Nanofluids have various operations and prospects in heat transfer engineering to produce novel technological equipment for cooling purposes. In response to nanofluid's possible application, the transient convective alumina-water nanofluid flow in a square vessel in the presence of magnetic field and exothermic chemical reaction has been numerically investigated. We consider a square vessel, where the lower boundary of the vessel is heated, the two vertical side walls are relatively cold, and the upper wall is insulated. The finite element method based on Galerkin scheme is used to solve the governing partial differential equations along the imposing boundary conditions. We verified the present results with the standard experimental published results. The flow and thermal forms, and local Nusselt number are investigated for the numerous appropriate parameters. The time effects on the heat transfer is examined. The result shows that as the Rayleigh number increased from 105 to 106, the heat transfer increased by 72.78%. Compared with the base fluid water, the heat transfer of the alumina-water nanofluid with a nanoparticle volume fraction of 6% increased by 10.42%. The magnetic field and the Arrhenius chemical reaction parameters regulates the nanofluid flow and the heat transfer.