The present numerical investigation examines the effect of magnetic field applied during buoyancy-motivated thermal energy transfer inside a square enclosure filled with a porous media where non-linear heating is applied from below. The potency of the magnetic field, porosity of the medium, and buoyancy are varied through the changes in Hartmann number, Ha (within a range of 0.1–500), Darcy number, Da (within a variety of 10–3–10–1) and Rayleigh number, Ra (within a variety of 104–106), respectively. The viable software package, Ansys fluent is utilized to identify the flow dynamics, and the inferences are drawn with the aid of flow patterns, temperature distributions, and heat transit rates obtained under different input parameters. It is identified that the heat transportation rate enlarges with Ra and lessens with Ha. The local Nu along the bottom boundary enhances 1.7 times as Ra is amplified from 105 to 106 while it decreases by 0.25 times as Ha is increased from 0.1 to 100. It can also be observed that the rate of heat transfer augments significantly with Da due to the enhancement of free convection within the enclosure.