<p>The current article investigates the Darcy–Forchheimer flow of Eyring–Powell nanofluid over a stretching surface in the regime of a magnetic dipole. The impact of non-linear radiation, variable thermal conductivity, variable viscosity, and a heat source is extensively analyzed. Furthermore, the Brownian and thermophoretic aspects of nanofluids with activation energy are explored. The nonlinear system of governing partial differential expressions has been deduced by an appropriate transformation technique. Further, this system is numerically solved by implementing the spectral collocation method and the Galerkin weighted residual method. The obtained results are graphed and discussed in the text. Also, the effects of different flow parameters on Eyring–Powell nanofluid fluid flow compared to viscous nanofluid flow are explained through graphs. It is obtained that fluid velocity is negatively influenced by variable viscosity, the ferromagnetic interaction parameter, and the Forchheimer number. The thermal field is positively affected by variable thermal conductivity, ferromagnetic interaction, and heat source parameters. The concentration profile is a diminished function of Schmidt number, Brownian movement, and reaction variables while raising the function of activation energy and temperature difference variables. Additionally, numerical computations are done to determine the effects of various factors on the mass gradient, temperature gradient, and velocity gradient. This study has practical applications in advanced cooling systems for electronics, solar energy harvesting, and nanofluid-based heat exchangers in industries like automotive and aerospace. The inclusion of magnetic dipoles is relevant for magnetohydrodynamic devices in nuclear and fusion reactors. Additionally, the findings can enhance thermal regulation in space technology and quantum systems.</p>