Effect of Diffusion and Heat Transfer in Eutectoid Solidification

A theoretical model is formulated to describe the processes of diffusion and heat transfer that occur in eutectoid solidification. Radial as well as unidirectional solute diffusion are considered in this formulation. The resultant non-linear differential equation is then linearised with the aid of the steady state solution of the heat flow equation in the solid. Evaluation of the order of magnitude of parameters occuring in this equation indicates the radial contribution to be dominant in the growth of the secondary fiber eutectic(oid) phase. Separation of variables and perturbation solutions using a suitable small parameter are then used to evaluate the steady state solution. It is found that a boundary layer exists where the concentration varies rapidly from the interface to the steady state value in the fiber, within a very small distance, about 10 microns. The boundary layer thickness and concentration differential across it are evaluated for a typical case.