In this study, we analyze a Casson micropolar hybrid nanofluid flow and heat transfer characteristics over a stretching sheet/cylinder. The analysis takes Joule heating and thermal radiation into account, as well as the variable thermal conductivity and the prescribed thermal conditions. The nanoparticles of $Ag$ and $CuO$ with base fluid $EG$ (Ethylene Glycol) are discussed. Additionally, the study explores the impact of an inclined magnetic field on the flow behavior. The governing partial differential equations are described, including the conservation of momentum, mass, and energy, which are transformed into a nonlinear ordinary differential equation using appropriate similarity transformations. Then, these equations are numerically cracked using a reliable computational technique. The study reveals significant influences of hybrid nanofluid properties on the velocity, temperature, and microrotation profiles. The inclined magnetic field significantly affects the fluid dynamics, leading to flow resistance and thermal performance variations. The results highlight the importance of these factors in enhancing the thermal efficiency of systems using hybrid nanofluids. The thermal thickness of the prescribed conditions (PHF and PST) for the temperature enhanced due to an increment in the factor of radiation. As more radiative heat is absorbed, the fluid internal energy increases, thus leading to a rise in the temperature because the absorbed radiation boosts the kinetic energy of the fluid molecules, thereby increasing the fluid temperature. The heat transfer of the sheet achieved more as compared to the stretching cylinder.

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.