Abstract
A mathematical model for the transient thermal behaviour of the main trough of a blast furnace (BF) is presented. The proposed model consists of the transient heat equation with mixed radiation-convection boundary conditions to model the cooling process. The heat equation is coupled with an integral equation posed on the inner boundary, which models the radiative heat exchange on the internal cavity formed by the trough and the refractory cover placed over the trough. The main scope of this work is to address the evolution of the temperature field during a full BF tapping. A reliable algorithm, capable of simulating entire trough campaigns, is presented.The open-source computing platform FEniCS is used to numerically solve the model using a finite element method. A manufactured solution test for the heat diffusion coupled with 2D nonlocal radiation is defined with the purpose of verifying the implementation, comparing the performance of different time discretization schemes and the adaptive time stepping algorithm. Concerning the BF tapping problem, the results show that during the time interval corresponding to a single tapping, the temperature in the radiation enclosure swiftly reaches the steady state value. Nevertheless, to obtain a steady state in the bulk of the solids, much longer time scales are needed due to the large thermal inertia of the structure.
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