Bioconvection in Eyring–Powell fluid with composite features of variable viscosity and motile microorganism density

The yield stress in non-Newtonian fluids is intriguing. Their behaviours and properties transform under different conditions, such as pressure, temperature, concentration, and motile density. Consider a fascinating biological system where temperature differences ignite microorganism activity and production rates, explaining the need for refrigeration and similar processes. As such, the current model breaks free from constant assumptions about fluid properties and mathematically predicts changes in thermal conductivity and mass diffusivity, while viscosity and motile variation are modelled as a composite function of microorganism density and fluid temperature. The bio-convection phenomenon arises when microorganisms self-propel the Eyring–Powell fluid past a three-dimensional Riga plate, driven by stretching velocity. It is an intriguing interplay. To gain deeper insights into the flow model parameters, the weighted residual method (Galerkin approach) is employed to solve the model systems while the findings are presented through tables and graphs. Improving the temperature- and microorganism-dependent variable viscosity significantly decreases the fluid velocities and motile density movement but enhances the temperature and fluid concentration. Conversely, the response of temperature- and microorganism-dependent variable motile density variation energizes the flow momentum and decreases the fluid concentration considerably. For the variable viscosity parameter, \(\xi _1 \in [0,0.5]\), the skin drag force and local motile number increase by 22.6% and 5.98%, respectively. Additionally, 100% increment in variable motile density number downsized the skin friction by 289.36% while the local motile density appreciates by 18.90%. In general, the results obtained here are found to be applicable in biophysics, environmental science, and engineering systems.