Chemically reactive bioconvection flow of Powell-Eyring hybrid nanofluid (HNF) over a Riga plate with gyrotactic microorganisms and thermal radition

This work explores the bioconvective flow of a Powell-Eyring HNF ($\mathrm{Go}$-$A{l}_2{O}_3$) over a Riga plate to improve thermal efficiency in biomedical devices, cutting-edge cooling systems, and applications utilizing renewable energy by combining electromagnetic actuation, nanoparticle-microorganism interactions, and non-Newtonian rheology in an efficient way. The model include the activation energy, radiating heat, Brownian and thermophoresis and motile microorganasim features. The model include single and two-phase NF models which account the Brownian, thermophoresis and nanomaterials load in a working fluid. The Rungg-Kutta numerical scheme is used to solve the system of dimensionless eqs. A comparative study has been done to examine the behavior of HNF and NF. The findings indicate that HNF exhibits high temperatures and concentration profiles than NF. The fluid velocity and drag coefficient display inverse trend against Hartman number. The chemical reaction parameter resulted in a significant increase in the Sherwood number with a high rate of 15.5 %. An increase in the Nusselt number with a high rate of 18.3 % due to higher Eckert number indicate frictional heating dominant effect. Effect of bioconvection Lewis and Peclet number on concentration are conflicting. The influence of Brownian parameter on Nusselt number with a decreased rate to 0.7 % indicate system coolong. The Sherwood number is the sensitive for activation energy and chemical reaction parameter. This work leverages the special characteristics of gyrotactic microorganisms in HNF to optimize heat and mass transfer in manufacturing and biomedical systems, such as microfluidics, bio-reactors, and energy-effective operations.