Numerical solution of the diffusion equation with moving boundary applied to modelling of the austenite–ferrite phase transformation

Modelling of the austenite–ferrite phase transformation by solving a diffusion equation with a moving boundary is the main aim of this work. The particular emphasis is put on the testing, to what extent models based on solving the diffusion equation are capable to describe properly the kinetics of transformation. Mathematical and numerical models describing γ−α phase transformation for granular ferrite were created. These models are based on the solution of the second Fick law for the 1D, 2D (the circle in the circle, the regular hexagon in the regular hexagon) and 3D (the sphere in the sphere) cases. Developed models were solved using the finite difference, as well as the finite element method. Results of the numerical simulations for ferrite volume fraction ff, ferrite grain size dα, and carbon segregation before the front of transformation were compared with the experimental data.