Two-dimensional numerical model is adopted to analyze the heat transfer process during solidification of the sample melted in an Arc-image furnace. Numerical solution of this complex problem enabled us to calculate the temperature distribution in both sample and substrate, including the phase change phenomena. Also, the effects of process parameters on the solidification of the sample melted on substrate that is cooled by water can be investigated numerically. The parameters include sample size, contact area size between the sample and the substrate, and degree of undercooling associated with rapid phase change and moving interface. The results obtained reveal that these parameters have strong effect on temperature distribution during solidification.