Theoretical study of solidification phase change heat and mass transfer with thermal resistance and convection subjected to a time-dependent boundary condition

The solidification of phase-change materials (PCMs) is a key process that occurs commonly in materials science and metallurgy, such as in the casting of alloys and energy management systems. There is a lot of literature in this area that assumes the PCMs are in close contact with the heat source or sink. However, a non-freezing wall frequently encloses them in practical situations. This work presents a phase change problem that describes the solidification of a semi-infinite PCM with thermal resistance. We assume that time-dependent heat flux drives the solidification process. The PCM first convert into mush and then into solid, which leads to a three-region problem. The current study accounts for both conduction as well as convection heat transfer mechanisms. Unfortunately, the exact solution to such problems with time-dependent flux-type boundary conditions may not be possible. Thus, there is considerable interest in deriving the analytical solution. The space–time transformation yields the analytical solution to the problem. A numerical example of $\mathrm{Al}-\mathrm{Cu}$ alloy with $5\text{\%}\mathrm{Cu}$ is presented to demonstrate the current study. Thermal resistance shows a pronounced impact on the temperature field. Lower thermal resistance offers faster solidification rate. It is found that as the heat transfer constant increases, the rate of propagation of solid–mush and mush–solid interfaces gets enhanced. In addition, the growth of thermal resistance is of linear nature, with variation in the value of $Q$. The solidified region has higher concentration than the mush region. The current study is applicable to both eutectic systems and solid solution alloys.