The role of nanofluids in the development of many electronic devices at the industrial level is very significant. This investigation describes the thermal exploration for a bioconvective flow of Maxwell nanoparticles over stretching and revolving the cylinder placed in a porous medium. The fluid flow is in contact with chemically reactive activation energy. The swirling flow is induced by the stretching rotary cylinder. The magnetic effect of constant strength B0 is practiced to the flow system in combination with thermally radiative effects and a heat source/sink for controlling the thermal effects upon the flow system. The thermophoretic and Brownian motion characteristics, due to the nanofluid flow, are captured by implementing the Buongiorno model. The central focus of this study is to explore the thermal and mass transfer for the flow problem accompanied by motile microorganisms. The governing equations have been converted to the dimensionless form with similar variables, and the homotopy analysis method (HAM) has then been applied for solution. It has been concluded in this investigation that fluid flow decays for escalation in the Maxwell, porosity, and magnetic parameters, and Forchheimer and bioconvection Rayleigh numbers, while upsurges with the augmenting values of the Buoyancy factor. With the increasing values of the Brownian number, thermophoretic and radiation factors upsurge the thermal profiles and decline the concentration profiles. Moreover, the density of motile microorganisms declines with the expansion in the Peclet number. The range for η is taken from 0 to seven to get the convergence of the graph.