A fin is an extended surface used to enhance the surface area of a heat transfer surface between a hot source and the outside environment. To maximise the rate of heat transportation, the exterior surface of heated equipment is equipped with fins of various geometries. Heat is exchanged using fins in radiators, refrigeration systems, superheaters, combustion engines, electrical equipment, electric transformers, space vehicles, and aircraft engines. Reflecting these applications, we analyse the effect of a magnetic field on the thermal properties of radiating porous rectangular fins. The proposed model is numerically analysed using the shooting method under the influence of radiation and convection, then compared with the DTM solution and both the solution found closer to each other. The effect of various dimensionless parameters on temperature transmission in magnetized rectangular-shaped porous fins is revealed using numerical results. It is revealed that, when the Raleigh, Hartmann, Peclet numbers, convective and radiative parameters increase, the fin?s thermal profile decreases, whereas the thermal profile increases with an increase in surface temperature, porosity, and ambient temperature. It is observed that the magnetic effect increases the heat transfer rate from porous rectangular fin surfaces. Accordingly, efficiency increases as Hartmann number, Raleigh number, and radiative parameter rise. Increasing Peclet number, surface temperature, and ambient temperature leads to a reduction in efficiency.