Abstract: During the slow cooling process of copper slag in the ladle, the cooling rate of copper slag in the liquid-solid phase transition temperature range is one of the key factors affecting the subsequent flotation. To analyze the liquid-solid phase transition behavior characteristics of copper slag at different positions in the slag ladle under the existing slow cooling system, this paper took a 12 m³ cast steel slag ladle from a certain factory as the research object, constructed a three-dimensional unsteady numerical heat transfer model based on the finite volume method, simulated and analyzed the liquid phase cooling rate and crust formation law of copper slag under the existing slow cooling system, and further explored the influence of air cooling duration change on the slow cooling process. The results show that during the slow cooling process of copper slag, affected by the combined action of the thermal resistance of the formed slag crust and the release of latent heat of liquid-solid phase transition, the internal cooling rate presents significant spatial inhomogeneity. The liquid phase cooling rate of copper slag near the inner wall of the slag ladle is relatively fast, which mainly occurs in the first 3 h of air cooling, and its volume accounts for less than 1/3; the cooling rate of the remaining areas is significantly lower, generally below 1 K/min. With the extension of air cooling duration, the copper slag crust continues to thicken; after 12 h of air cooling, the crust thickness increases by about 20 mm for every additional 2 h, which effectively reduces the "explosion" risk when copper slag is transferred to the water cooling stage. However, with the continuous thickening of the crust, its thermal resistance is further enhanced, which makes the promotion effect of the water cooling stage on the internal cooling rate of copper slag limited, and on the contrary, prolongs the time required for the complete solidification of copper slag. The research results can provide a theoretical reference for the optimization of the slow cooling system of copper slag ladles and the improvement of slag ladle structure and materials.