Irreversibility Analysis in the Tapered Wavy Wall of a Tubular Non-Newtonian Nanofluid with Gyrotactic Microorganisms

This research analyzes the wavy, axisymmetric flow of a Ree–Eyring non-Newtonian nanofluid, infused with motile microorganisms, within a porous, tapered cylindrical channel under a transverse magnetic field. This investigation presents a theoretical framework that may inform the improvement of energy efficiency and thermal management in biomedical engineering applications, such as drug delivery systems and microfluidic biosensors. The work provides an extended insight by a contribution to the evaluation of entropy generation, explicitly considering the influence of motile microorganisms, thereby bridging a gap in the existing literature. The comprehensive physical model further incorporates the combined effects of Joule heating, viscous dissipation, nonlinear thermal radiation, and chemical reactions. Methodologically, the governing nonlinear equations of the system were rendered tractable under long-wavelength and low-Reynolds-number assumptions and subsequently solved using the numerical Runge–Kutta–Fehlberg technique. The key conclusion is that, based on the present numerical model, careful selection of magnetic field strength and microorganism motility parameters may reduce irreversible energy losses, potentially improving the net usable work in advanced nanofluid transport systems for biomedical applications, subject to experimental validation. The most significant finding reveals that the magnetic field serves as a dual-purpose control parameter: increasing its strength boosts total entropy generation by 20–30% while simultaneously raising the Bejan number, confirming heat transfer as the dominant irreversibility mechanism in the system. Additionally, nanoparticle concentration diminishes substantially with elevated chemical reaction rates and Schmidt numbers, while microorganism density is highly sensitive to the Péclet number, which causes flow disruptions.