A Combined Parameter and Function Estimation Approach for Prediction of Solidification/Melting Process in a Smelting Furnace

In a high-temperature smelting furnace, the bank layer acts as a barrier to protect the brick wall against the highly corrosive liquid slag. The present contribution proposes an inverse heat conduction method as a simultaneous parameter and function estimation approach to precisely predict the time-varying bank thickness from temperature measurements inside the refractory brick wall. The crucial parameters that affect the bank formation include the thermal conductivity of both slag and refractory brick wall, and the heat transfer coefficient between the external wall of the furnace and the surrounding environment. These parameters, as well as the time-varying heat load of the furnace, constitute the unknowns of the inverse solution. The enthalpy method is adopted to simulate the phase change process. A combination of the finite difference approximation and the adjoint problem is employed to compute the gradient vector. The sensitivity and adjoint equations for a furnace with non-constant density Phase Change Material are derived for the first time in the present study. The verification of the proposed hybrid method has been performed via several simulated experiments. The results for the case with errorless measurement showed that the error of the solid front is within the range of approximately ±2%.