Abstract The flow of Eyring-Powell nanofluids containing motile microorganisms within the conical space between a rotating disc and cone is of significant relevance to bioreactor design, biotechnological processing, targeted microbial transport, and materials engineering. This study focuses on the steady, incompressible, non-Newtonian behavior of such a system, incorporating the effects of a vertically applied magnetic field, Ohmic dissipation, chemical reactions, and heat generation/absorption. The governing partial differential equations for momentum, energy, nanoparticle concentration, and microorganism density are transformed into a system of coupled nonlinear ordinary differential equations via suitable similarity transformations and solved numerically using the shooting method in Mathematica. The results reveal that increasing fluid elasticity (Weissenberg number) drastically suppresses axial pumping velocity, leading to reduced cell densities, slower production rates, and diminished product yield in bioreactor applications. Conversely, swirl velocity and mixing intensity are enhanced. The applied magnetic field increases tangential drag, raising the torque and power required for impeller rotation. For optimal fuel mixing or nutrient distribution, a lower chemical reaction rate is recommended. Furthermore, increases in the Lewis and Péclet numbers indicate a degradation in microbial presence, providing critical insights for the operational tuning of microbial bioreactors. The study underscores the importance of rheological, magnetic, and biochemical parameters in the design and optimization of advanced biofuel production systems and rotating thermal devices.
Khaled Elagamy (Tue,) studied this question.