A mathematical model of a direct-fired continuous strip annealing furnace

A mathematical model of a direct-fired continuous strip annealing furnace is developed. The first-principle model uses the heat balance to describe the dynamic behavior of the strip and the rolls. The mass and the enthalpy balance are employed to calculate the mass, the composition, and the temperature of the flue gas. The heat conduction equation of the furnace wall is discretized by means of the Galerkin method. Furthermore, the convective and radiative heat transfer interconnect all submodels of the furnace. For the calculation of the radiative heat transfer, the zone method is utilized. Finally, the assembled model is reduced by applying the singular perturbation method. A comparison of simulation results with measurement data from a real plant demonstrates the accuracy of the reduced model. Moreover, due to the moderate computational effort, the model is suitable for real-time applications in control and dynamic optimization.