The purpose of this investigation is to explore in depth a duct flow that incorporates the Al2O3/H2O nanofluid while it is subjected to an external field impact. The duct is made up of two opposing fins that are joined to the walls that are opposite each other. The temperature may be considered to be uniform at the cross-sectional plane of the duct. Additionally, the heat flow at the border is not variable. The finite volume approach was chosen because it offers a satisfactory balance between computing efficiency and the accuracy of its solutions. Importantly, our results indicate that the slowness of flow that is caused by increased Rayleigh numbers may be efficiently regulated by introducing an external magnetic field that has been carefully measured. The significance of this study demonstrates how magnetic-field modulation can be strategically employed to control thermal-hydraulic behavior in internally finned duct systems. The results provide valuable guidance for designing advanced cooling channels, energy devices, and thermal management systems where enhanced heat transfer and flow stability are required under magnetic field environments. The installation of an external magnetic field of moderate strength resulted in a drop of about 75 % in both the maximum velocity and temperature across the duct. Further, a jump of approximately 66 % in the average Nusselt number has been brought about by 25 % increase in the fin height. Through the use of this study framework, a link between thermal-hydraulic behavior and the application of magnetic force is established. The involvement of the Lorentz force, which offers resistance to the motion of the fluid by operating in a direction that is perpendicular to the direction in which the fluid is flowing, and the magnetic force, is brought about as a consequence of the magnetic forces. Consequently, it is possible to draw the conclusion that a larger Nusselt number is the result of both a higher Rayleigh number and a higher magnetic parameter.