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IMA Journal of Management Mathematics 1999 10(1):55-86; doi:10.1093/imaman/10.1.55
© 1999 by Institute of Mathematics and its Applications
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A mathematical model for the heat treatment of glass fabric sheets

A. BUIKIS and A. D. FITT

Institute of Mathematics, Latvian Academy of Sciences and University of Latvia, 1, Akademijas l. LV-1524 Riga, Latvia
Faculty of Mathematical Studies, University of Southampton Southampton SO17 1BJ, England

During the industrial process of glass fabric manufacture in Latvia, an oil that has earlier been added to the fabric must be removed. To accomplish this, the fabric is passed through a furnace where the oil is removed by burning. It is known that the oil removal process reduces the tensile strength of the fabric. The burning process is analysed via a simple mathematical model that allows the furnace parameters to be optimized. Using some of the well-established properties of glass, it is shown that it is the cooling rather than the heating process that adversely affects the final product. A thermoviscoelastic model is developed to predict the permanent stress in the glass fabric. Some suggestions for modifications to the process are also examined, and it is shown that, to a large extent, the strength of the fabric may be preserved without significantly adding to the cost or intricacy of the production process.


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