<p>This study presents a numerical analysis of steady Darcy–Forchheimer hybrid nanofluid flow over a stretching surface, considering the influences of thermal radiation and motile microorganisms. A hybrid nanofluid created from GO and MoS₂ nanoparticles in water (H2O) as the base fluid is employed in the analysis. Hybrid nanofluids are widely utilized in various fields such as heat exchangers, cooling systems, biomedical instruments, and agricultural applications. The governing model consists of nonlinear PDEs that apply appropriate similarity transformations to become a dimensionless system of ODEs. A three-stage Lobatto approach in MATLAB is employed to numerically solve the resulting solution. The model further investigates the dynamic roles of thermophoresis and Brownian motion. Both graphical and numerical illustrations of the deviations in velocity, temperature, concentration, and motile microbe distributions instigated by involving physical parameters. In the primary component of velocity of fluid deduction and enhance in the secondary component of velocity of fluid. The growing in thermal profile when growth in suction and radiation parameters. When growth in Brownian motion parameter then declined the concentration profile but boost against thermophoresis. Also, the profile of the motile microbe is demonstrated to be reduced by both Lewis number and Peclet number. These results contribute significantly to the advancement of heat transfer efficiency in engineered nanofluids.</p>