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The article explores the three-dimensional stream of silver (Ag), magnesium oxide (MgO), and motile microorganism water-based hybrid nanofluids as independent of time through a circular cylinder with a sinusoidal radius. The goal of this research is to optimize the rate of energy and mass transfer through a circular cylinder having a periodic radius. The phenomena are simulated as a system of partial differential equations containing momentum, temperature, concentration, and the profile of motile microbes, which were then simplified to a dimensionless system of ordinal differential equations using the similarity technique. The problem is solved by using the parametric continuation method, which is a numerical methodology. From the analysis, it has been perceived that both the energy and velocity fields significantly enhance with the rising effect of hybrid nanoparticles (Ag–MgO). The effect of chemical reaction enhances the mass transition rate because chemical reaction parameter influence exercises the molecules inside the fluid. The motile microorganism outline is elevated with the increment of Lewis and Peclet number.