Active‐passive controls of rotating tri‐hybrid nanofluid flow with gyrotactic microorganisms over a stretching bidirectional sheet

Bio‐convection, or biological transmission, is crucial for understanding microbial ecology, population dynamics, and microbial behaviour in complex environments, offering vast research opportunities. This article investigated the effects of a non‐uniform heat source/ sink on tri‐hybrid nanofluid flow comprising gyrotactic microorganisms over a bidirectional stretching sheet with active‐passive control boundary condition. This research explores new aspects such as bio‐convection and rotational fluid. The Buongiorno model is used to incorporate the effects of thermophoresis diffusion and Brownian motion. The associated boundary conditions and model equations are transformed into dimensionless ordinary differential equations (ODEs) form using the suitable similarity transformation. The Runge Kutta‐4 (RK‐4) shooting method is implemented in Mapple‐21 to produce informative numerical results. The results are displayed in tables and graphs for further investigation and discussion. The computational results reveal multiple important contributions from key model parameters. Both actively and passively controlled nanofluid flow and microorganism profiles are reduced for a higher value of bio‐convection Schmidt number and the Peclet number but increased for the rotational parameter. The density of microorganisms enhanced by 75.16%, 75.41%, and 75.49% for passive control and 59.65%, 60.01%, and 60.07% for active control as bio‐convection Schmidt number grows for nanofluid, hybrid nanofluid, and tri‐hybrid nanofluid.