The explicit finite difference method is used to the quenching of CrNi steel, the relationship between surface heat transfer coefficients and temperature is determinated by means of solving the inverse problem of heat conduct equation.

By using Linearization method in little time interval, from the heat conduition equation with the 1st-order phasetransformations, the foundation equations of Finite Elememts in solidifications of Metals is established in the paper. The numerical analog on symetric problem in solidification of a grayiron in sandform is obtained by means of triangular element, and the results tallies the corresponding test well.

In this paper, Norsette Method is used to solve the non-steady heat conduction problem. This method prevents the "oscillation" of numerical solution effectively.