Advanced Bioconvective Hydromagnetic Ree-Eyring Nanofluid Transport with Cattaneo–Christov Heat Flux and Gyrotactic Microorganisms in a Darcy–Forchheimer Medium

In recent years, bioconvection patterns have garnered considerable interest due to their vital role in various pharmaceutical, environmental, and industrial engineering applications. Motivated by these practical implications and the broader scope of inclusive innovation, the current work discovers the bioconvective hydromagnetic flow of Ree-Eyring non-Newtonian nanofluid through a vertically elongating surface in a Darcy–Forchheimer porous medium. The flow mechanism is influenced by multiple physical, systems, comprising a chemical reaction, Cattaneo–Christov heat flux, uniform magnetic field, activation energy, thermophoresis, viscous dissipation, Brownian motion and mobility of gyrotactic microorganisms. The governing PDEs of Buongiorno-Ree-Eyring model are transmuted into a system of nonlinear ordinary differential equations via similarity functions. These reduced differential equations are tackled numerically using bvp4c-function of MATLAB, and the outcomes are compared with those obtained from ANN model and earlier published literature to confirm accuracy. The detailed graphical and tabular analysis are carried out to calculate the impact of diverse fluid parameters on involved profiles and physical quantities. The results reveal that the microorganism concentration profile drops with rising values of the Peclet and bioconvective Lewis number. The outcomes of this investigation offer useful perceptions for improving thermofluidic mechanism and optimizing heat transport efficiency in nanofluid-based bioconvective devotions.