Mathematical Modeling of Flow and Heat Transfer Phenomena in Glass Melting, Delivery, and Forming Processes

Abstract

This article reviews the scientific and engineering principles and practices involved in the mathematical modeling of flow and heat transfer phenomena in industrial‐scale glass melting, delivery, and forming processes. The approach taken is to highlight the characteristic features of flow and heat transfer in each of the three processes, summarize the relevant transport and constitutive equations and boundary conditions, and illustrate practical applications of mathematical models. The article also describes modeling approaches used for auxiliary processes and phenomena associated with melting, delivery, and forming operations. Thus, modeling of batch melting, electric heating of glass melt, convection due to bubbling, combustion, turbulence, and viscoelasticity are discussed. Unlike melting and delivery processes, which share many similarities across the various glass industry segments, forming tends to be segment specific. So, the article focuses on one forming process (container) and, through it, emphasizes the key technical attributes of forming models. A selection of results is provided to bring out modeling capabilities and limitations. The article also provides a historical perspective on the development of advanced mathematical models and their industrial applications. Finally, key areas needing research and development are identified to further enhance the practical utility of mathematical models for the glassmaking processes.