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This work examines the effects of Riga plate flow in a Powell-Eyring bioconvection Powell-Forchheimer medium. For the Powell-Eyring base fluid, mobile microorganisms are taken into account in addition to nanoparticles. Additionally taken into account are chemical reactions and the effects of linear radiation. The governing PDEs with boundary conditions are transformed into an ODE by using similarity transformation. The resulting equations are solved using the homotopy analysis approach. A detailed description is given of the link between the relevant parameters and the density of dynamic microorganisms, motion, fluid temperature, skin friction rates, local Sherwood and Nusselt numbers, and nanocomposite volume. Gyrotactic microorganism-containing nanoparticles have potential applications in biotechnology, microfluidic devices, microbial fuel cells, and enzyme biosensors. Various features of several physical characteristics are addressed through the use of tables and graphs.