Study of gyrotactic motile microorganisms in powell-eyring nanofluid with non-fourier and non-fick’s theories

Some of the fluids having non-Newtonian properties are polymers, molten plastic, pastes, nutritional diets, and fuels. Polymers like molten plastics are used in injection molding to make plastic products, pastes such as toothpaste and shampoo are easy to distribute because of their shear thinning behavior (it maintains its shape unless some force is exerted), nutritional diets such as cheese, cream, and yogurt allow easy packaging and spreading. Non-Newtonian fluids enhance the efficiency of oil recovery operations. Also, it is utilized as drilling mud to handle the pressure, filling gaps, and liquefy the drill bits during drilling processes. The motivation for using the three-dimensional magnetized Powell–Eyring nanofluidic model is to obtain the improved performance of heat transfer that includes advanced cooling systems in electronics and drug targeting in biomedical applications. The rheological demeanor in three dimensions enables for more meticulous predictions of flow manner and pressure drop, essential for engineering designs. With the help of magnetic field, the alliance of nanoparticles can be potentially controlled, further improving thermal conductivity and heat transfer rates. The novelty of this study includes Forchheimer heating law, mixed convection, thermal radiation, non-uniform heat source/sink, and Arrhenius activation energy. Further, the Cattaneo–Christov heat and mass flux (CCHFM) model delivers a more precise description of energy and mass transmission in viscoelastic flow regimes by containing a finite thermal relaxation time. By acquiring non-Fourier heat conduction effects and transient heat transfer phenomena, this model offers unique insights into the behavior of complex fluids and enhances our concept of heat and mass transfer processes in viscoelastic materials. In bioconvection, the motile microorganisms reveal a swimming pattern, where individual cells actively drive themselves through the fluid using cilia and flagella. The overall motion of such microorganisms generates fluid flows, which can manifest as vortices, jets, or other fluid structures. The role of gyrotactic bacteria in bioconvection provides foresight into microbial ecology, and biotechnological applications such as biofuel production, and wastewater treatment. These features of the designed model make it differ from the existing studies. The related nonlinear flow model is altered into a system of coupled ordinary differential equations using suitable transformations. Numerical integration scheme named shooting method with the Runge–Kutta fourth–fifth-order algorithm is applied. The influence of the pertinent parameters upon fluid velocity, temperature, concentration, and bioconvection is observed. Furthermore, friction factor, Nusselt number, and transport rate for motile microbe values are shown for a key parameter. The current results are compared with numerical solutions and found good agreement. A higher thermo-Biot number and radiation parameter reveals thermal efficacy, and a reverse trend is observed for thermal relaxation parameter. The mass relaxation time declines the concentration profile whereas bioconvective Lewis's factor and activation energy parameter improve it. The magnetic parameter enhances the drag force, decaying energy transport rate is noticed for higher thermal relaxation parameter, and bioconvection Lewis number advances the transmission rate of microorganisms.