Thermohydromagnetic performances of alumina–water nanofluid in a trapezoidal vessel that considered the inclined magnetic field were investigated numerically. The bottom wall of the enclosure is heated uniformly, whereas the upper wall is adiabatic. The remaining walls are kept cold. The mathematical problem was tackled through the Galerkin finite element method. The simulated results were verified with the experimental ones. The flow and thermal fields, and local and average Nusselt numbers for the pertinent parameters were investigated. The results showed that the heat transfer rate increased by 3.6% for the addition of 5% nanoparticle volumetric fraction within the base fluid. The heat transfer rate increased by 101% for the increment in Rayleigh number from 103$103$ to 105$105$. The heat transfer rate dwindled by 18% for the increase of Hartmann numbers’ intensity of 0–20.