Mathematical modelling and numerical simulation of the heat transfer in a trough of a blast furnace

In this article, we address the numerical simulation of the cross section of a blast furnace (BF) trough to ensure its durability based on the location of the critical isotherms, so the objective is to know the heat transfer from the trough walls in contact with the hot liquids flowing inside (hot metal and slag) to the lining of the trough, which is in contact with air. With this aim, we propose a 2D heat transfer mathematical model which is solved using a finite element method (FEM). The proposed model is based on energy balance equation, and Fourier's law to relate the heat flux and the temperature gradients are assumed. The convective and radiative heat transfers as well as Dirichlet temperatures are included as boundary conditions, and the radiation view factor concept is considered, introducing an additional nonlinearity in the model. This factor plays a key role in the radiation heat transfer between the slag surface and the wall inside the trough in contact with air, which receives the radiation of the slag. The proposed 2D heat transfer model is applied in two sections: at the middle of the trough and downstream. The numerical simulations are performed using a FEM, and their numerical results are compared with the experimental data from a measurements campaign in a BF. The results demonstrate that the model can reproduce quite accurately the temperature distribution in BF troughs.