Numerical treatment of diffusional phase transformation through fully implicit control volume method

Abstract

Solid state, diffusion controlled phase transformation kinetics with a moving boundary has been quantified using a fully implicit, fixed grid, finite difference method based on the control volume approach. In a departure from the usual modeling techniques for phase change problems, the region undergoing phase change has also been considered as a control volume. A new equation for the interface flux balance has been obtained that minimises the mass balance error that normally plagues the numerical solution of moving boundary problems. The model has been validated with the calculated phase thickness based on binary equilibrium diagram and available experimental data in the literature for the Cu–Zn system and a good match has been obtained. The results obtained by the present formulation are compared with those obtained from the other models. In addition to the improved accuracy of the prediction because of elimination of the mass balance error, the proposed method has the usual advantages of a fully implicit scheme.

Keywords:

• DIFFUSION
• MOVING BOUNDARY
• ALLOYS
• MODELLING
• CONTROL VOLUME