Evaluating of melting-ice process in a vertical pipe with consideration of net sensible heat

Abstract

In ice-melting process, motion of liquid–solid interface is complicated due to moving boundary, which is also called Stefan interface problem. Although the Stefan model has been widely utilized, it frequently overestimates the melting rate. In the present study, the net-sensible-heat of the phases are taken into account as an additional physical effect to the Stefan model for one-phase case and two-phase cases. The proposed model applied differential forms of energy conservations for each phase and the whole system with a practical or engineering approach. For the particular case of an ice-melting process in a vertical pipe, the results showed that, for the one-phase case, the migration of the interface of the proposed model was lowered by 18.5%, 12.0% and 4.3% compared to the Stefan model, Neumann solution and “modified Berggren Equation”, respectively, after a simulation period of 25 days. For the two-phase case, a similar trend of interface migration was achieved for the proposed and Stefan models. The former was approximately 11.4% lower than the latter after about 12 days, following this the difference between the models thereafter remains stable for the remainder of the simulation period. Additionally, the proposed model’s sensitivity is also examined by varying the inputs of surface temperature, initial temperature, and pipe-length change. It was observed that the coefficients of proportionality of the proposed models and relevant models have reasonable agreement.