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Radiative Heat Transfer and Applications for Glass Production Processes

  • Martin FrankEmail author
  • Axel Klar
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2010)

Abstract

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.

Keywords

Radiative Transfer Half Space Transfer Equation Radiative Transfer Equation Discrete Ordinate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgements

We wish to thank all our collaborators and co-authors, in particular B. Dubroca, T. Götz, J. Lang, E.W. Larsen, M. Seaïd, G. Thömmes, R. Turpault and R. Pinnau. Parts of this work have been taken from the articles [18, 23, 24, 25, 27, 38, 47, 48, 76, 85]. This work was supported by German Research Foundation DFG under grants KL 1105/7 and 1105/14.

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.University of KaiserslauternKaiserslauternGermany
  2. 2.Fraunhofer ITWMKaiserslauternGermany

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