Thermal radiation analysis of magnetized Darcy-Forchheimer flow of Williamson nanofluid with activation energy and entropy generation: A Cattaneo-Christov model

• Entropy generation in MHD Williamson nanofluid flow is numerically analyzed. • Non-Fourier heat transport examined using the Cattaneo–Christov model. • Keller–Box method efficiently solves the governing nonlinear ODEs. • Thermal radiation increases temperature and heat transfer by up to 14.72%. In recent years, researchers have extensively investigated the behaviour of thermal boundary layers under various assumptions to meet modern engineering demands. However, a review of the existing literature reveals that no comprehensive study has examined thermal transport in magnetohydrodynamic (MHD) Darcy-Forchheimer flow of a Williamson nanofluid past a stretching sheet, accounting for non-linear mixed convection, suction/injection effects, and entropy generation. To address this gap, the present study investigates how variable thermal flux, heat generation, viscous dissipation, and suction affect the Darcy-Forchheimer flow of MHD Williamson nanofluid over a vertical stretching surface, utilising the Cattaneo-Christov heat flux model to account for thermal relaxation time. The resulting equations are solved using the implicit Keller-Box Method (KBM). The existence of a magnetic field, along with porosity, reduces the flow of the field. The fluid’s temperature increases due to the heating effect of the heat source. However, it decreases with the thermal relaxation parameter. A chemical reaction facilitates a decrease in the concentration field. Furthermore, the heat transfer rate increases by 14.72% as the radiation parameter rises from 0.3 to 0.9, and by 22.61% as the mixed convection parameter increases from 0.2 to 0.8. Additionally, an increase in the activation energy reduces the mass transfer rate. This extension is essential for various biomedical and industrial applications, including power generators, nuclear reactor cooling, magnetic drug targeting, oil recovery, and geothermal energy.