, Volume 47, Issue 6, pp 447–470 | Cite as

A stochastic model for solidification

I. The basic equations, their analysis and solution
  • Shobha Dass
  • Gautam Johri
  • Lakshman Pandey


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.


Stochastic solidification binary melt kinetic phase diagrams 




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Copyright information

© the Indian Academy of Sciences 1996

Authors and Affiliations

  • Shobha Dass
    • 1
  • Gautam Johri
    • 1
    • 2
  • Lakshman Pandey
    • 1
    • 2
  1. 1.Govt. M.H. College of Science and Home ScienceJabalpurIndia
  2. 2.Department of Post Graduate Studies and Research in PhysicsRani Durgavati UniversityJabalpurIndia

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