Theoretical modeling of a phase change heat transfer problem with a pre-melted or pre-solidified region

Abstract

Heat transfer problems involving phase change occur in a wide variety of engineering applications. Except a few simple cases, most phase change problems do not have an exact solution, and a number of approximate analytical methods have been developed. This paper presents a theoretical solution for a one-dimensional phase change problem that includes a pre-melted or pre-solidified length between the region of interest and a time-dependent temperature boundary condition. Such a scenario can occur in multiple engineering applications when the heating or cooling process is intermittent in time. The theoretical approach involves iteratively solving the coupled problem involving thermal conduction and phase change, utilizing a perturbation-based method for the phase change problem with a time-dependent boundary condition. The resulting theoretical solution compares well with numerical simulations. Results are used for analyzing the effect of geometry, thermal properties and other parameters on the nature of heat transfer and phase change in this problem of much technological importance. These insights may be helpful in analyzing and optimizing heat transfer in several applications such as phase change based cooling of Li-ion cells during intermittent operation.