Mixed convection flow of Casson nanofluid over a nonlinearly stretching sheet with entropy generation, non-Fourier heat flux, and non-Fickian mass diffusion

This study examines entropy generation within a two-dimensional flow involving mixed convection of a Casson-type nanofluid over a sheet that stretches nonlinearly. This analysis incorporates critical physical effects, including first-order velocity slip, convective heating, convective mass transfer, suction, viscous dissipation, and Brownian and thermophoretic motion, all under passive control conditions. This research is enhanced by the inclusion of non-Fick’s mass and non-Fourier heat flux model to comprehensively evaluate mass and heat transfer rates. An analytical approach, the homotopy, supported by the BVPh 2.0 package, was used to derive series solutions and compute residual errors for the governing equations. This study presents a thorough interpretation of how key flow parameters influence concentration, temperature, and concentration distributions, Bejan number, and entropy generation, with graphical illustrations provided for clarity. The Sherwood and Nusselt numbers and the coefficient of skin friction were also analyzed numerically and tabulated. The results show an inverse relationship between the distribution of temperature [Θ(ξ)] and Pr (Prandtl number), while the parameters of Casson (β), magnetic field M, and Biot (Bi) exhibit positive correlations with temperature and concentration profiles. In particular, both M and β positively influence the concentration distribution [Φ(ξ)], while Pr affects negatively. Temperature relaxation time (γt) and concentration relaxation time (γc) were found to have opposing impacts, with one increasing and the other decreasing their respective profiles. Notably, the first-order slip parameter (α) reduces all profiles under consideration. Convergence analysis revealed that the series solution stabilizes for iterations k ≥ 5, with the Nusselt number and coefficient of skin friction maintaining consistent values with iterations k ≥ 10. This study confirms the reliability of the HAM in solving complex nonlinear systems and offers insights into optimizing thermal and concentration boundary layer characteristics in Casson nanofluid flows.