Transient analysis of heat transfer with phase change in thermoplastic injection molding plays an important role to predict solidification in many material-manufacturing processes. Solidification results in a moving solid-liquid interface during filling. Two approaches of the finite element method, namely the apparent heat capacity model and the enthalpy model, for the solution of the Stefan problem in a fixed domain are examined. A two-dimensional, transient, non-newtonian and non-isothermal thermal field of a polymer in a rectangular domain is selected as study case.