The article deals with magnetic field damping of free-convective flows in cavities similar to those used in artificial growth of single crystals from melts (horizontal Bridgman configurations) and having aspect ratios A equal to 1 or 4. The combined effect of wall electrical conductivity and direction of the magnetic field on the buoyancy-induced flow of gallium was investigated numerically. The validation of the numerical method was achieved by comparison with both experimental and analytical data found in the literature. The plotted results for variation of velocity, temperature and Nusselt number in terms of the Hartmann number Ha and Rayleigh number Ra showed a considerable decrease in convection intensity as the magnetic field is increased, especially for values of Ra situated around 10(5). The calculations also showed that the horizontally directed magnetic field (perpendicular to the y-z plane) is the most effective in controlling the flow and hence the speed of growth of the crystal and its composition in dopants. Also, wall electrical conductivity enhances damping by changing the distribution of the induced electric current to one which augments the magnitude of the Lorentz force in regions where it acts as a sink and diminishing it in the remaining parts of the cavity.