The effect of temperature dependent electrical conductivity on flow and temperature fields in slags in ESR systems
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3.23 exp ( : ~ )
is shown in Fig. 4. The derived activation energy for the diffusion of Mn in Pt, 305 k J / m o l , is close to the value of 286 k J / m o l reported by Kidson and Ross s as the activation energy for the self-diffusion of Pt. The agreement between the experimental data and Eq. [1] indicates that the rate of pick-up of Mn by the Pt foils is controlled by diffusion of Mn in Pt, and permits evaluation of the chemical diffusivity of Mn in Pt. Grateful acknowledgement is made to the National Science Foundation who supported this work under their Grant Number DMR77-03426.
1. B. K. D. P. Rao and D. R. Gaskell: Met. Trans. A, 1981, vol. 12A, p. 207. 2. B. K. D. P. Rao and D. R. Gaskell: Met. Trans. B, in press. 3. B. K. D. P. Rao and D. R. Gaskell: Met. Trans. B, in press. 4. J. Crank: The Mathematics o f Diffusion, p. 47, Oxford Press, London, 1956. 5. G. V. Kidson and R. Ross: Proc. Int. Conf. Radiosotopes Sci. Res., Paris, 1957, vol. 1, p. 185.
2) that the electrical conductivity of these systems is independent of temperature. The former assumption is thought to be reasonable, because of the low value o f the magnetic Reynolds number, however the second assumption is more questionable, because of the substantial temperature differences that may exist in these systems. In a previous paper 5 we have presented a somewhat a d h o c examination of the possible role played by a temperature dependent electrical conductivity in modifying the temperature fields in a laboratory scale ESR system. The purpose o f this communication is to examine this problem in a more systematic manner. The general mathematical description of the electromagnetic force field, temperature field and velocity field in ESR systems is available in previous publications; 2,5 for this reason our attention will be confined to discussing the role of a temperature dependent electrical conductivity in modifying the electromagnetic force field and the heat generation patterns. Using the M H D approximation the dimensionless form of the electromagnetic field equation takes the following form: jod?l * = - V *
V*xD* x
or*
+Re"V*•215
[1]
where: /~*
=
12IIHo, V * = L o V , V*= V / V o , o* = o1% [2]
complex amplitude of the magnetic field intensity, V velocity vector, o r = electrical conductivity, ~
The Effect of Temperature Dependent Electrical Conductivity on Flow and Temperature Fields in Slags in ESR Systems M. C H O U D H A R Y AND J. SZEKELY There are numerous metals processing operations, where a high current is passed through a molten, conducting medium and the resultant combined effect of "joule heating" and electromagnetic forces gives rise to convective flows. Electroslag refining, electroslag welding, aluminum smelting and the operation of various "submerged arc" furnaces are representative examples. The recent mathematical models of these operations, relied on the simultaneous solution of Maxwell's equations, the Navier-Stokes equations and the thermal energy balance equation.~-s Two important assumption have been made, name
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