The effect of an imposed magnetic field on Rayleigh-Bénard convection in a constricted 2-D geometry is numerically simulated in this paper. The enclosure is heated from below and the top wall is kept cooled while the two side walls are kept thermally insulated. The magnetic field is imposed horizontally or vertically in separate cases. The middle section of the enclosure is smoothly constricted in some simulations. It is observed from the results that for an increase in the Hartmann number or constriction ratio the motion of the fluid is suppressed and hence the Nusselt number decreases. The number of convection rolls increases with increase in the constriction ratio. The flow solution abruptly turns from steady state to oscillatory flow as the Rayleigh number increases from Ra = 8000 to Ra = 10; 000 for the case of no constriction. The magnetic field along the horizontal direction shows nearly the same effect as the vertical magnetic field and the Nusselt number decreases with increase in Hartmann number in both cases. At Hartmann number Ha = 20, the motion is completely suppressed irrespective of the constriction, for the Rayleigh numbers we have studied. © 2014 Elsevier Ltd. All rights reserved.