The influence of thermal convection in the thin molten layer on close-contact melting processes

In the present study, we develop and validate new modeling approaches for analyzing the influence of thermal convection in the thin molten layer on close-contact melting processes. We focus on the fundamental configuration of a solid vertical cylinder melting on a heated horizontal surface under forces induced by both gravity and a uniform pressure. First, we present a new model for the case of a heated isothermal surface. We show that analytical expressions for the temporal evolution of the melt fraction and the dimensionless molten layer thickness can be derived. Then, we demonstrate that our new model is an exact and generalized form of previously suggested modeling approaches. Moreover, we develop a new approximate model for the problem and extensively compare its predictions against the exact solution and other existing approximate approaches. Furthermore, we utilize our new model for analyzing the influence of the Stefan number and the dimensionless external force on the close-contact melting dynamics. In particular, our analysis reveals that the effectiveness of pressure-enhanced melting degrades as the dimensionless external force magnitude increases. Then, we derive, for the first time, a numerical model that predicts the influence of thermal convection under constant heat flux conditions. Also, we present two analytical models — traditional pure heat conduction model and a new approximate approach that takes into account the influence of thermal convection. These analytical approximations allow us to yield a new simple criterion for the thermal convection dominated regime under constant heat flux conditions. We extensively compare between the different modeling approaches and show that the pure heat conduction model overpredicts both the melting rate and the dimensionless molten layer thickness. On the other hand, our new approximate model provides accurate and quick estimations for the exact solution. Finally, we analyze via our model the effect of the external force magnitude on the close-contact melting process.