Thermal radiation and activation energy effects on triple-stratified Darcy–Forchheimer flow of micropolar nanofluid with gyrotactic microorganisms over a porous vertical stretching sheet

This study presents a unified mathematical model for the triple-stratified Darcy-Forchheimer flow of a micropolar nanofluid containing gyrotactic microorganisms over a porous vertical stretching sheet by simultaneously incorporating thermal radiation, viscous dissipation, activation energy, Brownian motion, thermophoresis, mixed convection, and porous medium effects. The mathematical formulation accounts for momentum, thermal, solutal, nanoparticle, and microorganism stratifications together with bioconvection induced by gyrotactic microorganisms. Appropriate similarity transformations are employed to convert the governing nonlinear partial differential equations into a coupled system of ordinary differential equations, which is solved numerically using the MATLAB bvp4c boundary value solver. The coupled effects of the governing parameters on the velocity, microrotation, temperature, nanoparticle concentration, and motile microorganism density distributions are systematically examined. In addition, the variations in the local skin-friction coefficient, local wall couple stress, local Nusselt number, local Sherwood number, and local density number of motile microorganisms are comprehensively analyzed. The numerical results reveal that thermal radiation enhances the fluid temperature and thickens the thermal boundary layer, while activation energy increases nanoparticle concentration by weakening the chemical reaction rate. The Darcy-Forchheimer porous medium parameters suppress the fluid velocity owing to increased flow resistance, whereas triple stratification significantly modifies the thermal and concentration boundary layers, thereby affecting the heat and mass transfer characteristics. Furthermore, micropolar effects and gyrotactic microorganisms substantially influence the flow structure and enhance suspension stability through bioconvection. The present investigation provides new theoretical insights into the coupled momentum, heat, mass, and bioconvective transport mechanisms of micropolar nanofluids in stratified porous media, establishes a reliable benchmark for future experimental and high-fidelity CFD investigations, and offers potential applications in geothermal energy systems, chemical reactors, bioengineering processes, thermal management technologies, and advanced energy conversion systems.Clinical trial registration: Not applicable.