Optimal set values of zone modeling in the simulation of a walking beam type reheating furnace on the steady-state operating regime

Highlights: • The adjoint equation is introduced to the PDE optimal control problem. • Lipschitz continuity for the gradient of the cost functional is derived. • The simulation time and iterations reduce by a large margin in the simulations. • The model validation and comparison are made to verify the proposed math model. - Abstract: In this paper, this study proposed a new method to solve the PDE optimal control problem by introducing the adjoint problem to the optimization model, which was used to get the reference values for the optimal furnace zone temperatures and the optimal temperature distribution of steel slabs in the reheating furnace on the steady-state operating regime. It was proved that the gradient of the cost functional could be written via the weak solution of this adjoint problem and then Lipschitz continuity of the gradient was derived. Model validation and comparison between the mathematics model and the experiment results indicated that the present heat transfer model worked well for the prediction of thermal behavior about a slab in the reheating furnace. Iterations and simulation time had shown a significant decline in the simulations of 20MnSi slab, and it was shown by numerical simulations for 0.4 m thick slabs that the proposed method was better applied in the medium and heavy plate plant, leading to better performance in terms of productivity, energy efficiency and other features of reheating furnaces.