Model development of coupled thermal and mass transport in a rheological non-Newtonian nanofluid with motile microorganisms induced by a Riga plate embedded within a Darcy–Forchheimer porous medium

This study analyzes the bioconvective flow of Powell-Eyring nanofluid over a Riga plate in a Darcy-Forchheimer porous medium, incorporating viscous dissipation and motile microorganisms. The governing partial differential equations are reduced to ordinary differential equations using similarity transformations and solved via the Homotopy Analysis Method (HAM). The effects of key parameters on velocity, temperature, concentration, and microorganism density are examined. Results show that fluid velocity decreases with stronger magnetic fields, mixed convection, Powell-Eyring fluid properties, and buoyancy ratio, but increases with the modified Hartmann number. Temperature rises with thermal radiation, Eckert number, Brownian motion, and Biot number, while mass transfer is enhanced by higher Schmidt number and chemical reactions. Increasing the bio-convection Lewis and Peclet numbers reduces microorganism density. These insights can guide the optimization of nanofluid and bioconvective processes in porous media, microfluidics, biomedical applications, and energy systems.