<p>We numerically investigated the magnetofluid dynamics of a Maxwell hybrid nanofluid consisting of graphene oxide (GO) and titanium dioxide (TiO₂) in the flow of a sodium alginate (SA) solution over a porous stretching sheet under the influence of magnetic induction. The classical energy equation is enhanced by incorporating viscous dissipation and exponential heat generation effects. Additionally, the impact of mass suction on the surface of the flow region is considered. Analysis compares the thermal and magnetic features of hybrid nanofluid (<i>GO-TiO</i>_<i>2</i><i>/SA</i>) to nanofluid (<i>GO/SA</i>) through graphical and tabular data. A novel numerical scheme, combining a direct (order reduction) method with a recursive (successive-over-relaxation) approach, is developed to solve the discretized coupled ordinary differential equations of the problem. The effects of key governing parameters on velocity, thermal, and induced magnetic field profiles are presented through graphs. It is worth noting that the shear stress at the surface decreases, while the Nusselt number increases with the magnetic field and suction parameters under the combined influence of magnetic induction, exponential heat generation, and the Maxwell fluid parameter. Tabular data confirms that the Nusselt number increases by up to 5.48% with the induced magnetic field and by up to 2.04% with mass suction in the case of hybrid nanoparticles. The findings of this research are valuable for various industrial and biomedical applications where flow regulation is required under the influence of a magnetic field, such as cooling systems in nuclear reactors and targeted drug delivery in biomedical engineering.</p>