Transport analysis of Darcy–Forchheimer mixed convection in Powell-Eyring nanofluid flow over a Riga plate with Cattaneo-Christov heat flux and gyrotactic microorganisms

This study examines the flow of a Powell-Eyring nanofluid across a Riga plate, including factors such as thermal radiation, Cattaneo-Christov heat flux, heat generation, chemical reaction and gyrotactic microorganisms. The aim is to construct a mathematical model to analyse the interactions among momentum, heat, mass and microbes, which are crucial for advanced thermal systems and chemical engineering. We use MATLAB's bvp4c method to numerically solve a collection of nonlinear ordinary differential equations derived from a set of general partial differential equations. Graphs and tables illustrate how critical physical factors influence the velocity, temperature, concentration of nanoparticles and quantity of microorganisms in transit. The Darcy-Forchheimer resistance, magnetic field and velocity slip all impede fluid flow. The numerical findings show that with increasing the Darcy-Forchheimer parameter, the modified Hartmann number and the porosity parameter, the velocity field is strongly suppressed while the thermal boundary layer thickness is increased with thermal radiation, Brownian motion, thermophoresis and heat production. The concentration profile decreases with greater chemical reactions and increases with thermophoresis and activation energy. Rising Peclet and bioconvection Lewis numbers diminish motile microbe density. The findings help develop thermal management systems, thermal exchangers, biological migration devices, electromagnetic flow controllers and nano-fluid energy systems.