Modelling of the glass heat-conditioning process by the application of orthogonal projection in the method of weighted residuals

A particular form of the method of weighted residuals (m.w.r.), based on orthogonal basis functions, is used to obtain an approximate closed-form solution for the partial differential equation with polynomial type boundary conditions characteristic of the glass heat-conditioning process. The technique is applied to the modelling of steady-state temperature distributions in a glass-conditioning forehearth, and the results for a short forehearth show good correlation with measured distributions and those predicted by the finite-difference method. The solution equation incorporates a parameter which is seen to be related to furnace design. By forming an error index, suboptimal surface temperature profiles can be obtained and it is suggested that this could form the basis of an online feedforward control scheme.