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Show 8 characterized by an effective (i.e., convective plus radiative) heat transfer coefficient which is estimated from the literature [7]. A total of ten thermocouples were installed in the LIF [2], nine in the load and one below the roof. The load was simulated by filling several baskets with cast pig iron parts. The baskets filled with parts are very complex geometrically and could not be modeled. The recorded near-roof temperatures were not corrected for the heat losses/gains from the thermocouple bead; therefore, no meaningful comparisons of model predictions and measurements could be made. Effect of Band Model Before a parametric study was conducted the effect of the choice of the band models on the thermal performance of the furnace was examined. Figure 5 shows the surface temperature variations of panel, top wall and load. Included for comparison are the load temperatures for each band model. The panel temperature variation is taken from the operating data given in the LIF experiment [2]. The other temperatures are calculated using emissivity data of unoxidized iron for the load surface given in Fig. 4. The top wall temperature is practically the same for the different band models. The calculated load temperatures are different especially between the two-band models and the gray model. The results of five-band model are the most accurate, and the relative error can be calculated using the load surface temperature given in Fig. 5. The relative error in the gray model is about 15.7% (105 K difference), while that of a two-band model is about 3.7% (24.8 K difference) at t = 4.4 hr. The discrepancy in temperatures predicted using the gray and five-band models for the unoxidized iron is due to the strong dependence of the emissivity on the wavelength (see Fig. 4). If the load is replaced by another one whose emissivity is less strongly dependent on the wavelength, such as oxidized iron, unpolished aluminum or polished aluminum, these differences among the results for the different band models are much smaller. The results are summarized in Table 2. In view of the uncertainties in the radiation properties of materials, it is, therefore, concluded that the two-band model is sufficiently accurate for calculating the temperature distribution in the load. Effect of the Load Emissivity and of Load Material The effects of the load emissivity and of the load material on the performance of the furnace are examined using the two-band model. The main discussion is focused on the load temperature, furnace efficiency and temperature distribution in the load. This is owing to the fact that these parameters directly impact the productivity, product quality and furnace efficiency. But, some additional results are also presented when they are relevant Load Temperature. Load surface temperature variations are shown in Fig. 6 for four different materials and surface conditions. For the same materials, as the surface emissivity increases, the surface temperature also increases, because according to Kirchhoffs law, absorptivity is also high. However, for different materials this is not the case. For example, compared with unoxidized iron and unpolished aluminum, the unoxidized iron is heated to a higher temperature in spite of its lower emissivity. The reason for this result lies in the much higher thermal conductivity of aluminum as heat is conducted more effectively from the surface to the interior of the load. This tendency is also evident in Figs. 7 and 8. Figure 7 shows that the net heat flux at the unpolished aluminum load surface is much higher than that of unoxidized iron. However, as shown in Fig. 8, in spite of higher heat flux, the temperature gradient in the unpolished aluminum is smaller, especially near the surface, because of its much higher thermal conductivity. Therefore, unpolished aluminum can absorb a larger amount of heat, but its |
