Simulation of the solidification process during continuous casting

When casting mechanical parts, heat transfer occurs from the hot liquid metal to the water-cooled mould and the temperature decreases from that of the cast to the surrounding temperature. The process involves three successive stages: the cooling of the liquid metal, the solidification and finally the cooling of the solid metal. This work consists of the elaboration of a mathematical model governing the different processes mentioned above for zinc and aluminum. The modeling leads to a system of non-linear differential equations based on the heat equation, boundary and initial conditions which depend on the shape of the part, the mould and the cooling system. So, the aim of the study consists of the numerical determination of the temperature evolution and the solidification front versus time and the influence of the protective layer covering the inner surface of the mould for cylindrical billets. This problem is solved by the finite difference method.