| OCR Text |
Show 7 The boundary condition at the inner (top) surface of the load zones exposed to the heat flux from the heaters and the furnace walls is 9T. -k, L 9y = -(qc+qr) (17) top where the convective (qc) and radiative (qr) heat fluxes at the load surface are calculated equations discussed. The boundary conditions imposed at the load bottom are Way = kw dTJ*y <18> and TL = TW. (19) Method of Solution The baseline LIF geometry, dimensions, operating conditions thermophysical properties of materials used in the calculations are summarized in Table 1. The geometry is identical to that of the experimental LIF [2]. The first step in the solution procedure involves the zoning of the furnace into isothermal surface zones. This is illustrated in Fig. 3, which is essentially an unfolded representation of the three-dimensional geometry of the furnace illustrated in Fig. 1(a). The panel heaters, load and furnace walls have been divided into a large number of rectangular surface zones. The next step involves the calculation of the configuration factors (F. .) between various isothermal surface zones of the furnace. These are evaluated using analytical expressions provided by Siegel and Howell [5] for generic configurations. For the baseline geometry, the load was divided into 14x4 (or 56 zones), and the eight (8) F RH panels each are represented by a single isothermal zone. The furnace walls (the side walls and the roof) were divided into 13 zones each, and the two end walls into eight (8) zones each, as shown in Fig. 3. A total of 135 zones were employed in the numerical calculations. The effect of zoning size was examined by using finer isothermal zones on the walls. Estimated relative errors in calculated temperatures and heat fluxes on the load surface were at most 0.1%. Therefore, the cruder zones, as shown in Fig. 3, are employed for the parametric studies. Furthermore, time step independence on the results was also examined employing steps of 5 s, 10 s and 20 s. The maximum relative errors based on the results of 5 s step were 0.7% (10 s) and 1.7% (20 s), respectively. Therefore, a 10 s time step is employed in the calculations reported. RESULTS AND DISCUSSION Numerical calculations were carried out for the base configuration and parameters listed in Table 1. The thermophysical properties were assumed to be constant except for the surface emissivity as indicated in equation (9). The dependence of the emissivity on the wavelength is shown in Fig. 4. Four typical materials are examined for the load emissivity, and one is the furnace wall and the panel heater [6]. The cutoff wavelengths for three types of band models are also shown in Fig. 4, that is, gray, two-band and five-band models. The panel heater is made from flat stainless steel, and the furnace wall consists of fibrous insulation which is encased in stainless steel on both faces. Therefore, the load inside of the LIF can be assumed to be totally surrounded by oxidized stainless steel walls. The thickness of the load is determined in such a way that the total mass is identical to that used in the LIF [2]. The heat transfer rate to the ambient is |
