This study presents the results on the changes of crucible thermal conductivity and inflow of Ar, and constructed the mathematical model about heat transfer into furnace. As process variables, simulation model was designated thermal conductivity of crucible to 0.5 W M-1 K-1, 1 W m-1 K-1, 2 W m-1 K-1, 4 W m-1 K-1, and inflow rate of Ar to 15L/min, 30L/min, 60L/min. Initial condition and boundary condition were set respectively in two terms of process. Each initial conditions were set up by the preceding simulation of heat and fluid flow. The primary goal is the application of unidirectional growth of Si ingot using the result. In the result of the change of heat conductivity of crucible, the higher higher thermal conductivity of crucible shows the shorter solidification time and the bigger temperature difference. And the flow patterns are changed with the inflow rate of Ar. Finally, we found that the lower crucible`s thermal conductivity, the better crucible is at polycrystalline Si ingot growth. But in case of Ar inflow, it is hard to say about good condition. This data will be evaluated as useful reference used in allied study or process variable control of production facilities.