The phase change problem in materials with internal heat generation in a cylinder

We analyze the evolution of the solid-liquid front during melting and solidification in materials with constant internal heat generation, under prescribed temperature and heat flux conditions at the boundary of an infinite cylinder. We employ a sharp interface approach and assume that the motion of the front is slow relative to the temperature changes in both phases of the material. We derive infinite series solutions for the temperature in each phase and a nonlinear first-order differential equation for the evolution of the interface. Additionally, we solve the problem using the catching of the front into a node method and the Ansys Fluent enthalpy-porosity method. The latter incorporates a mushy zone that is a mixed solid-liquid transition zone. All three methods provide consistent results, especially when the mushy zone is taken into account. The series and front catching solutions develop a finite time overheated zone during melting, whereas the enthalpy solutions do not exhibit this phenomenon. We show that the evolution of the overheated and mushy zones is very similar in shape and time for both boundary conditions.