This research investigates bioconvective nanofluid flow across a linearly stretching surface within a permeable medium in a two-dimensional boundary layer, driven by its relevance to advanced cooling systems and biomedical engineering applications. The model considers water-based \(Ti{O}_{2}-\) water and \(Cu-\) water nanofluids, incorporating thermal radiation via the Rosseland approximation and an applied magnetic field. The governing equations are altered into dimensionless form using non-similarity transformations and reduced to coupled ordinary differential equations (ODEs) through the local non-similarity (LNS) method, solved numerically using MATLAB’s bvp4c solver. Results, validated against existing benchmark studies with less than 0.25% deviation, reveal several key parametric effects. Increasing the magnetic parameter \((M)\) enhances drag but reduces velocity, with the skin-friction coefficient rising by 3.24%, 4.34%, and 1.61% for \(Ti{O}_{2}-\) water and 7.02%, 2.44%, and 1.32% for \(Cu-\) water as \(M\) increases from 0.2 to 0.8. The local Nusselt number shows dual behavior: for \(Ti{O}_{2}-\) water, heat transfer increases by 11.34% at \(M=\) 0.4 but decreases by 1.90% at \(M=\) 0.6, while \(Cu-\) water exhibits up to 29.59% enhancement at \(M=\) 0.4 before decreasing by 19.72% at \(M=\) 0.8. The Eckert number \((Ec)\) weakens heat transfer due to viscous dissipation, reducing the Nusselt number by 28.6% \(Ti{O}_{2}-\) water) and 2.95% ( \(Cu-\) water) as \(Ec\) rises from 0.1 to 1.9. Conversely, the radiation parameter \(({R}_{\text{t}})\) promotes heat transport, enhancing the Nusselt number by up to 3.7% for \(Ti{O}_{2}-\) water and 0.7% for \(Cu-\) water. Increasing the stretching/porosity parameter (λ) reduces both skin-friction and heat transfer, while a higher Peclet number enhances microorganism density, reinforcing bioconvective stability.
