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Show A further simplification was introduced by considering only a section of a cross-fired glass furnace. In the current project only the end-section of such a furnace was modelled. This allowed use of computational grids small enough that the computer code of the model could be executed on PC's. The model developed for above approach is described in detail in the following sections. 3-D Zone Model As already mentioned, the present study is based on a 3-D heat transfer and combustion zone model (Ref. 6). This model has successfully been applied in the past for thermal performance studies of a variety of boiler, industrial and pilot-scale furnaces (Ref. 7) including furnaces almost completely insulated by refractory walls like a glass furnace. The model is especially suitable for the latter furnaces, since emphasis is laid on accurate treatment of multi-directional radiative exchange, which is by far the dominant mode of heat transfer in these high temperature furnaces. In zone-type models such as the current one, the combustion space is sub-divided by a net of well-stirred volume zones, and by a net of corresponding boundary zones. Average zone temperatures are obtained for total energy balances set up for each zone. The heat balance for a volume zone is formulated by Eq. (1) (1) where Qr and Qs are the net heat fluxes over the zone boundaries by radiation and advection, respectively. Qd' which is small in high temperature furnaces, represents the convective transport through a wall boundary layer from a near wall volume zone to an adjacent surface zone. Qch' finally is the net heat release in the volume zone due to flame reactions obtained from species balances solved in addition to the volume zone heat balances. Contrary to the more expensive finite-difference combustor models, the advective mass flow rates necessary to calculate the terms Qs in Eq. (1) are not obtained from a simultaneous solution of momentum balances, but are rather input into the zone model, thus allowing to spend available computational resources for a more accurate simulation of radiative exchange. The multi-directional transport of radiative energy between all wall and surface zones (i.e. term Qr in Eq. (1» is calculated with the semistochastic method (Ref. 6). This method which is derived from Monte-Carlo calculation techniques is illustrated in Fig. 1. Qr is expressed by Eq. (2) : 3 |