A mathematical model is concerned with the natural bioconvective flow over a radiative vertical cylinder embedded in a Darcy porous medium drenched with a nanofluid containing both nanoparticles and gyrotactic microorganisms. The model utilized for the nanofluid consolidates the impacts of Brownian motion and thermophoresis in the presence of passively controlled boundary conditions and the Rosseland approximation is applied to characterize the radiative heat flux in the energy equation. Appropriate transformations are used to reframe the PDEs of the modeled system into a nonsimilar form. The obtained data are authenticated with an outstanding agreement. In this regard, the engineering quantities of interest are calculated widely with a greater grade of accuracy and therefore abstracted tabularly. To explain the influence of the emerging important flow-field parameters on the curves of velocity, temperature, and microorganisms concentration, as well as the local Nusselt and motile microorganism numbers. Several elucidations are carried out successfully along with detailed illustrations. The presented theoretical investigation has a considerable role in engineering where nanofluids flow is applied to organize a bioconvection process for the development of power generation and mechanical energy. One of the more important features of bioconvection is the aggregation of nanoparticles with motile microorganisms requested to augment the stability, heat and mass transmission.