The Effect of Thermal Diffusion on Decarburization Kinetics
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t paper by the current authors,[1] results were reported for the decarburization of Fe-Cr-C levitated droplets with CO2-Ar gas mixtures, using the equipment shown in Figure 1. It was found that mass transfer correlations such as the Ranz and Marshall[2] and Steinberger and Treybal[3] equations, while widely employed, do not describe the data obtained from the droplet experiments. Based on analysis of the rate data, a new correlation was proposed that accounts for contributions from both natural and forced convection and is appropriate for mass transfer involving levitated droplets: 1
1
Sh ¼ 2 0:317ðGr0 ScÞ4 þ3Re0:415 Sc3 ;
½1
where Sh, Gr¢, Sc, and Re correspond to the Sherwood, mean Grashof, Schmidt, and Reynolds numbers, respectively. While it is true that natural convection may assist with mass transport from the droplet to the surroundings in a shrinking-sphere experiment as in the case of the Steinberger–Treybal experiments, it may hinder the process, as indicated by the negative sign in Eq. [1], if the concentration gradient and the temperature gradient are in opposite directions. The presence of a steep temperature gradient near the gas–metal interface, an inherent feature of the levitation technique, gives rise to variation in gas properties and
flow patterns across the boundary layer and as a result, mass flux due to thermal diffusion becomes significant. The objective of the present discussion is to provide an alternative approach to rationalize the reported discrepancy between the existing models and the experimental measurements by considering the implications of the effect of thermal diffusion on reaction kinetics in the presence of large temperature differences between the two phases. The work by Sain and Belton[4] suggests that interfacial reactions are faster than both liquid transport and gas transport. In the high carbon regime, the transfer of carbon is faster than the flux of oxidant species arriving at the gas–metal interface. Therefore, at high carbon content the experimental reaction rate is controlled by gas diffusion. The reaction geometry associated with the levitation technique, consists of gas mixtures flowing over a liquid sphere of surface area A with weight W. The decarburization rate can be related to the flux of arriving gaseous oxidant, JCO2 , using the expression: dðwt pct CÞ 1200A ¼ JCO2 dt W 1200A ShDAB P b ¼ XCO2 XiCO2 ; W dp RTf
½2
where DAB is the mutual diffusion coefficient, P is the total pressure, dp is the diameter of metal droplet, R is the gas constant, and Tf is the film temperature, XbCO2 is the mole fraction of CO2 in the bulk gas at the edge of the boundary layer and XiCO2 is the mole fraction of CO2 at the surface of the liquid sphere. In the gasphase controlled regime, the mole fraction of CO2 at the gas–metal interface is negligibly low. In a levitated droplet experiment, thermal equilibrium is reached when the heat dissipation through radiation and convection equals the heat gain through induction by the applied electromagnetic field. The steep temperature gra
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