A fully analytical solution for 1-D advection-conduction heat transfer problems with non-isothermal solid↔liquid phase change

An unprecedented analytical solution for steady 1-D advection-conduction thermal problems with substances undergoing non-isothermal solid↔liquid phase change is introduced in this communication. The proposed solution allows for solid and liquid phases with contrasting physical and transport properties, and the mathematical handling in the mushy zone is ensured via averaging techniques based on the solid phase fraction temperature derivative. The suitability of such approach is demonstrated by comparison with accurate (refined) numerical solutions based on the improved element-free Galerkin (IEFG) method, and tested for Péclet (Pe) numbers ranging from 0.1 to 20. The solution is applicable to different microscopic solid↔liquid phase change models, i.e. equilibrium and non-equilibrium rules. This analytical solution can be applied in the analysis of ferro-alloys wire feeding in secondary steel-making, and also material addition in wire arc additive manufacturing (WAAM) processes. The model developed has exhibited an excellent agreement with the numerical solutions for the entire range of Péclet numbers considered, regardless both the phase change temperature range (difference between solidus and liquidus temperatures) and the microscopic model considered.