Bioconvection flow of Williamson nanofluid due to gyrotactic microorganisms on curved surface with Cattaneo Christov heat and mass fluxes

Characterizing complex fluid dynamics along non-flat boundaries is crucial for developing advanced micro-biofluidic engineering devices, advanced heat exchangers, and target-specific pharmaceutical delivery systems. This study aims to investigate the bioconvective boundary layer flow of a Williamson nanofluid containing gyrotactic microorganisms over a curved stretching sheet. The physical modelling framework assumes an unsteady-state, two-dimensional, incompressible flow subject to a continuous magnetic field and wave-like transport governed by Cattaneo-Christov heat and mass fluxes. Similarity variables are utilized to reduce the governing partial differential equations into a nonlinear ordinary differential system, which is solved analytically via the Homotopy Analysis Method. The results demonstrate that increasing the geometric surface curvature parameter directly lowers fluid resistance and broadens the velocity boundary layer while, elevating the thermal relaxation time parameter introduces heat transfer delays that systematically shrink the localized thermal boundary thickness. The present work has a close agreement with the published work.