This research investigates hemodynamic behavior in stenosed arteries using a rheological model that integrates hybrid nanoparticles (copper and graphene) suspended in blood. A mathematical framework is developed to analyze flow dynamics in an inclined artery with mild stenosis, incorporating electromagnetic fields, Hall currents, heat generation, and porous media effects governed by Darcy’s law. Simplifications under mild stenosis and low Reynolds number conditions enable analytical solutions via the homotopy perturbation method (HPM) and Akbari Ganji Method (AGM). The minimal error observed for axial velocity is \({2.34\times 10}^{-10}\) , while that for temperature is \({8.87\times 10}^{-10}\) . Key findings reveal that hybrid nanoparticle enrichment reduces blood flow resistance, and elevated Hall parameters significantly decrease wall shear stress at the arterial boundary. Additionally, an increase in the Darcy number leads to higher axial velocity in all cases. Streamline visualizations demonstrate altered flow patterns in stenosed regions under varying nanoparticle volumes and electromagnetic inputs. Notably, Hall currents exert a pronounced influence on nanoparticle–enhanced flow behavior, underscoring their relevance in biomedical contexts. The efficacy of HPM and AGM in resolving nonlinear momentum equations is validated, supporting their utility in modeling complex bio–nanofluid systems. These insights advance applications in targeted drug delivery, bio–nanofluid mechanics, and therapeutic device design. They offer pathways for optimizing nanoparticle–mediated treatments in cardiovascular diseases and oncology.
