Eigenfunction-based solution for one-dimensional solid-liquid phase change heat transfer problems with advection

Abstract

Heat transfer problems involving solid-liquid phase change occur in a wide variety of engineering applications. Most phase change heat transfer problems do not admit an exact analytical solution, and therefore, development of approximate analytical methods is of much interest. This work analyzes a one-dimensional phase change heat transfer problem in the presence of advection due to fluid flow. An approximate, eigenfunction-based solution for the temperature distribution and propagation of the phase change front with time is derived, which may be interpreted as a generalization of the classical quasistationary method. It is shown that even a single term of this series offers improved accuracy compared to the classical quasistationary solution. The method is shown to retain good accuracy even at large values of the Stefan number where approximate analytical methods usually lose accuracy. Results are shown to be in good agreement with numerical simulation results. As expected, in the absence of advection, results are shown to reduce to well-known Neumann and Stefan solutions. The impact of various problem parameters, including Stefan and Peclet numbers on the rate of phase change front propagation is investigated. The theoretical treatment presented here can also be used to solve similar mass transfer problems with a chemical reaction front where species advection may play a key role. This work improves the theoretical understanding of phase change heat transfer in the presence of advection, and may find applications in the design and optimization of engineering processes and systems involving phase change.