The purpose of this paper is a numerical study to investigate the effects of external horizontal magnetic field on heat transfer characters within a pure molten metal filled a vertical 3D cylindrical crucible. The inner and outer walls of annulus are kept at constant temperature and the upper and lower walls are thermally insulated. The model is based on magneto hydrodynamic natural-convection theory and low Reynolds number approximation. Finite volume approach and fully implicit scheme is adopted to discrete corresponding equations. Results have been conducted for three different geometrical sizes, Rayleigh and Hartman Numbers. The 3D simulation results indicate a strong relation between heat transfer, the magnetic field strength and the aspect ratio of the crucible. In addition, this model shows that the azimuthal distribution of velocity and temperature fields affected greatly in crucible in presence of external magnetic field. The model has been validated availiable results. The findings of this study are expected to be useful for enhancing the design of solidification systems.