Both three-dimensional (3D) and quasi-two-dimensional (Q2D) numerical simulations are conducted to study the natural convection in an electrically insulated cavity with imposed horizontal magnetic fields (MF) normal to the main circulation, where two opposite vertical walls are kept at different temperatures and the other four are thermally insulated. We mainly focus on flows at Hartmann (Ha <= 10(4)) and Grashof (Gr <= 4 x 10(7)) numbers. It is found that, with lower MF, the strengthening of the main convection, which is due to the suppression of the secondary flow along the MF lines by the Lorentz forces, results in the enhancement of heat transfer. Once the Q2D is achieved, the convection and the heat transfer would be damped by the further increase of MF. Our numerical results have confirmed that the damping velocity and kinetic energy of main convection are scaled as Gr/Ha (see Ref. Tagawa et al. (2002)). At the same time, the computed average Nusselt number (Nu) agrees well with the experimental results of Okada and Ozoe (1992), which can be correlated as a function of Ha/Gr(3/4) rather than Ha/Gr(1/3). (C) 2018 Elsevier Ltd. All rights reserved.