The effects of a slow rotating magnetic field on Thermoelectric Magnetohydrodynamics during alloy solidification were investigated using a micro-scale numerical model. For conventional directional solidification it was shown that in general the time-dependent acceleration force on the fluid flow is negligible. Using an undercooled growth model with directional solidification approximations the effect on dendritic morphology is predicted, suggesting thermoelectric induced flows will create a significant increase in secondary branching and preferential growth directions on one side of the primary trunk. The extent of macro-segregation under these conditions was also estimated.