This study discovers the mass and heat transfer characteristics of a magnetohydrodynamic GO-Ag-CuO-Al₂O₃/EG nanofluid streaming past a shrinking sheet under the force of various physical effects. The Powell-Eyring fluid model is engaged to account for the effect of a magnetic field, a stagnation point, viscous dissipation, radiation, Joule heating, and suction. Through similarity transformations, the governing partial differential equations are reduced to a system of ordinary differential equations, which are then resolved numerically using the bvp4c solver in MATLAB. The results affirmed that raising the heat transfer complements the thermal boundary layer, whereas reductions in the skin friction coefficient contribute to a reduction in drag force. Moreover, the velocity profile rises because of the shrinking effect, while the temperature profile decreases. The enhanced thermal conductivity provided by the quaternary nanoparticle suspension (GO-Ag-CuO-Al₂O₃) suggests that this fluid can maintain lower surface temperatures under high-heat flux conditions compared to mono or hybrid nanofluids. Consequently, these characteristics are particularly advantageous for electronic device cooling and heat exchangers in renewable energy systems where rapid heat dissipation is critical. Furthermore, the observed reduction in drag force under the influence of the magnetic field provides a theoretical basis for optimizing energy efficiency in magnetohydrodynamic pumps and metallurgical processing. These findings offer specific design parameters for boosting thermal management in industrial applications involving tetra-hybrid nanofluids.