In the modern gas turbine, elevating the turbine inlet temperature is a key strategy to improve thermal efficiency and power performance. However, this temperature imposes significant thermal stress on the turbine component, leading to issues such as creep, thermal fatigue, oxidation, and corrosion which adversely affect the durability. To address these challenges various cooling techniques have been developed, including the use of internal rib turbulators and conductive coolant materials to ensure efficient thermal management. This study explores the impact of mist/steam flow and mist particle size within a cooling channel featuring an inclined rib turbulator. The findings reveal that introducing mist at specific mass ratios synergistically enhances secondary flow velocities. Smaller particles significantly improve heat transfer efficiency due to their rapid evaporation. Specifically, at a mist/steam mass ratio of 10% and a mist particle size of 10 μm, the enhancement values for Nusselt number ratio and thermal performance factors are 9.76% and 4.45%, respectively. Therefore, a 10 μm particle size is optimal for achieving the highest heat transfer and cooling efficiency within varying mist/steam mass ratios. These findings indicate significant potential for improving gas turbine efficiency and longevity, thereby reducing operational costs and maintenance frequency in the industry.