equilibrium can be overestimated by the numerical and semi-analytical solutions if only conservation of energy is considered. Finally, by applying mass conservation, a significant error decrease between the numerical and semi-analytical solutions and the predicted values at thermodynamic equilibrium is observed.