Articles written in Pramana – Journal of Physics
Volume 47 Issue 6 December 1996 pp 447-470
A 3-dimensional (2-space, 1-time) model relating the diffusion of heat and mass to the kinetic processes at the solid-liquid interface, using a stochastic approach is presented in this paper. This paper is divided in two parts. In the first part the basic set of equations describing solidification alongwith their analysis and solution are given. The process of solidification has a stochastic character and depends on the net probability of transfer of atoms from liquid to the solid phase. This has been modeled by a Markov process in which knowledge of the parameters at the initial time only is needed to evaluate the time evolution of the system. Solidification process is expressed in terms of four coupled equations, namely, the diffusion equations for heat and mass, the equations for concentration of the solid phase and for rate of growth of the solid-liquid interface. The position of the solid-liquid interface is represented with the help of a delta function and it is defined as the surface at which latent heat is evolved. A numerical method is used to solve the equations appearing in the model. In the second part the results i.e. the time evolution of the solid-liquid interface shape and its concentration, rate of growth and temperature are given.
Volume 48 Issue 4 April 1997 pp 891-922
A stochastic model to study the solidifcation process developed in part I is applied to various binary alloys having different values of interaction energies. The results obtained for the time evolution of temperature and concentration, rate of growth and shape of the solid-liquid interface are presented.
Volume 96, 2022
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