Thermodynamic irreversibility and stability of dual solutions in Maxwell-type ternary nanofluid flow over a stretching/shrinking sheet with slip and heat effects

In industrial systems involving complex fluids and heat transfer, challenges such as energy loss, thermal inefficiency, and unstable flow behavior often limit performance. This study investigates entropy generation and the stability of dual solutions in the flow of a Maxwell ternary nanofluid over a stretching/shrinking sheet, incorporating velocity slip, temperature jump, and a heat source/sink. The governing equations are solved using the bvp4c method in MATLAB. Results show that ternary hybrid nanofluid (THNF) significantly enhances thermal performance, with up to 0.22% and 0.28% higher thermal efficiency than binary and mono nanofluid, respectively, at $\lambda =-1.5$. Heat transfer and skin friction increase with suction, velocity slip, and elasticity, while entropy generation decreases with higher $K$ and slip. The first solution is found to be stable, while the second is unstable and physically inadmissible. To improve heat transfer and reduce drag, effective strategies include using THNF, enhancing suction, optimizing $\delta$ and $K$, increasing heat absorption ($H$), and setting the temperature jump to 0.2 and 0.8. The novelty lies in providing the first comprehensive study of entropy generation and stability in Maxwell-type THNF flows under complex boundary effects. These findings inform the design of efficient, low-loss thermal systems in energy, electronics, and advanced manufacturing.