Modeling and simulation of entropy optimization in Darcy–Forchheimer flow of magneto-Ree–Eyring nanofluid with suction/injection and motile microorganisms

Recent studies indicate that nanofluids are crucial for solar heat exchange operations and solar energy collectors. Furthermore, the importance of energy and mass transfer in entropy creation is significantly increased in a number of industrial and engineering processes, such as mechanical power collectors, air conditioning, food processing, refrigeration, and heat exchangers. As a result of this advancement, this research is aimed to explore the comparative study on bioconvective Darcy–Forchheimer flow of an incompressible hydromagnetic Ree–Eyring nanofluid over a chemically activated expanding sheet in suction and injection cases while including the consequences of radiation, energy generation, and convective boundary conditions. Boundary layer approximation is utilized to represent this investigation’s primary partial differential equations (PDE). Then, using the appropriate transformation, the models are rebuilt into nonlinear ordinary differential equations (ODE). Utilizing the BVP5C inbuilt MATLAB package, the numerical solutions for this examination are established. Further, the graphical and tabular representations allow us to analyze the impacts of several relevant features on the microorganism’s density, concentration, entropy creation, velocity, temperature, friction factor, Sherwood, and Nusselt number distribution. The outcomes reveal that the velocity field of the liquid movement is declined by applying positive amounts of the Darcy–Forchheimer and magnetic parameters, respectively. Boosting values of the radiation, thermal ratio parameter, and temperature Biot number assist an increase in the thermal field. It reveals the augmented entropy generation with the rising values of bioconvection Lewis number and Brinkman number. Furthermore, the mass transfer rate increases with larger values of the Brownian parameter and chemical reaction parameter.