Construction and Evaluation of a Numerical Model for Heat Transfer in a Ladle During Pre-heating : A Finite Volume Approach to the Diffusion Equation using Julia

Abstract: Heat transfer is key to understanding many processes in engineering. At a steel mill heat transfer is absolutely crucial to understanding most of the processes. One such a process is the pre-heating of a freshly relined ladle. The goal of this project was to develop code which could solve the diffusion equation, in an arbitrary three-dimensional geometry, subject to Dirichlet, Robin, Neumann, and certain kinds of non-linear boundary conditions. In order to approximate the solution the code uses a cell centred finite volume methodology. In order to verify the computational correctness of the code it was used on three simple cases where analytic solutions are known, a rarity for three-dimensional boundary value problems. A mathematical model for the heat conduction inside a ladle at Ovako’s site in Hofors was developed. The model was evaluated based on measurements on the outside of the ladle as well as from a temperature probe inside the bottom of the ladle. The model was found to adequately agree with the measured temperature. The code can thus be used to find a more optimal heating regiment of the ladle, possibly reducing emissions.