Entropy generation analysis of MHD buongiorno hybrid nanofluid flow with Darcy–Forchheimer effects and second-order chemical reaction

This study investigates the steady two-dimensional magnetohydrodynamic (MHD) boundary-layer flow of a water-based hybrid nanofluid over a linearly stretching elastic surface in the presence of a uniform transverse magnetic field. The hybrid nanofluid is composed of titanium dioxide (TiO2) and copper oxide (CuO) nanoparticles dispersed uniformly in water, modelled using Buongiorno's nanofluid framework to account for Brownian diffusion and thermophoresis effects. The governing continuity, momentum, energy and concentration equations are formulated by incorporating viscous dissipation, Joule heating, effective thermal conductivity and nanoparticle mass flux. To generalise the model, Darcy–Forchheimer porous medium resistance is introduced in the momentum equation, while a second-order homogeneous chemical reaction term is included in the concentration equation. Buoyancy effects are neglected to emphasise the dominant influences of surface stretching and Lorentz forces. The resulting nonlinear coupled system is transformed into a dimensionless form and solved numerically using the MATLAB bvp4c solver. A detailed parametric analysis is carried out to examine the effects of magnetic field strength, porous medium parameters, nanoparticle diffusion and chemical reaction rate on velocity, temperature and concentration distributions. Furthermore, thermodynamic irreversibility is quantified through entropy generation and Bejan number analyses, highlighting the relative contributions of heat transfer, fluid friction, magnetic effects and mass diffusion. The results demonstrate that increased Darcy–Forchheimer resistance significantly suppress fluid motion while enhancing entropy generation, whereas stronger chemical reactions reduce nanoparticle concentration and solutal boundary-layer thickness. These findings provide useful insights into the control of transport phenomena and irreversibility in hybrid nanofluid systems relevant to thermal engineering and energy conversion applications.