Bioconvection Darcy–Forchheimer Flow of Ree‐Eyring Nanofluid Over a Riga Plate With Arrhenius Activation Energy and Viscous Dissipation

ABSTRACT This work examines the intricate interactions of heat radiation, viscous dissipation, the Cattaneo–Christov thermal model, gyrotactic microorganisms, Arrhenius activation energy, and Darcy–Forchheimer flow affecting Ree‐Eyring nanofluid behavior across a Riga plate. The non‐Newtonian characteristics of the Ree‐Eyring fluid are quantitatively represented by integrating porous media flow resistance, radiative heat effects, activation energy of chemical reactions, and the bioconvective motion of gyrotactic microorganisms. The resulting nonlinear system is solved numerically using a hybrid approach: Mathematica's NDsolve tool is employed to obtain accurate initial guesses, and MATLAB's BVP4C collocation solver is then used for high‐accuracy profiles with adaptive mesh refinement. This detailed research examines the influence of the Peclet number, radiation parameter, activation energy, and Hartmann number on velocity, temperature, nanoparticle concentration, and microbe density. The results indicate that an increase in Darcy–Forchheimer number and porosity reduces fluid velocity. Conversely, temperature increases with heightened intensity of the heat source, augmented Brownian motion, and radiation. The concentration of nanoparticles decreases with increased thermophoresis and activation energy. Furthermore, an increase in the bioconvective Lewis number and Peclet number decreases the density of motile microorganisms. These findings help improve heat and mass transmission in microfluidic devices, heat exchangers, and bioconvection‐driven bioreactors. This study advances the creation of multifunctional bio‐nanofluid systems to improve medication delivery and bioreactor efficacy.