Peristaltic Eyring-Powell Nanofluid Flow Linking with Microorganisms across a Curved Channel

Abstract The study of peristaltic Eyring-Powell nanofluid (EPF) with microorganisms is crucial in biomedical and industrial processes, improving drug delivery systems, bioreactors, and targeted microorganism transport. The EPF in a curved peristaltic channel under the influence of a uniform normal magnetic field (MF) and inside a permeable material is therefore considered in the current issue. The flow also comprises microorganisms and is motivated by the effects of porous media, Joule heating, non-Newtonian dissipation, and chemical reactions. The current work innovation stems from the inclusion of nanoparticles and microorganisms through non-Newtonian fluid flows in a curved channel, utilizing the curvilinear coordinates, which have several implications in engineering, industry, and biology. The flow under contemplation is caused by peristaltic waves that have a constant wavelength and amplitude. The problem’s governing equations are modeled using curvilinear coordinates. The goal is to maintain simplicity, and subsequently, so the problem is illustrated in the wave frame instead of the fixed frame. Under low Reynolds number and long wavelength approximation in the wave frame of reference, the mathematical framework addresses energy, momentum, nanomaterial’s volume fraction, and microbe concentration together with appropriate boundary conditions (BCs). The solutions of the governing system are handled with the help of shooting criteria and an appropriate numerical implicit method via the fourth-order Runge-Kutta (RK-4). The physical outcomes concerning flow parameters are presented to indicate the enhancement and decay factors of all relevant distributions, together with the heat and mass transfer coefficients. It is found that the factors that enhance the existence of nanoparticles and heat broadcast are the same that decay the presence of microbes, which gives practical importance to the current issue.