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The flow and heat transfer characteristics of a three-dimensional cavity filled with a conductive fluid are investigated in this study. The three-dimensional Navier-Stokes equations and energy equation are solved directly using our self-developed algorithm, SCM-ACM, which combines the spectral collocation method (SCM) with high-precision and exponential convergence, and the artificial compression method (ACM) with easy implementation and good numerical stability. In this paper, we examine the effects of Hartmann numbers ranging from 0 to 100, magnetic field direction, and Grashof numbers ranging from 1×10⁴ to 1×10⁶ on the structure of the flow and temperature fields, with a Prandtl number of 0.71. The results show the Grashof and Hartmann numbers have a significant impact on the flow and temperature structure in the middle of the cube, but little effect on that near the walls. As the Grashof number increases, a stable thermal stratification is formed at the center of the cube, and a thermal boundary layer is formed near the horizontal wall. The increase in Grashof number enhances the heat transfer rate and increases the temperature difference between the upper hot fluid and the lower cold fluid in the cube. Furthermore, the increase in Grashof number enhances the convective intensity near the wall, leading to the formation of more vortices, which move towards the corners due to the combined action of centrifugal force and inertia. On the other hand, the Hartmann number has a stabilizing effect on the flow and weakens the heat transfer, while at higher Grashof numbers, the magnetic effect becomes more pronounced. When Ha>50, the magnetic effect is no longer significant. The magnetic field parallel to the temperature gradient (B_X) is more effective in suppressing heat transfer than the magnetic field perpendicular to the temperature gradient (B_Y).