Nonlinear Inverse Heat Transfer Analysis in a Melting Furnace Using a High-order Modified Levenberg-Marquardt Method

The nonlinear inverse heat transfer problem is important in numerous scientific research and engineering applications. Considering the erosion-corrosion phenomenon of refractory brick walls in the melting furnace is a necessary research process for safe operation of the furnace. In this paper we present a nonlinear inverse heat transfer analysis approach for predicting wall erosion and time-varying thickness of the bank layer covering the inner surface of refractory brick walls of a melting furnace. The direct problem is a nonlinear one-dimensional mathematical model for the phase change process using the enthalpy method, which describes the concentrate melting process in the melting furnace. The numerical solution of this mathematical model uses finite difference method. In the nonlinear inverse heat transfer problem considered here, the time-varying heat flux and the thickness of the bank layer are unknown. We aim to determine these unknown parameters using temperature measurements obtained from the sensor. The inverse approach is based on the high-order modified Levenberg-Marquardt method (HMLMM) combined with the Broyden method. HMLMM combined with Broyden method can save a lot of Jacobian calculations and reduce the computational cost. Numerical results show that the proposed method is computationally more efficient than the inverse method in which the conventional Levenberg-Marquardt method (LMM) is used.