| Annealing is one of the most important as well as essential phases of glass manufacturing. This work explores heat transfer within automotive float glass during the annealing phase and thus becomes a useful tool for helping to optimize the productivity of high quality glass parts in the automotive industry. An unsteady, one-dimensional model was first developed using Patankar's finite difference approach to predict the temperature history of the glass part as it moves through different heating zones of the annealing furnace. All the temperature dependent properties such as radiation conductivity, effective emissivity and specific heat were first determined for a wide range of temperatures, and for different types of glasses. After completion of the one-dimensional analysis with a wide variety of parameters, a two-dimensional program was also developed. These models were made general enough to simulate different conveyor velocities and any number of annealing zones of equal or unequal length. As many as five varieties of float glass were modelled. The size of the glass template is also variable as long as the template is a cuboid. These models also estimate the power extracted by the glass pieces during annealing. The use of a variable grid, proper convergence criterion and relaxation factors, tabulation of some properties in the very beginning of the program are the advantages of these models which are due to efforts to economize the models with respect to computer time and storage. Finally, the above models were expanded into a fully three-dimensional, transient heat transfer model. This model was tested for various conveyor velocities, different zones of heating and as many as five varieties of glasses. All the three models predicted a conveyor velocity of 2.8 in/sec to be an appropriate velocity at which the template must travel in order to yield a uniform temperature field throughout the glass piece at the exit of the furnace. Excellent agreement was observed among the results from the one-dimensional, two-dimensional and three-dimensional models for different test conditions. A peak temperature field was observed across half an inch distance from all the four sides/edges of the template while the template resided in the first few zones. This could very well be the source of high thermal stresses leading to the possibility of cracks. |
