We used a numerical analysis method to find the effect of the Ar flow rate on the silicon ingot growth in a directional solidification system (DSS) and to find the optimal Ar flow rate for the growth of a polycrystalline silicon ingot. The simulation software used was Fluent and the finite volume method was used to construct the boundary conditions. We used the freeze/melt model to perform the thermal field analysis of ingot growth in a DSS furnace. In the analysis, we considered the effect of the Ar flow rate on the thermal conduction, thermal convention, and thermal radiation, which affect the growth of a silicon ingot in a DSS furnace. We found that the Ar flow rate, thermal pads, heaters, and insulated side panels usually affected the growth of a silicon ingot in a DSS furnace. We also simulated the effect of the Ar flow rate on the temperature gradient, heat dissipation rate, and the shape of the solid-liquid phase while changing the temperature field. The analysis results can be used to adjust and optimize the internal parts of a DSS furnace to optimize the process of silicon ingot growth.