FRACTAL FLOW MODEL FOR DARCY–FORCHHEIMER COUPLE STRESS CLUSTER INTERFACIAL NANOLAYER MAGNETIZED METALLIC NANOFLUID FLOW THROUGH A POROUS CHANNEL

This study is a comprehensive analysis of the thermal and fluid dynamics of magnetized metallic nanofluids flowing through a porous channel under the influence of Darcy–Forchheimer effects and couple stress theory. The fractal flow model is used to explore the interfacial behavior of nanolayers, focusing on the impact of various dimensionless parameters such as thermal diffusivity, Casson fluid parameter, magnetic parameter, Reynolds number, and Prandtl number on the velocity, temperature, and porosity profiles. The governing equations, formulated using Darcy–Forchheimer theory and modified by couple stress, are solved. Results reveal that increasing the thermal diffusivity reduces the temperature profile, while higher values of the Casson fluid and magnetic parameters increase it. Similarly, variations in the Reynolds and Prandtl numbers significantly affect heat transfer within the system. These findings provide crucial insights into optimizing heat transfer in engineering applications involving magnetized nanofluids in porous media, with potential applications in industrial and biomedical fields.