Centreline segregation during continuous casting of steel is highly detrimental to the end-product mechanical properties. In this study, a 3D multi-scale and multi-physics model is developed and validated that directly predicts alloy segregation occurring in peritectic steel grades having centreline equiaxed grain morphology. The model consists of four models: (1) a 1D macroscale heat transfer and solidification model, (2) a 3D mesoscale dendritic solidification model, (3) a 3D mesoscale dendritic fluid flow model, and (4) a 3D mesoscale solute transport and redistribution model. The use of a mesoscale domain where the solid and liquid phases are separately discretized allows for consideration of physical phenomena affecting segregation that are classically hidden by the averaging procedures of fully continuum approaches. Thus the new model is able to account for the multiple phenomena occurring during continuous casting while also directly considering the stochastic effects resulting from grains having randomly-placed nuclei as well as interactions between the liquid and solid phases. The results demonstrate that solute partitioning combined with intra-dendritic fluid flow leads eventually to liquid channels enriched with solute that result in centreline segregation. The predicted composition in these discrete liquid channels shows excellent agreement with a Mn centreline segregation profile experimentally-measured via microscopic X-ray fluorescence of a commercially-cast steel slab. Finally, the effects of alloy composition, and soft reduction on the degree of centreline segregation are examined.