Simulation of unsteady MHD Powell-Eyring fluid model over an inclined porous surface with oxidative microbial activity

• First Formulation of a multiphase unsteady flow over an inclined surface • Analysis of Heat and Mass transfer with nonlinear radiation and variable conductivity • Coupled Bio-convection model including Brownian motion and thermophoresis in porous media • Magnetic field strength and porous resistance strongly regulate This paper explore at the unsteady magnetohydrodynamic (MHD) boundary layer flowing of a Powell-Eyring fluid model on an inclined, permeable and extending surface in a porous media. Brownian motion, thermophoresis, varying thermal conductivity, nonlinear radiation, internal heat production and first-order chemical reaction are also included as well as the effect of oxidative microorganisms in the model. Multiplied by similarity transformations, the governing PDEs are then systematically simplified to a system of coupled non-linear ODEs, which are problematically solved numerically by using the Runge-Kutta-Fehlberg method. These findings show that with an augmentation in the magnetic field parameter, the fluid is slowed down considerably by the Lorentz force and also boosts the temperature by the Joule heating. The parameter of porosity suppresses the flow and decreases the rate of heat and mass transfer. The phenomenon of shear-thinning (determined by the Powell-Eyring parameter) maximizes the fluid movement and diffusion of masses. There is also reduced oxidation and concentration of microorganisms with high magnetic and porous resistance. Some of the thermal parameters that have significant influence on temperature and concentration profile are the Eckert number and Biot numbers. Its applications can be seen in heat transfer, chemical processing as well as biomedical fluid transport.