<p>The Eyring–Powell nanofluid with gyrotactic microorganisms, concentration of nanoparticles, Cattaneo–Christov heat and mass transfer in the presence of thermal radiation on the upper horizontal surface of a paraboloid system is investigated. The similarity transformations are used to convert the governing partial differential equations into a collection of ordinary differential equations. Homotopy analysis method (HAM) is applied to find the analytical solution of the problem. By mean of HAM, the solutions of the governing nonlinear differential equations with boundary conditions arising from the Eyring–Powell nanofluid flow are assessed. This solution provides an effective representation for four separate profiles, with each parameter showing its effects through different curves. Graphs illustrate the effects of all non-dimensional parameters on the fluid flow, temperature, nanoparticle concentration, and gyrotactic microorganisms motion. There exists a close agreement between the present and published work.</p>