A numerical model aimed at simulating the segregations during the columnar solidification of a binary alloy is used to investigate the effects of a forced convection. Our objective is to study how the segregation characteristics in the mushy zone are influenced by laminar flows driven both by buoyancy and by AC fields of moderate intensity. Various types of magnetic fields have been tested, namely travelling, rotating magnetic field and slowly modulated electromagnetic forces. The calculations have been achieved on two types of alloys, namely tin-lead and aluminiumsilicon. It is shown that the flow configuration changes the segregation pattern. The change comes from the coupling between the liquid flow and the top of the mushy zone via the pressure distribution along the solidification front. The pressure difference along the front drives a mush flow, which transports the solute in the mushy region. Another interesting type of travelling magnetic field has been tested. It consists of a slowly modulated travelling magnetic field. It is shown that in a certain range of values of the modulation period, the channels are almost suppressed. The normal macrosegregation remains, but the averaged segregation in the mushy zone is weaker than in the natural convection case. The optimal period depends on the electromagnetic force strength as well as the cooling rate. The latter phenomenon cannot occur in the case of rotating magnetic fields, since in that configuration the sign of the pressure gradient along the solidification front remains unchanged. Recent solidification experiments with electromagnetic stirring confirm the predicted macrosegregation patterns.