In the work of Den Ouden the level-set method has been used to model the growth and dissolution in a steel alloy of the precipitate cementite and the diffusive phase austenite. The movement of the interface between the two phases is controlled by the diffusion of carbon and a reaction on the interface between the two phases. In this thesis research a similar model and method is given for a three-phased model with an extra diffusive phase. This third phase is ferrite, which nucleates on the interface of austenite and cementite when the temperature is dropped below the eutectoid temperature for a high carbon steel alloy. The difference between austenite and ferrite is the matrix structure of the iron atoms. This influences how much carbon the phase can contain. The difference in structure also results in different properties of the steel with respect to strength, hardness, etc. Modeling the growth of this three-phased steel alloy could eventually lead to useful insights for high-carbon steel production.\\
Extra difficulties arise by the introduction of a second diffusive phase. These difficulties concern defining sufficient interface boundary conditions between the different phases, capturing the different phases with the level-set method, creating a qualitative good mesh capturing these phases, recovering gradients on an interface and getting correct carbon concentration value in the triple points because of the interface boundary conditions. Except for the latter problem, the results of this research show decent results. The effect of cooling on the growth of ferrite is also shown and explained.