DIFFUSION IN MATERIALS WITH VARIABLE-TEMPERATURE .2. 2-DIMENSIONAL AND 3-DIMENSIONAL PROBLEMS

The analogy between the differential equations which describe diffusio n with constant diffusivity, time-dependent diffusivity, and temperatu re-dependent diffusivity in non-isothermal conditions is now extended to obtain solutions for two- and three-dimensional problems. The solut ions for non-isothermal conditions are derived by substitution of inde pendent variables, and correspond to a change in scale of radial dista nces on varying the cooling or heating rate. The dependence of the amo unt transferred across the interface on the rate of change in temperat ure is also described, and the relative effects can be predicted by se lecting suitable combinations of experimental conditions. This conclus ion can be extended to diffusion-controlled growth or dissolution of p articles.