Advanced thermal characterization of MHD couple-stress nanofluid flow with bioconvection and radiation over a stretching cylinder

This research accounts bioconvection influence in convectively heated magnetized couple-stress material confined by cylindrical stratified regime. The mathematical modeling includes Brownian diffusive together with thermophoretic aspects, while suspension stability is ensured by considering bioconvection features owing to gyrotactic microorganisms. Robin-type thermosolutal conditions are deployed to elaborate heat–mass transmission at the magnetized cylindrical surface subject to suction/injection (wall transpiration). The investigation further considers radiation impact in energy expression. The governing mathematical (partial differential) expressions are transmuted into nonlinear ordinary differential equations (ODEs) by implementing apposite variables. These ODEs are computed analytically by utilizing homotopy scheme, assuring convergence via selection of suitable auxiliary variables. The influences of key variables on non-dimensional profiles are systematically scrutinized. The velocity exhibits an increasing trend when curvature, mixed convection and injection parameters are escalated. However, it demonstrates opposite behavior when Reynolds number, Hartman number, couple stress, and bioconvection variables are increased. The outcomes provide valuable perception into nanofluidic transportation in state-of-the-art coating technologies, bio-microsystems, and thermal energy mechanisms where magnetized nanomaterials are considered subject to bioconvection phenomena.