<p>This research examines the Carreau fluid model’s unsteady flow under magnetic forces. For the Carreau fluid model, the effects of viscous dissipation, heat radiation and bioconvection of micro-organisms are also considered, along with thermophoresis and Brownian motion. The movement of micro-organisms causes bioconvection, a noteworthy event in fluid mechanics. Due to hydrodynamic instability and maintaining spinning microscopic micro-organisms in suspension, its value cannot be overlooked. Bioconvection is considered to have a wide range of applications, including the refinement of scientific models, as well as its use in bio-microsystems, biomedical fields and environmentally responsive products. Here, new mass flux boundary conditions (BCs) are thought through for the already completed task. Additionally, the set of partial differential equations (PDEs) produced is transformed into a coupled system of ordinary differential equations (ODEs) and the resulting ODEs are then solved using the well-known numerical method known as bvp4c. All significant parameter effects are graphically displayed. Higher thermal radiation values are thought to increase in the thermal field. The thermophoresis factor also exhibits this behaviour, although the thermal field is perceived to decrease with increasing Prandtl numbers. Additionally, as the Peclet’s number increases, the number of bacteria present reduces.</p>