Generation, incorporation, and accumulation of carbon (C) were investigated by transient global simulations of heat and mass transport during the melting process of Czochralski silicon (CZ-Si) crystal growth. Contact reaction between the quartz crucible and graphite susceptor was introduced as an extra origin of C contamination. The contribution of the contact reaction on C accumulation is affected by the back diffusion of C monoxide (CO) from the gap between the gas-guide and the crucible. The effect of the gas-guide coating on C reduction was elucidated by taking the reaction between the silicon carbide (SiC) coating and gaseous Si monoxide (SiO) into account. Application of the SiC coating on the gas-guide could effectively reduce the C contamination because of its higher thermochemical stability relative to that of graphite. Gas flow control on the back diffusion of the generated CO was examined by the parametric study of argon gas flow rate. Generation and back diffusion of CO were both effectively suppressed by the increase in the gas flow rate because of the high Peclet number of species transport. Strategies for C content reduction were discussed by analyzing the mechanisms of C accumulation process. According to the elucidated mechanisms of C accumulation, the final C content depends on the growth duration and contamination flux at the gas/melt interface.