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Show -IlaUj s. . =- -+aU-i 1, IJ 2 aX i ax j Cs = 0.1 (4) Regarding turbulent heat transfer, the turbulent Prandtl number is supposed to 0.9. The following non-dimensionalized equation for the conservation of energy is solved, and is completely incorporated with the fluid flow. ~~ + d~.(Ul) =a:~lRe~r::l- d~.(UjT') +~ad J J J J (5) - A aT u'.T' = ----- J PrtaX j (6) Radiation Model: READ(Radiative Energy Absorption Distribution) method, Taniguchi et al(1986), which can take account of local conditions for radiant heat transfer, is employed for the radiant heat transfer. The soot production can be neglected in the slab reheating furnace. The flue gas is treated to 'gray gas', and the absorption coefficient is determined based on Hottel's data (1967). Using the model, the radiant heat transfer term QRad in equation(5) can be written as, QRad ~ -4( 1- a j ) kjO~4 + ~ ~ I-a j )Rdj -+ jk joT; :: + ;( 1- aw )Rdw -+ jEWoT! ~ (7) where the self absorptivity as and the READ value Rd are obtained from equation (8) using the Monte Carlo Method and the Radiative Heat Ray Method (Hay as aka et al 1986). a. = ~ AI!1 . . . tN, ....... n = 1 Rd. . = ~ M':l ~ .. /(N - ~ M':l ~ .) J ....... D=1 J-- D=1 J--J (8) Combustion Model : No reaction model is used in the simulations, but the rate distribution of carolification of the burner measured in the experiments is given as the boundary condition. There are three reasons for that; first, too much computational time and memory are required to incorporate with numerical combustion analysis owing to very small and short scale of combustion phenomena, secondly the distribution of carolification strongly depends on the shape of a burner and it is very difficult to predict accurately, and thirdly combustion does not affect the global fluid flow field qualitatively (Ikeda et aI. 1995). Numerical S( 1n : The finite difference method is used for spatial discretization, and convection terms are discre ... _...J-by the donor-cell method of the central/upwind scheme, and Adams-Bashforth method is used for temporal discretization. HSMAC (Highly Simplified Maker And Cell) method is employed to calculate velocities and pressure (Hirt & Cook, 1972). The solution of the individual equations sets of the fluid is obtained by a form of Gauss-Seidalline-by-line iterations, and the energy conservation equation is solved using the implicit method by TDMA erri-Diagonal Matrix Algorithm). /D |