Thermal and bioconvective analysis of Williamson fluid over a porous curved stretching surface under homogeneous–heterogeneous reactions

This work presents a numerical analysis of the flow and heat transfer characteristics of a non-Newtonian Williamson fluid moving over a curved, porous stretching surface, with both homogeneous and heterogeneous chemical reactions accounted for. Using similarity transformations, the complex coupled equations governing momentum, thermal energy, species concentration, and microorganism movement are converted into a boundary value problem and solved numerically. The study quantifies that increasing the bioconvection Lewis number can reduce microorganism concentration by nearly 18%, while elevated Schmidt numbers decrease species diffusion by around 22%. Surface curvature improves thermal transport efficiency by roughly 15%, and the porous medium introduces significant resistance to the flow. Chemical reactions dramatically influence concentration profiles by either amplifying or diminishing mass transfer depending on reaction rates. These outcomes are directly applicable to enhancing the design and performance of bioreactors, polymer extrusion cooling systems, and chemical processing units involving reactive shear-thinning fluids.