Numerical insights into enhanced heat transfer mechanisms in TiO₂-Au ethylene glycol nanofluids within Darcy porous media using fractional calculus

This study investigates the behavior of magnetohydrodynamic (MHD) boundary layer flow involving hybrid nanofluids containing Titanium Dioxide TiO2 and Gold (Au) nanoparticles dispersed in ethylene glycol (EG). These hybrid nanofluids have gained significant attention due to their enhanced thermal properties, making them suitable for advanced industrial and technological applications. The governing equations for the flow and heat transfer are formulated using fractional calculus, providing a more accurate model of the viscoelastic properties of the fluid. Additionally, the effects of thermal radiation, MHD, and porosity are incorporated to reflect realistic scenarios encountered in heat exchangers, electronic cooling systems, and biomedical devices. The complex fractional partial differential equations governing the system are solved numerically using the finite difference method in combination with the L1algorithm, ensuring an efficient and accurate solution process. To confirm the validity of our approach, we conducted an error analysis by comparing the solutions with exact solutions to verify the accuracy of our results. The study reveals that the porosity parameter (λ3) increases the skin friction coefficient (|Cf|) by 3.52% for hybrid nanofluids. Additionally, the thermal fractional parameter (γ) enhances the Nusselt number (Nu) by 3.52% for hybrid nanofluids. Through this numerical analysis, the potential of hybrid nanofluids to enhance heat transfer performance is demonstrated, offering substantial benefits in industries such as renewable energy, electronics, and aerospace engineering. Furthermore, the results underscore the superiority of the fractional model over the classical model in capturing complex thermal and flow dynamics, providing deeper insights into advanced fluid behavior.