Analysis of Radiative Heat Transfer in an Indirect-Fired Strip Annealing Furnace based on Integral Equations

A dynamical model of a tunnel furnace for strip annealing is proposed. The continuous furnace has a uniform cross section and is divided into several heating zones, where the local temperatures are used as model inputs. The presented model is tailored to control and optimization applications and takes into account the most important underlying physical phenomena, i.e., the energy balance of the strip and the heat transfer due to radiation. For determining the radiative heat transfer, radiation balances in the form of integral equations are used. Approximate solutions of these equations are obtained by means of the method of weighted residuals. To facilitate an accurate representation of the strip temperature, the strip motion is described based on Lagrangian coordinates, which is especially useful for capturing the temperature transition at welded joints between consecutive strips. The capabilities of the model are explored in simulation studies.