Modeling and analysis of Casson-Carreau fluid flow past an exponentially expanding curvilinear sheet with active microorganisms

This study investigates the synergistic effects of magnetohydrodynamics (MHD) and internal heat generation on heat and mass transfer in the flow of a Casson–Carreau hybrid fluid across an exponentially curved stretched sheet, while accounting for the impact of gyrotactic microorganisms. The model incorporates buoyant forces, nonlinear heat radiation, and a first-order chemical reaction to precisely depict bioconvective transport mechanisms. Utilizing similarity transformations, the complex, coupled nonlinear partial differential equations governing the flow are reduced to a system of ordinary differential equations. These are subsequently addressed numerically using a reliable BVP4c-based shooting method. The influence of key parameters, including the Casson and Weissenberg numbers, buoyancy parameter, heat source parameter, bio-Schmidt number, and bio-Péclet number, is thoroughly analyzed. The physical characteristics, including the skin friction coefficient, Nusselt number, Sherwood number, and local motile microbe density, are thoroughly evaluated and examined. These findings offer significant insights into the design of chemical processing systems, biomedical devices, and applications related to bioconvective transport.