The effect of natural convection on solute segregation in the horizontal Bridgman configuration is studied. The objective is to check whether a single non-dimensional number, based on the fluid flow induced interface shear stress, is able to capture the physics of the mass transport phenomena. A number of heat and mass transfer numerical simulations are carried out in the laminar convection regime, and the segregation results are found to be in good agreement with the predictions of the scaling analysis. At the higher convective levels relevant for the comparison with existing experimental data, a direct computation of the segregation phenomena is not possible, but numerical simulations accounting for turbulence modeling can provide the interface shear stress. With this procedure, a good agreement between the experimentally measured segregation and the predictions of the scaling analysis is again observed, thus validating the choice of the interface shear stress as a key parameter for the segregation studies.