Mathematical simulation and experimental verification of melting resulting from the coupled effect of natural convection
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I.
INTRODUCTION
ADDITIONS have been used extensively in the treatment of liquid steel and in various other pyrometallurgical processes. In these addition practices, the melting rates of the additions directly determine their recovery. Moreover, additions affect the melt chemistry of the finished products and the production cost.[1,2] The exothermicity of the additions plays an important role in enhancing the melting rates. A better understanding of the phenomena occurring during exothermic melting is important for the optimum use of exothermic additions in the pyrometallurgical industry. Although transport phenomena taking place in the melting process have been studied in the past decade, these studies relied only on the energy equation to characterize the very complex transport phenomena involved.[1-12] Since these phenomena are strongly coupled, in order to illustrate the effect of exothermic heat on the melting process, a rigorous mathematical description with the simultaneous solution of fluid flow and heat and mass transfer is required. The investigation of such a process from a theoretical viewpoint is also motivated by its representation of a unique moving boundary problem, which is characterized by specific physical phenomena. An analysis of these phenomena indicates that this moving boundary problem is further complicated by the presence of a heat source. The reason for this complication is due to the fact that a heat sink (i.e., melting of a solid) and a heat source (i.e., exothermic heat of mixing) occur simultaneously within close HONGFA HU, formerly Graduate Student, Department of Metallurgy and Materials Science, University of Toronto, is Research Scientist, Institute of Magnesium Technology, Saint-Foy, PQ, Canada G1P 4N7. STAVROS A. ARGYROPOULOS, Associate Professor, is with the Department of Metallurgy and Materials Science, University of Toronto, Toronto, ON, Canada M5S 3E4. (Author to whom correspondence should be addressed.) E-mail: [email protected]. Manuscript submitted November 29, 1995. METALLURGICAL AND MATERIALS TRANSACTIONS B
proximity. The presence of the heat source in this kind of moving boundary problem may have two effects. First, it would cause the moving boundary to move faster (i.e., melt faster). Second, it would enhance the fluid movement in the vicinity of the moving boundary (i.e., accelerated fluid flow conditions). The objective of this study was to develop a mathematical model that would be capable of predicting the coupled transport phenomena occurring when a solid melts exothermically in a stagnant liquid. An extensive two-phase validation of the model was carried out. In the first phase, the model was validated by a low-temperature physical model. This physical model considered the melting of ice in sulfuric acid solutions. In the second phase, the verified model was applied to a metal system, involving the melting of silicon in liquid high carbon iron.
II.
THEORETICAL CONSIDERATIONS AND MATHEMATICAL FORMULATION
The analysis of the physical phenomena involved i
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