Bioconvection and Mixed Convection Flow around a Vertical Thin Needle with Variable Surface Fluxes

This work investigates mixed convection flow over a vertical thin needle with variable surface heat, mass, and microbial flux, incorporating the influence of gyrotactic microorganisms. The governing partial differential equations are transformed into ordinary differential equations using appropriate similarity transformations. These transformed equations are then numerically solved employing MATLAB's Bvp4c solver. The study's primary focus lies in examining the influence of various dimensionless parameters, including the mixed convection parameter, power-law index, buoyancy parameters, bioconvection parameters, and needle size parameter, on the velocity, temperature, concentration, and microbe profiles. The results demonstrate that these parameters significantly impact surface (wall) temperature, surface fluid concentration, surface motile microbe concentration, and the corresponding velocity, temperature, concentration, and microorganism profiles. The study's findings offer valuable insights into the intricate dynamics of mixed convection flow with bioconvection and have potential applications in diverse fields such as biomedicine and engineering.