Unsteady Mixed Bioconvection Flow of Eyring–Powell Nanofluid with Motile Gyrotactic Microorganisms Past Stretching Surface

The provided mathematical analysis aims to scrutinize the behavior of gyrotactic microorganisms to depict their role in heat and mass transfer in an unsteady mixed convection stretched flow of special Eyring–Powell nanofluid loaded by nanoparticles and gyrotactic microorganisms with simultaneous impact of Lorentz forces and zero nanoparticle flux condition at boundary. A two-phase type is presented for modeling the nanofluid. Thought of microorganisms is adopted just to stabilize the pendant nanoparticles due to bioconvection which has been promoted by combined impacts of both buoyancy and magnetic field forces. The controlling highly nonlinear partial differential equations with the auxiliary conditions have been mutated into ordinary differential equations via a convenient similarity approach. Governing mutated equations have been solved computationally by means of fifth-order Runge–Kutta–Fehlberg scheme with 10−6 tolerance level, the numerical calculations were presented. Further, our computations illustrate that a significant impact of unsteady parameter by examining the factor values of skin friction and the local density numbers. While A parameter leads to weaken skin friction, it boosts the local density number. The coefficient of heat and motile microorganism transfer rates strengthen, when mixed convection parameter λ improves. While base fluid parameter ϵ weakens the rate of heat transfer, it enhances the local density number. In addition, comparison was provided between Newtonian and non-Newtonian Powell–Eyring fluid on velocity and temperature distributions to confirm the methodology. Comparison with given results for special conditions is presented and seen to be highly satisfactory.