Radiative heat transfer and applications for glass production processes

In glass manufacturing, a hot melt of glass is cooled down to room temperature. The annealing has to be monitored carefully in order to avoid excessive temperature differences which may affect the quality of the product or even lead to cracks in the material. In order to control this process it is, therefore, of interest to have a mathematical model that accurately predicts the temperature evolution. The model will involve the direction-dependent thermal radiation field because a significant part of the energy is transported by photons. Unfortunately, this fact makes the numerical solution of the radiative transfer equations much more complex, especially in higher dimensions, since, besides position and time variables, the directional variables also have to be accounted for. Therefore, approximations of the full model that are computationally less time consuming but yet sufficiently accurate have to be sought. It is our purpose to present several recent approaches to this problem that have been co-developed by the authors.