A Fully Analytical Solution for 1-D Advection-Conduction Heat Transfer Problems with Non-Isothermal Solid-Liquid Phase Change

Abstract

This work presents an analytical solution for steady 1-D advection-conduction heat transfer in materials undergoing non-isothermal solid-liquid phase change. The model accommodates contrasting thermophysical properties between solid and liquid phases and mathematically handles the mushy zone using averaging techniques based on the solid fraction temperature derivative. Validated using numerical solutions based on the element-free Galerkin (IEFG) method across a range of Péclet numbers, the solution demonstrates excellent agreement regardless of the phase change temperature range or the microscopic model (equilibrium or non-equilibrium). This approach is applicable to processes such as wire arc additive manufacturing and secondary metallurgy.