A 3D meso-scale discrete-element model has been developed to simulate fluid flow during dendritic solidification of steel. The model domain is a representative volume element consisting of a set of equiaxed dendritic grain envelopes along with extra-dendritic liquid channels, where the final grain shape is given by a Voronoi tessellation. Solidification of each grain is simulated via a volume average approach. The output of the solidification simulation at a given solid fraction is used as the input mesh for the fluid flow simulation. A single domain Darcy-Brinkman model is used to calculate the pressure field within the liquid channels, with Poiseuille flow assumed to occur in the extra-dendritic region, and Darcy flow assumed to occur within the dendrite envelope. Mass conservation over each element is then used to derive a flow equation that is solved via the finite element method. The results of this new model are first compared with a previously-developed granular model [1] where fluid flow only occurs between the grains, and then compared with different forms of the Carman-Kozeny equation. It is shown that the intra-dendritic liquid fluid flow plays a major role in the semi- solid pressure field, and thus needs to be included when investigating hot tearing susceptibility in engineering alloys undergoing dendritic solidification.