Thermal behavior and efficiency enhancement of CuO - Al₂O₃ hybrid nanofluids using fractional calculus

Hybrid nanoparticles significantly enhance thermal system efficiency and performance. This article investigates the impact of convection, diffusion, thermal radiation, and chemical reactions on an H₂O-based fractional Carreau hybrid nanofluid containing \( {\text{CuO - Al}}_{{\text{2}}} {\text{O}}_{{\text{3}}} \) ${\text{CuO - Al}}_{\text{2}}{\text{O}}_{\text{3}}$ within a porous media. A distinctive aspect is the application of fractional-order derivatives in the flow equation, enhancing model accuracy by integrating both integer and non-integer orders, using the Caputo definition for fractional calculus. Governing equations are dimensionally reduced and discretized via the explicit finite difference approach, ensuring stability through stringent convergence criteria. Quantitatively, results indicate that an increase in the Prandtl number \( \mathbb{P}_{\mathfrak{r}} \) ${\mathbb{P}}_{\mathfrak{r}}$ from 0.5 to 2.0 results in a 40% reduction in the temperature profile, highlighting reduced thermal diffusion. The Nusselt number, representing heat transfer enhancement, increases by approximately 19% when the fractional-order parameter \((\alpha )\) $(\alpha )$ is raised from 0.5 to 0.8. Additionally, the Sherwood number shows a strong dependence on the Schmidt number \( \mathbb{S}_{\mathfrak{c}} \) ${\mathbb{S}}_{\mathfrak{c}}$ , with a 25% reduction in concentration profile observed for higher \( \mathbb{S}_{\mathfrak{c}} \) ${\mathbb{S}}_{\mathfrak{c}}$ values. The findings align strongly with recent studies, validating the model’s robustness and offering a comprehensive framework for further modeling of porous media flows in practical applications, such as gas turbines, catalytic converters, and condensers.