Irreversibility Analysis of Xue Model in Stagnation Point Flow of Hybrid Nanofluid with Modified Fourier Law

Hybrid nanofluids, known for their enhanced thermal properties, have a wide range of applications in industries such as transportation, electronics, and biomedicine. This study presents an irreversibility analysis based on the modified Fourier law within the Xue model and incorporates it into the energy equation to investigate the stagnation-point flow Al 2 O 3 /H 2 O nanofluid and Al 2 O 3 +Cu/H 2 O hybrid nanofluid over a stretchable sheet. This aspect has not been discussed in previous studies. The proposed model considers the effects of radiative heat flux, Lorentz forces, chemical reaction, viscous dissipation, Joule heating and internal heat generation. The governing equations are reduced into nonlinear ordinary differential equations using similarity transformations and are solved numerically using shooting method. The results are validated against the bvp4c method and also compared with existing literature. The findings indicate that the magnetic field parameter significantly influences both mass and heat transfer. An increase of 33.33% in the magnetic field parameter reduces the heat transfer rate by 8.20% in the hybrid nanofluid and by 8.01% in the nanofluid. Furthermore, a 25% increase in the internal heat source parameter leads to a considerable reduction in the heat transfer rate, with a decrease of 43.83% in the hybrid nanofluid and 40.79% in the nanofluid. Moreover, an increase in radiative heat flux decreases the entropy of the fluid. These results provide valuable insights for improving the efficiency of hybrid nanofluids in high-temperature cooling systems, aerospace technologies, and biosensor applications.