Thermal Radiative Flow and Entropy Generation in MHD Williamson Hybrid Nanofluid (Cu+Ag)/H2O Over a Porous Stretching Sheet With Non-Fourier Heat Flux and Heat Source

This study investigates the radiative magnetohydrodynamic (MHD) flow of Williamson and hybrid Williamson nanofluids (Cu–water and Cu + Ag–water) over a porous, linearly stretching sheet with suction and internal heat generation. Although nanofluids have been extensively studied, limited research addresses the combined influence of non-Fourier heat flux, viscous dissipation, thermal radiation, and entropy generation in Cu + Ag/water Williamson hybrid nanofluids. The novelty of this work lies in its comprehensive analytical modeling of these coupled transport phenomena and in providing a comparative assessment between Cu–water and Cu + Ag–water Williamson nanofluids under realistic boundary conditions. The governing nonlinear equations are reduced using similarity transformations and solved analytically through the Homotopy Analysis Method (HAM), which offers excellent convergence control for highly nonlinear systems. Results show that the Cu–water nanofluid exhibits higher velocity due to lower viscosity, while the Cu + Ag–water hybrid nanofluid demonstrates superior thermal conductivity and enhanced heat transfer. The wall shear (skin friction) increases with We but decreases with M, K, and S, reflecting the competing roles of elastic effects versus magnetic braking, porous drag, and suction-induced momentum reduction. Meanwhile, the Nusselt number decreases with M, K, and Q, but increases with Nr, S, and γ, indicating that radiative transport, boundary-layer thinning, and thermal relaxation steepen −θ′0, thereby offering a concise guideline for balancing heat-transfer enhancement against frictional penalties. An increase in the thermal relaxation parameter γ delays the heat-flux response in the Cattaneo–Christov model, which weakens thermal diffusion, lowers the boundary-layer temperature, and improves thermal stability. As a result, the wall temperature gradient steepens, increasing −θ′0 and enhancing the Nusselt number. Entropy generation is intensified by the magnetic parameter M, porous resistance (permeability) parameter K, and Brinkman number (Br), but it is suppressed by the Weissenberg number (We) and temperature-difference effects. Overall, the findings provide valuable insight for optimizing hybrid nanofluid-based systems in cooling, micro-electro-mechanical systems (MEMS), and sustainable thermal management applications.