The presence of free convective heat transfer in an enclosure filled with a congealing melt leads to the output of a product with a nonuniform structure involving large grains. On applying a proper magnetic field to the melt in the enclosure, the convective flows are decreased and uniform and small grain structures are obtained. In this work, using the finite volume method, we investigated the application of a magnetic field to the convective heat transfer and temperature fields in steady and laminar flows of melted gallium in a long annulus between two horizontal cylinders at the Prandtl number 0.02. The inner and outer walls of the annulus are at T_C and T_H temperatures, respectively, with T_H > T_C. We also investigated the effect of the magnetic field intensity and the Hartmann number on the flow and temperature fields, the influence of the variation of other parameters, like the Rayleigh number, the angle of magnetic field application, the ratio of the inner to outer radii of the annulus on the flow and temperature field. It has been reveales that on changing the field angle to the horizon, the Nusselt number (Nu) is increased, which is of importance in a specific range of Hartmann numbers. Also with increase in the Rayleigh number, the change in Nu with the magnetic field intensity does not occur. In studying the influence of the outer radius to inner radius ratio on Nu at a fixed Rayleigh number, we have found that with increase in the diameter ratio, the Nu number increases.