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Show Heat Transfer Equation Energy transport equation V (pUH)-? -{{{fJb / <7,) + (A / C,))V/Y) = Srad+ S/!a»* +Ssiab (8) The specific heat at constant pressure was defined as a polynomial function of temperature. Srad, Sname and Ssiab are source terms representing radiation, combustion and energy transportation by the steel strip respectively. R A D 3 D calculates Srad by the Monte Carlo method. Sflame, heat release rate by combustion, was assumed and distributed to the numerical cells downstream of the burner exit. The heat release rate was distributed empirically to represent a typical gas flame. Ssiab is calculated by following equation and distributed to the numerical cells corresponding to the steel strip: Ssiab = v A p Cp(Te-Tp) (10) where v and A are the moving speed and cross section area of the steel strip respectively. Tp and To are the temperature of the cell and that of the upstream cell respectively. 4. Prediction of conventional burner system 4.1 Analytical model First, numerical analysis was conducted for a typical muffle type furnace with conventional burner system to validate numerical models used. The furnace was as high as eight-floor building. A number of burners were installed tangentially, with each pair of burners located at the same height (see Fig.3). A pair of flues was located at the bottom of the furnace. Flow, combustion, thermal conduction and convective and radiative heat transfer were taken into account in the combustion zone, while thermal conduction and radiative heat transfer were calculated in the reducing zone (see Fig.2). The muffle is treated as a conducting solid. The heating curve of the steel strip was calculated by Eq.(10). In total, 83,886 cells were used for flow calculation and 924 cells for radiation. The predicted heating curve of the steel strip was compared to an empirical 1-dimensional prediction that is regularly performed by furnace designers'5'f6>. 4.2 Results and Discussion Figs.4 and 5 show the predicted distribution of flow and temperature at the bottom part of the furnace respectively. One-fifth of the furnace height is shown in Figs.4 and 5. Fig.4 demonstrates that near the bottom of the furnace axial downward flow toward the flues is dominant over tangential flow. While the burner configurations are originally designed to create circulating tangential flow around the muffle, the substantial amount of the flue gas 4 |