Unsteady Bioconvection Flow of a Tangent Hyperbolic Hybrid Nanofluid Through a Darcy–Forchheimer Porous Medium: Impacts of Thermal Radiation, and Activation Energy in Assisting and Opposing Flow Regions

The aim of the current study is to investigate the effect of the presence of microorganisms on the heat and mass transfer of the assisting and counterflow of an unsteady hybrid tangent hyperbolic nanofluid. This nanofluid contains copper and aluminum as nanoparticles in the basic fluid (water). In addition to the presence of mobile microorganisms that work to stabilize the nanoparticles. The fluid flows in a porous medium through a horizontal extended plate, and a magnetic field and thermal radiation are applied. The partial differential equations governing the problem are converted into ordinary differential equations using appropriate transformations. The resulting equations are solved numerically using the bvp4c algorithm implemented in MATLAB. Impacts of important controlling parameters on the velocity, temperature, concentration, and concentration profiles of motile microorganisms are discussed. The effect of key parameters on the Nusselt number, skin friction coefficient, Sherwood number, and density of the motile microorganisms is also tabulated. The study reveals that increasing the instability coefficient enhances both the mass and heat transfer rates of the flows. Additionally, it is observed that the wall shear stress generated by the surface over which the fluid moves increases. Increasing chemical reactivity leads to a drop in the concentration of nanoparticles, while their concentration improves with increasing activation energy. Furthermore, increasing bioconvection parameters contributes to a decrease in the concentration of microorganisms. Thermal radiation, on the other hand, significantly affects the heat transfer process. A higher temperature ratio parameter and the Weissenberg number led to a reduction in heat transfer efficiency while enhancing mass transfer efficiency and raising microorganism density. Similarly, an increase in the porosity coefficient and the Weissenberg number intensified the shear stress exerted on the fluid, resulting in a higher surface friction coefficient due to increased flow resistance. It is observed that the Nusselt number is higher in the counter‐flow case, while the Sherwood number is higher in the assisted flow case. These results offer significant benefits in various applications, such as medicine, energy, and industry.