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In this paper, the free convective heat transfer of nanofluids in a square cavity is simulated using a numerical method. The angle of the cavity could be changed in the horizontal axis from 0 to 90 degrees. The cavity is exposed under a constant magnetic field. Two opposite walls of the cavity are cold and warm, and the rest of the walls are insulated. On the hot wall, there are two fins with the same wall temperature. The equations were discretized by the finite volume method (FVM) and then solved using the SIMPLE algorithm. Three different fin configurations (straight, inclined and curved) were studied in terms of heat transfer rate and generation of entropy. According to the simulation results, the heat transfer rate was improved by tilting the fins toward the top or bottom of the cavity. At Ra = 105 and Ha = 20, the maximum heat transfer rate was achieved at a cavity inclination of 90° and 45°, respectively, for straight and curved fins. In the horizontal cavity, heat transfer rate could be improved up to 6.4% by tilting the fins and up to 4.9% by warping them. Increasing the Hartmann number from 0 to 40 reduced the Nusselt number and entropy generation by 37.9% and 33.8%, respectively.