Irreversibility analysis in stagnation-point flow of Casson bioconvective hybrid nanofluid under chemical reaction and stratification effects

Entropy generation (EG) in hybrid nanofluid flows (HNFs) plays a crucial role in determining the efficiency and performance of thermal systems. It serves as a measure of irreversibility within these complex fluid flows, which directly impacts energy transfer and thermal conductivity. By analyzing EG, we can assess how effectively HNFs minimize energy losses, ultimately leading to improved overall efficiency in thermal management systems. The present study focuses on the analysis of heat transfer and EG in stratified bioconvective and magnetohydrodynamic Casson HNF flow near the stagnation point. The flow in HNF is generated due to stretched sheet. The surface of the sheet is considered porous. Radiation, heat source, and Joule heating effects are considered in the expression for thermal energy. While reporting the concentration equation impact of a chemical reaction is accounted. The bioconvection phenomenon within HNF is considered. The HNF is formed by inserting copper $$\\left( {{\\text{Cu}}} \\right)$$ and silver $$\\left( {{\\text{Ag}}} \\right)$$ nanoparticles in engine oil-based Casson liquid. The EG for the flow considered is modeled by using the second law of thermodynamics. The flow representing model equations is transformed into a non-dimensional system through transformations. To solve the dimensionless reduced system, we have implemented the NDSolve code in Mathematica. Behavior of HNF versus diverse parameters is graphically analyzed. Engineering quantities are scrutinized numerically. The results reveal that the HNF velocity profile decreases with increasing magnetic and porosity parameters, whereas the HNF temperature rises with higher magnetic parameter and Eckert number but decreases with increasing Prandtl number. The concentration field is reduced under stronger chemical reaction effects. Moreover, EG significantly increases with the Brinkman number and diffusion parameters, indicating enhanced irreversibility. The findings provide important insights into optimizing thermal efficiency and minimizing energy losses in advanced engineering and bio-thermal systems utilizing hybrid nanofluids.