Thermal and solutal boundary layer of a third grade Ellis fluid over a vertical cylinder with cross-diffusion and reaction effects

We investigated the boundary-layer flow, heat, and mass transfer characteristics of a third-grade Ellis fluid over a vertical stretching cylinder. The Ellis model was modified with third-grade fluid terms, properly representing the shear-dependent viscosity and higher-order nonlinear stress behaviors characteristic of fluids used for industrial purposes and polymers. Governing equations were derived to account for momentum, thermal, and solutal transport, while emphasizing the coupled influence of the Soret effect (mass flux due to thermal gradients) and the Dufour effect (heat flux induced by concentration gradients). Moreover, the species transport equation incorporated a first-order chemical reaction for modeling. Through the use of similarity transformations, the original nonlinear partial differential equations were converted into a set of coupled ordinary differential equations, which were then solved using numerical techniques. The impacts of various physical factors are presented in both tabular and graphical form. Velocity increased due to an increase in the Ellis fluid factor. The Ellis fluid parameter indicated that the fluid's effective viscosity decreased under shear. As a result, higher values of the Ellis fluid parameter reduce flow resistance, increasing the velocity profile throughout the surface.