Comparative study of mass-accommodation methods and energy balances for melting paraffin wax in cylindrical thermal energy storage systems

Abstract

This study introduces two innovative methods for modeling how paraffin wax melts inside a centrally heated annular space. Both approaches tackle the challenge of volume changes during melting by ensuring total mass is conserved, keeping the material mass constant, and adding a new equation of motion. To manage these volume shifts in a cylindrical setup, one method allows the outer radius to expand or contract radially, while the other treats the extra liquid volume as a dynamic variable along the central axis. Each method’s energy–mass balance at the boundary between the liquid and solid yields equations that describe how the interface moves, with only slight differences that still respect mass conservation. When melting occurs rapidly, the steady-state values for both volume and interface position are directly linked to the densities of the liquid and solid forms. The methods were put to the test in a vertical annular region filled with para!n wax, where thermodynamic properties were fine-tuned by minimizing the gap between measured and predicted temperatures. The widely used local energy balance at the melting front can sometimes mislead, depending on starting conditions, boundaries, and material traits. In contrast, the total energy balance method aligns closely with equilibrium, as shown by its agreement with thermodynamic equilibrium in saturated mixtures, and it delivers much smaller errors than the local approach. In a melting experiment using para!n RT50 inside a thermally insulated cylinder, the local energy balance underestimated the melting front position by 2.4% to 6.9%, whereas the total energy balance method kept discrepancies between 0.28% and 5.71%.