Thermal modelling and optimization-based control of a batch diffusion furnace

A mathematical model based on physical principles is presented for the thermal behavior of a batch diffusion furnace and its load. This model is designed to both remain graspable for optimization-based control design and preserve the essential (nonlinear) effects. Particular attention is paid to radiation, which constitutes the principal mode of heat transfer, is the dominating nonlinearity and significantly adds to the model complexity. Using finite volume semi-discretization with the net radiation method and semi-analytically determined radiation view factors yields a modular, easily adaptable mathematical model. An example heat-up problem is solved in a simulation environment using dynamic optimization.