Numerical Study of Natural Convection in a Corrugated Porous Cavity Saturated with a Nanofluid of Al2O3–Cu/Water Hybrid Type: The Combined Effect of Variable Viscosity and Soret–Dufour Double-Diffusion

This study numerically investigates unsteady natural convection and Soret–Dufour double-diffusion in a two-dimensional sinusoidally wavy porous cavity saturated with an Al2O3–Cu/Water hybrid nanofluid (φ = 0.02), using a Darcy–Brinkman formulation with temperature-dependent viscosity and Rosseland thermal radiation. The governing equations are solved on a boundary-fitted grid; an independent Method of Manufactured Solutions verification confirms second-order accuracy, with a finest-grid (120 × 120) L2 error of 2.6807 × 10−5 and a fine-grid GCI of 0.013225%. Within the investigated dimensionless range, Nuavg increases with the Rayleigh number, wall-wave amplitude, radiation parameter, and viscosity-thinning magnitude, while the hybrid nanofluid yields a 2.8–3.2% enhancement over pure water. Because no independent experimental measurements or complete dimensional operating envelope are available, the reported engineering implications are presented as model-based guidance rather than validated design prescriptions.