Utilizing Python for numerical analysis of bioconvection in magnetized Casson-Maxwell nanofluid systems with gyrotactic microorganisms: An investigation of dominant factors

• Analyzes bioconvection in magnetized Casson-Maxwell nanofluid systems. • Studies the impact of Lorentz force and porosity on fluid velocity. • Examines Peclet number's effect on microorganism density and motility. • Investigates magnetic field influence on skin friction in nanofluids. This study numerically investigates bioconvection in a magnetized Casson–Maxwell nanofluid with gyrotactic microorganisms using the Buongiorno model to analyze thermophoresis and Brownian motion effects. The Casson-Maxwell fluid model captures the complex rheological behavior of non-Newtonian fluids and the dynamics of microorganism motion. Boundary conditions and governing equations are transformed into dimensionless forms for simulation via Python, using similarity and solvebvp functions. Key findings show that increasing the magnetic parameter (Ma) from 0. 1 to 0. 5 reduces the velocity gradient near the surface by 20 %, while higher porosity (Pm = 0. 5) decreases flow velocity by approximately 15 % due to increased medium resistance. Radiation (Ra = 0. 5) and heat generation (Qm = 0. 1) parameters enhance temperature profiles, raising the normalized temperature by 12 % at η =5. Due to reactive species consumption, higher chemical reaction rates (Kc = 0. 1) and Schmidt number (Sc = 10) reduce concentration profiles by 18 % near the surface. The Peclet number (Pe = 10) decreases microorganism density by 25 % over the domain, balancing advective and diffusive transport. The study highlights the magnetic field's impact on skin friction for Casson and Casson–Maxwell fluids, providing valuable insights into bioconvection in reactive nanofluid systems for applications in thermal management systems, bioreactors, and energy devices.