In the context of more electrical aircraft and reduction of fuel consumption, aircraft manufacturers are moving towards more complex and transient ice protection systems. The operating of these systems involves several unsteady heat and mass transfer phenomena. Modelling and numerical simulation play an important role in the investigation of these unsteady phenomena. In this paper, a model for unsteady ice build-up and melting is presented. The model is based on a triple layer assumption. In addition, a tailored numerical methodology for solving the governing partial differential equations is also described. It is based on a Galerkin finite element method and a Gauss-Seidel like implicit time marching scheme. The global method is validated and its capabilities are demonstrated on several cases.