Computational modeling of entropy-optimized Casson nanofluid transport over corrugated porous surfaces with nonlinear radiation and Dufour diffusion

Efficient transport of momentum, heat, and species through porous media is fundamental to the design and optimization of advanced chemical engineering systems, including catalytic reactors, membrane separation units, porous heat exchangers, electrochemical devices, and thermal energy technologies. However, predictive computational models that simultaneously account for complex fluid rheology, cross-diffusion, nonlinear radiation, and thermodynamic irreversibility over realistic engineered surfaces remain limited. This study presents a comprehensive numerical investigation of steady natural convection of a Casson nanofluid over a sinusoidally corrugated vertical surface embedded in a Darcy–Forchheimer porous medium under a transverse magnetic field. The principal novelty lies in the unified integration of Casson non-Newtonian rheology, Dufour cross-diffusion, nonlinear thermal radiation based on the full fourth-power Rosseland approximation, entropy generation analysis, and corrugated surface topology within a single computational framework. The governing parameters are varied over physically representative ranges (Grashof number G r = 5 − 15 , Hartmann number M = 0.5 − 5.0 , Casson parameter β c = 0.5 − 5.0 , Dufour number D u = 0 − 3.0 , radiation parameter R d = 0.5 − 3.0 , temperature ratio θ w = 1.1 − 2.0 , nanoparticle volume fraction φ = 0 − 0.10 , wave amplitude a = 0 − 0.5 , and wavelength λ = 1.0 − 5.0 ) , consistent with conditions relevant to compact heat exchangers and porous catalytic reactors. Unlike conventional flat-surface models, the corrugated geometry captures periodic boundary-layer oscillations and more realistically represents engineered surfaces employed for process intensification and transport enhancement. Coupled nonlinear governing equations are solved using a robust Galerkin Finite Element Method implemented in Fortran 90/95, while streamline and isotherm visualizations provide additional insight into underlying transport mechanisms. Results demonstrate that Dufour diffusion enhances the average Nusselt number by approximately 23%, nonlinear thermal radiation produces thermal boundary layers up to 55% thicker than those predicted by linearized models, and increasing wave amplitude improves heat-transfer performance by nearly 18%. Entropy analysis further reveals that magnetic-field-induced Joule heating becomes the dominant source of thermodynamic irreversibility at higher Hartmann numbers, providing valuable guidance for energy-efficient process operation. An optimal corrugation wavelength of λ ≈ 2.0 − 3.0 and an optimal nanoparticle loading of φ ≈ 0.05 are identified as the conditions that jointly maximize thermal performance while limiting hydrodynamic and entropic penalties. Overall, this study establishes a reliable computational framework for transport-process optimization and delivers practical design insights for intensified heat and mass transfer in nanofluid-based chemical process equipment, porous catalytic reactors, membrane systems, electrochemical technologies, and other sustainable thermal processing applications.