Solidification and control of a liquid metal column

In this paper, two different 1D mechanistic models for the solidification of a pure substance are presented. The first model is based on the two-domain approach, resulting in 2 partial differential equations (PDEs) and one ordinary differential equation (ODE) with 2 boundary conditions, 2 interface conditions, and one initial condition: the Stefan problem.In the second model, the metal column is considered as one-domain, and one PDE is valid for the whole domain. The result is one PDE with two boundary conditions.The models are implemented in MATLAB, and the ODE solver ode23s is used for solving the systems of equations. The models are developed in order to simulate and control the dynamic response of the solidification rate. The control scheme is based on a linear PI controller.