Multiphysics Simulation and Sensitivity Analysis of Magneto‐Bioconvective Nanofluid Transport in a Darcy–Forchheimer Porous Medium over a Cylindrical Surface

This study addresses the critical need to enhance heat and mass transport in nanofluid‐based biotechnological and biomedical systems through bioconvective mechanisms. The aim is to investigate magneto‐bioconvective flow of a Williamson nanofluid containing gyrotactic microorganisms over a flexible cylinder embedded in a Darcy–Forchheimer porous medium. The model incorporates thermal radiation, Arrhenius activation energy, Brownian motion, thermophoresis, and wall slip effects to capture realistic transport physics. Governing partial differential equations were transformed into ordinary differential equations via similarity variables and solved numerically using MATHEMATICA 10. Results demonstrate that thermal radiation and thermophoresis elevate temperature distributions, whereas increased Williamson fluid parameter, Forchheimer number, porosity, and magnetic field strength suppress velocity and concentration profiles. Sensitivity analysis further reveals that thermophoresis significantly enhances heat transfer while the Lewis number critically controls microorganism distribution, offering actionable insights for optimizing nanofluid applications in energy and biomedical engineering.