Mathematical modeling of sulfide flash smelting process: Part II. Quantitative analysis of radiative heat transfer
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I.
INTRODUCTION
IN Part
I, ul a mathematical model to describe the various processes occurring in a flash furnace shaft was presented. The model incorporates turbulent fluid dynamics, chemical reaction kinetics, and heat and mass transfer. Key features of the model include the use of the k-e turbulence model, incorporating the effect of particles on turbulence, and the four-flux model for radiative heat transfer, which is an important mode of heat transfer in the flash smelting furnace. A flash smelting flame contains components which are highly emitting, absorbing, and scattering, Radiative heat transfer processes in a flash furnace include nonluminous gaseous emission, luminous particulate emission, and radiation from the furnace wall. The major emitting gaseous species in the flash smelting system is SO2. The contributions of other gaseous species, such as SO and SO3, are assumed to be negligible because of their low concentrations. The species 02 and N2 do not affect the radiation field because they are simple symmetrical molecules and essentially transparent to radiation. [2] A radiation beam traversing a medium is attenuated due to absorption and/or scattering. [3,4[ The absorbed flux is that which does not re-emerge from the body as either a transmitted or scattered flux; it is converted into stored internal energy, thus raising the body temperature. For a gray body at thermal equilibrium, the absorptivity is equal to the emissivity, because the spectral distribution does not affect the absorptivity and emissivity. Is'6[ The radiation beam is partly scattered (reflected) due to the presence of solid particles. While absorption is the transformation of radiant flux into thermal energy, scattering redistributes the radiation flux into other directions. In flash smelting furnaces, the presence of particles or droplets provides sources for scattering and emission. Several investigators have studied and reviewed the radiation heat transfer occurring in pulverized coal combustion systems. [3,7-1~ Fields t4] discussed in detail the ra-
Y.B. HAHN, formerly Graduate Student, Department of Metallurgical Engineering, University of Utah, is Research Engineer with Lucky Metals Corporation, Seoul, Korea. H.Y. SOHN, Professor, is with the Department of Metallurgical Engineering, University of Utah, Salt Lake City, UT 84112-1183. Manuscript submitted December 13, 1988. METALLURGICAL TRANSACTIONS B
diation heat transfer in pulverized coal flames. He used a four-flux model based on the work by C h u and Churchill. [6[ Very little work has been done on the incorporation of the radiative heat transfer in describing a flash smelting process except by Ruottu, I11[ who considered the emission and absorption phenomena. However, he neglected the scattering, which is an important subprocess in a particle-laden flow system. He further assumed the same temperatures between the gas and the particle. This assumption is not reasonable for a flash smelting system ul in which, in the upstream zone, cold sulfide particles are first heat
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