Darcy–Forchheimer buoyant flow of chemically reactive Williamson fluid with swimming microorganisms over a porous curved stretching surface

This research holds importance as it deepens the scientific understanding of nonlinear magneto-bioconvective transport in reactive non-Newtonian fluids within curved porous structures, which is essential for optimized design in thermal, biomedical, and nanoengineering systems. The primary objective is to examine the Darcy–Forchheimer buoyant motion of a chemically reactive Williamson fluid containing swimming microorganisms over a porous curved stretching surface exposed to a transverse magnetic field. The governing nonlinear equations, formulated in a curvilinear coordinate system to incorporate curvature effects, are transformed into dimensionless similarity forms and numerically solved using MATLAB’s bvp4c boundary value solver. The computational results demonstrate that both the Forchheimer and Williamson parameters significantly resist fluid motion while enhancing heat and solute diffusion, whereas curvature and bioconvective parameters noticeably alter microorganism dispersion. These outcomes underscore the intricate coupling among magnetic forces, porous resistance, and biochemical reactivity, offering valuable insights for developing efficient heat exchangers, bioreactors, and porous media-based microfluidic devices.