This study conducts a numerical investigation into the heat transfer enhancement of $\mathrm{Fe}_3 \mathrm{O}_4$-distilled water nanofluid within a magnetically influenced environment. The research is centered on the analysis of the impact of varying magnetic field strengths on the heat transfer characteristics in a controlled tube setting. The tube, possessing an inner diameter of 25.4 mm and a length of 210 mm, serves as the medium for the flow of nanofluid, initially at 300 K. The influence of magnetism on the nanofluid's thermal boundary layer and the formation of fluid vortices is meticulously examined, leveraging the application of magnetic fields ranging from one to three Teslas. In this context, the study observes the behavior of magnetic particles under these fields, revealing their attraction or repulsion, subsequently inducing turbulence and modifying flow patterns. It is noted that increased flow velocities tend to shield the magnetic field's thermal effects. A key focus is placed on the Nusselt number and $\mathrm{Y}^{+}$ as indicators of heat transfer efficiency, both of which demonstrate significant variations with changes in the magnetic field strength and fluid velocity. The Nusselt number, in particular, escalates to a peak value of 128.7 when exposed to a 0.1 m/s flow velocity and a magnetic field of 3 Teslas. The findings suggest an interrelation between increased magnetic field strengths and the entrance of the fluid into a turbulent state, thereby facilitating an efficient temperature transfer to the fluid. Notably, this research sheds light on the prospect of using ferrofluid-based cooling systems in electrical equipment, highlighting the potential of magnetically manipulated nanofluids to enhance heat transfer capabilities. The investigation delineates how the interplay between magnetic fields, fluid velocity, and nanofluid properties can be optimized for improved thermal management in various applications.