Axisymmetric modeling of the thermal cooling, including radiation, of a circular glass disk

Achieving correct tempering in thin glass is very important to prevent undesired stress and breakage. Computer simulation can elucidate and control the tempering process. For semitransparent materials like glass, heat transfer by thermal radiation is substantial; for thick glass, it may dominate over convection and conduction. The present paper investigates the tempering of thin glass. A circular glass disk supported by a metallic mold cools down by natural convection. The process can be modeled mathematically by coupling the heat and radiative transfer equation in the glass disk with the heat transfer in the support mold. Even at the glass and support mold interface, radiation exchange must be considered. Mechanical behavior is modeled using the mechanical equilibrium and applying the constitutive law for glass during cooling. For the numerical radiation simulation, the Abaqus® commercial software package was combined with an in-house C code. Based on the differences in temperatures and stresses between simulations that only take surface radiation into account and those that consider surface as well as internal radiation, it has been shown that, even for thin glass, internal radiation cannot be ignored.