Radiative heat transfer and entropy generation in MHD Williamson hybrid nanofluid flow over a Darcy–Forchheimer medium with heat source

Entropy generation (EG) analysis is a fundamental tool for evaluating irreversibility and thermodynamic efficiency in hybrid nanofluid (HNF) flows, as it quantifies energy losses arising from heat transfer and fluid friction. It enables the identification of dominant sources of irreversibility and the determination of optimal operating conditions. Consequently, EG analysis plays a crucial role in enhancing heat transfer performance while minimizing thermodynamic losses in advanced thermal systems. In this study, we have analyzed EG in magnetohydrodynamic Williamson HNF flow with characteristics of transfer of heat over a permeable stretched sheet along with Darcy Forchheimer effects. The impacts of radiation, dissipation, and heat source are accounted in the expression of thermal energy. The relation for concentration is reported by taking the influence of chemical reaction. The HNF is constructed by suspending copper [Formula: see text] and aluminum oxide [Formula: see text] nanoparticle into water-based Williamson liquid. For modeling of EG thermodynamics, second law is utilized. Formulation resulted system of partial differential equations (PDEs). To obtain ordinary differential equations (ODEs) from PDEs, similarity transformations are utilized. ODEs are solved via NDSolve code in Mathematica. The various variables effect on flow velocity, Bejan number, concentration, temperature, and EG are graphically studied. Engineering quantities are scrutinized numerically. The results indicate that as the magnetic variable increases, the temperature also rises. In contrast, an increase in the Prandtl number leads to a decrease in temperature. When both the magnetic parameter and porosity increase, the velocity field of the hybrid nanofluid decreases. The concentration field declines with an enhancement in both the chemical reaction and the Schmidt number. Improvements in EG are observed with higher values of diffusion, the temperature difference ratio, and Brinkman variables. The Bejan number increases with rising diffusion and temperature difference ratio, but it decreases with higher Brinkman variable values.