Transport phenomena in electric smelting of nickel matte: Part II. Mathematical modeling
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I.
INTRODUCTION
IN the electric smelting of nickel matte, Soderberg selfbaking electrodes are used to transfer heat to the slag for calcine smelting. The electrodes are immersed in an electrically conducting slag, and it is commonly believed that the electrical energy is converted into heat by ohmic losses in the slag. Therefore, the distribution of the generated heat is principally determined by the electrical field intensity distribution and the electrical conductivity of the slag; the latter quantity is a function of the slag composition and temperature. As discussed in Part I of this article,[1] the furnace geometrical factor may be used to relate the conductivity of the slag to the resistance between electrodes. While that approach is simple, it does not yield the heat generation distribution in the slag. To obtain this distribution, Maxwell’s equations[2,3] for the electric field intensity must be solved, along with the appropriate fluid flow and heat transfer equations. This is the subject of the present part of the article. Dilawari and Szekely[4,5] were the first to tackle this class of problem; they studied electroslag remelting of steel ingots that had the similar feature of joule heating of the slag, coupled with convection in the slag. In a subsequent article, Choudhary and Szekely[6] addressed electric smelting. More recently, Jiao and Themelis[7] and Jardy et al.[8] used similar techniques to simulate electric furnace behavior in nonferrous smelting. However, none of these computational models has been validated with full-scale plant data. In the present article, a comprehensive mathematical model is presented to simulate the slag and matte phases in an electric Y.Y. SHENG, formerly Post Doctoral Fellow with the Department of Materials Science and Engineering, McMaster University, is Research Scientist, Noranda Technology Centre, Pointe Clairs, PQ, Canada H9R 1G5. G.A. IRONS, DOFASCO/NSERC Professor of Process Metallurgy, is with the Department of Materials Science and Engineering, McMaster University, Hamilton, ON, Canada L8S 4L7. D.G. TISDALE, Process Engineer, is with the Smelter Complex, Falconbridge Limited, Falconbridge, ON, Canada P0M 1S0. Manuscript submitted April 12, 1996. METALLURGICAL AND MATERIALS TRANSACTIONS B
furnace operated by Falconbridge Limited. The model uses plant data for some of the boundary conditions, and relies on the information acquired in the experimental investigation of the electric furnace in Part I. The computed results for electrical variables, such as electrical potential, current, and power, as well as temperature distributions in both slag and matte phases, are compared with the plant data. Computed flow fields in both the slag and the matte phases are also presented.
II.
MATHEMATICAL MODEL
A. General Considerations In principle, this problem involves the three-dimensional, unsteady-state coupled solution of Maxwell’s equations, the Navier–Stokes equation, and the associated equation for heat transfer. Three major simplifications were made to Maxwell’s equ
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