An analogy, between the differential equations which described diffusion under constant diffusivity, time-dependent diffusivity, and temperature-dependent diffusivity in non-isothermal environments, was extended so as to derive solutions for 2-dimensional and 3-dimensional problems. The solutions for non-isothermal conditions were derived by substituting independent variables, and corresponded to a change in scale of the radial distances upon varying the cooling or heating rate. The dependence, upon the rate of change in temperature, of the amount which was transferred across the interface was also described. It was noted that various effects could be predicted by selecting suitable combinations of experimental conditions.

J.R.Frade: Journal of Materials Science, 1997, 32[17], 3557-63