Institute of Metals Division - The Effect of Variable Temperature on Unsteady-State Diffusion in Metals and Slags

The paper discusses simultaneous heat conduction and diffusion. These problems may arise in slag-metal kinetics and in connection with rapid heating or cooling of specimens. A mathematical formulation is given and it is shown that the transients due to either the variability of the diffusion coefficient with temperature, or thermal diffusion, are unlikely to be important for molten or solid metals and slags. The negligibility of these effects is due to the large values of the ratio thermal diffu-sivity/molecular diffusivity. In many problems relating to transport-controlled metallurgical kinetics the diffusion process is accompanied by the transfer of heat; large-scale metal refining or metal reduction may be quoted as examples. It has been shown that due to turbulent mixing in these systems the relevant transport phe- nomena are best described in terms of "surface renewal models" which require the solution of the unsteady-state diffusion equation.1-1 Problems involving simultaneous diffusion and heat conduction are also encountered in the laboratory in connection with rapid heating or cooling of specimens. The effect of variable temperature on diffusion may be twofold: a) in the absence of "cross effects" the problem, due to variable temperature, is that of diffusion with a variable diffusion coefficient; b) if the Soret Effect is nonzero, thermal diffusion must also be taken into account in the formulation. Although information is available on thermal-diffusion transients in a steady-temperature gradient,4'5 little work has been done on the effect of unsteady temperatures on either the diffusion coefficient or on thermal diffusion.' In the following a formulation is given and solutions presented with a view of examining the areas where these effects may be important.