Consequences of total thermal balance during melting and solidification of high temperature phase change materials

The incorrect behavior of numerical solutions in thermally isolated systems has been explained recently by considering volume changes during the liquid-solid phase transition, through total mass conservation. In this work, examples are found where the numerical solutions still show an incorrect behavior in thermally isolated systems. The solutions at thermodynamic equilibrium reveal the existence of pathological cases in some materials, even though, the total mass of the system is conserved. Through the examples shown in this work, a conceptual error is found in the equation of motion for the interface. The system size and amount of melted or solidified mass obtained from a local energy-mass balance at the interface are not invariant and can overestimate or underestimate the stationary state values. The proposed equation of motion for the interface is found by imposing energy conservation in adiabatic systems, and thermodynamic equilibrium values are well reproduced through the proposed equation. Energy conservation leads to an extra term in the equation of motion for the interface, which is proportional to the density difference between liquid and solid phases. Additionally, in systems with isothermal-adiabatic boundary conditions, total thermal balance through the entire system is proposed. Total thermal balance also leads to an extra term in the equation of motion for the interface, which can have significant contributions depending on the type of material and operating conditions. Finally, the dynamics of the phase transition can be pictured by introducing an equivalent latent heat of fusion that incorporates the effects of total thermal balance.