Thermal and mass transport characteristics on bioconvective magnetohydrodynamic Casson–Williamson fluid flow across a vertical plate with 2-d and 3-d insights

This study explores the magnetohydrodynamic bioconvective Casson–Williamson (CW) fluid flow over an infinite vertical permeable plate, with a focus on the combined effects of Arrhenius activation energy, heat sink, and gyrotactic motile microorganisms. In contrast to standard Newtonian models, the CW framework incorporates shear-thinning non-Newtonian behavior, which is critical in biological and industrial processes. The integration of activation energy with bioconvection processes in a dual non-Newtonian environment is novel, having not previously been addressed for vertical porous plates. The governing nonlinear partial differential equations are reduced to a system of ordinary differential equations and numerically solved with the robust Lobatto IIIa-based bvp4c MATLAB solver. Two- and three-dimensional representations show how magnetic fields, porosity, radiation, thermophoresis, Brownian motion, and chemical reactions affect velocity, temperature, solute concentration, and microbe distributions. The main findings suggest that activation energy improves concentration profiles; however, bioconvection Lewis number and Peclet number reduce microbial density. In addition, the Brownian motion parameter improves temperature field as well as mass transport rate. The discoveries improve our knowledge of coupled heat and mass transport under complicated boundary conditions, with practical implications in bioengineering, materials processing, and environmental fluid dynamics. Validation against previous research supports the correctness of the current model and emphasizes its broader physical breadth.