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• A full 3D numerical model for transient flow field, temperature, solidification, and segregation during slab continuous casting. • An improved capture criterion for inclusion entrapment that including the primary dendrite arm spacing, solute concentration, force analysis, and critical capture speed is proposed. • Prediction on the number, size, and spatial distribution of inclusions on the entire cross section of the CC slab. • Four accumulation zones of inclusions along the thickness of the CC slab are predicted. In the current study, the LES turbulent model, heat transfer, solidification, species transport model, and discrete phase model (DPM) were coupled to investigate the three-dimensional transient flow, temperature, solidification, segregation, and inclusion transport during the slab continuous casting (CC) process. The number, size, and spatial distribution of inclusions on the entire cross section of the CC slab were successfully predicted using the coupled full solidification model, DPM, and capture criteria at the solidification front. The improved capture criteria that considering the primary dendrite arm spacing (PDAS), different forces acting on inclusions, and the critical capture speed, successfully eliminated the banded distribution characteristics of inclusions under the simple capture criterion. The prediction results were in good agreement with the detection results. Four accumulation zones of inclusions along the thickness of the CC slab were predicted, including the 1/4 thickness and 3/4 thickness from the loose side, and the layer beneath the surface of the CC slab. Two accumulation zones near the layer beneath the surface of the CC slab were issued from the double roll flow pattern in the CC strand. The probability of inclusions contacting the solidification front in the upper recirculation zone increased, increasing the entrapment rate. The accumulation zones near the 1/4 thickness and 3/4 thickness from the loose side were corresponded to the peak value of the Marangoni force on inclusions at the 1/4 thickness and 3/4 thickness from the loose side. The Marangoni force increased the probability of inclusions being pushed to the solidification front. In addition, the accumulation near the 1/4 thickness from the loose side became more severe as the diameter of the inclusions increased due to the buoyancy. [Display omitted] [ABSTRACT FROM AUTHOR]