Thermo-bioconvective instability of thermotactic microorganism with nanofluid layer: Darcy–Brinkman model

Investigating bioconvection in nanofluids with thermotactic microorganisms is key to advancing technologies in fields such as biomedical engineering and thermal management, where understanding these interactions can lead to more efficient systems and innovative solutions. This study examines the initiation of bioconvection in a porous medium containing a nanofluid with thermotactic microorganisms in a dilute suspension. This system is confined between two horizontal parallel walls, heated from above. Buongiorno’s model outlines the flow governing equations, Pedley’s model is used for microorganism concentration and the porous medium is stimulated with Darcy–Brinkman model. To incorporate density effects, the Oberbeck–Boussinesq approximation is implemented. A linear stability analysis is conducted, resulting in the ordinary differential equations problem derived from normal mode analysis and using the bvp4c method. The presence of nanoparticle and modified Darcy number stabilizes the system while porosity shows the dual nature. The Péclet number pre-pone the onset of bioconvection. The system stabilizes as cell diffusivity decreases or as thermal diffusivity increases.