A theoretical and numerical macroscopic modelling of the solidification of binary structure is presented. The growth of a solid-liquid (mushy zone), represented by a heterogeneous porous medium, is considered. A macroscopic model for momentum, heat and mass transfer during solidification is derived using the volume averaging method, and the effective transport proprties (permeability, effective diffusivities, exchange coefficients) are defined by associated closure problems. Consequently, the effects of the dentritic geometry (tortuosity) and of microscopic transfer phenomena (dispersion, interfacial exchange) are introduced in the average balance equations, and in the representation of the effective transport coefficients. This closure method provides an original approach of solidification modelling. The resulting macroscopic model is based on the local thermal equilibrium assumption while a two-phase description of macroscopic species transfer is provided, using solid and liquid mass exchange coefficients. A finite volume numerical method is used for the model resolution. O the contrary, to the previous two time steps schemes applied to multi-phase models, we develop a stable single time step algorithm by using appropriate variables (superficial concentrations). The abilities of the physical model are illustrated by numerical simulation of the solidification of NH4Cl(10%)-H2O and Pb-48%Sn binary mixtures in cavities. Particularly, a strong coupling between the convective flow patterns and macrosegregation is emphasized.