The influence of the existence of the Lorentz force in the Rayleigh-Bénard (RB) convection flow in the smoothly constricted cavity from the top is presented in this paper. The liquid metal with Prandtl number of Pr = 0.02 is used with the Rayleigh number of Ra = 105, and the magnetic field is imposed in terms of Hartmann number (Ha) = 0-50. The vertically driven buoyancy force is kept constant for all simulation by maintaining the same Ra. The present flow solver with magnetohydrodynamics (MHD) principle is developed in the open source CFD toolkit OpenFOAM. The Navier-Stokes equation is coupled with Maxwell’s equation of electrodynamics to cope up the MHD based flow physics in the cavity. The thermal energy equation with Boussinesq approximation is added in the solver to study natural convection flow in the presence of the magnetic field. The orientation of magnetic field has different nature and direction of induced Lorentz force in the cavity. The imposed magnetic field normal to the gravity has the tendency to suppress the convection roll formation. Conversely, it has been observed that the magnetic field imposed in the direction to parallel to gravity bifurcates the flow and assist in the formation of several convection rolls. The detail discussion of the variation of Lorentz force in the cavity and its effect on the streamlines, isotherms, and the average Nusselt number is reported.