Abstract: A mathematical model using stream function, vorticity and cemperature as basic varibles is developed to represent the heat transfer and natural convection in the solidification prooess of castings. The solutions of the governing equations are carried out by means of a semi-implicit finite difference scheme based on fixed grid methodology. Consideration is given to the latent heat evolution and velocity conditiion in the liquid-solid phase zone(inte-rface).A specific enthalpy method associated with the alloy equilibrium phase diagram is employed to account for the latent heat of phase change. A new revision approach according to solid fraction is proposed for the treatment of the zero velocity condition as liquid region turns to solid. Moreover, the possibility of applying the present model to the problems of irregular geometries is discussed. In the last part of the paper, a tpyical freezing problem is solved, and the influence of natural convection on the solidification of castings is analysed in detail.

Key words: Solidification Process, Numerical Computation, Heat Transfer, Natural Convection