A novel two-dimensional continuum mixture theory model for paraffin wax melting in a cavity heating from side considering volume change

Abstract

Paraffin wax presents a considerable potential for thermal storage technologies, given its high latent heat. Therefore, the accurate and systematic modeling of its melting process bears significant importance. Yet, existing mathematical models fail to adequately address the velocity driven by the density change during the melting process. In this research, we introduce a novel model for paraffin wax melting within a square enclosure subject to side heating. Unlike current models, our approach posits that flow within the mushy zone is dictated by the mass equation, not Darcy’s equation, and thus excludes the usage of mushy zone constant. This assumption, premised on the idea that the density-deviation-driven flow precludes the bulk flow from penetrating the mushy zone, is confirmed through a carefully designed visual experiment. Utilizing our melting model, we construct a mathematical model anchored in the continuum mixture theory. Through a comparative analysis of results acquired by numerical methods and experimental data, we find that our innovative mathematical model effectively predicts real-world scenarios with remarkable precision. Furthermore, we explore the influence of flows within the mushy zone on the melting process. Our findings indicate a significant deviation in results when assuming zero velocity in the mushy zone, suggesting that the density-deviation-driven flow is numerically negligible. However, it is crucial to note the physical relevance of the density-deviation-driven flow in accurately predicting the melting process. The absence of this consideration allows the bulk flow in the liquid region to permeate the mushy zone, thereby introducing substantial errors.