Numerical and analytical solutions of one-dimensional freezing of dilute binary alloys with coupled heat and mass transfer

Abstract

The purpose of the present study is to present simple and effective numerical and analytical solutions of one-dimensional solidification of dilute binary alloys. Although the numerical and analytical results are presented here for one-dimensional radially symmetric inward spherical solidification, the methods of solution are valid for several other one-dimensional problems. It is assumed that the heat and mass transport takes place only by diffusion and there is local thermodynamic equilibrium at the freezing front which is assumed to be planar. In the present study, solidus and liquidas curves are assumed to be linear, however, more general phase diagrams can also be accommodated. Numerical results are presented for wide ranging values of the ratios of diffusivities. The occurrence of steep concentration gradients at the freezing front does not require any special modification of the numerical scheme. Using the present analytical method, all the previously existing exact analytical solutions which pertain only to the semiinfinite region can be derived in a systematic way.