Stability and quadruple solution dynamics of unsteady ternary hybrid nanofluid flow over a stretching/shrinking wedge

Abstract

The stability analysis of quadruple solutions in unsteady ternary hybrid nanofluid flow past a stretching/shrinking wedge is conducted to optimize boundary layer characteristics, enhancing heat transfer and reducing thermal resistance. Based on an industrial process, the mathematical model determines critical values for first–second and third–fourth solutions using the BVP4C function in MATLAB. Key parameters, including the unsteadiness parameter, stretching/shrinking parameter, wedge parameter, suction/injection, and hybridity, influence flow dynamics, and heat transfer, with validation confirming alignment with previous studies. The skin friction coefficient and Nusselt number increase for a shrinking wedge with higher unsteadiness, nanofluid type, and suction/injection. The first and third solutions are stable, while the others are not. At a stretching/shrinking parameter of -9 and a nanoparticle volume fraction of 0.04, the ternary nanofluid achieves 0.28% higher thermal efficiency than the binary nanofluid, which exceeds the mono-nanofluid by 0.59%. The novelty of this study lies in identifying quadruple solutions and their critical values for none, two, and quadruple solutions, contributing to advancements in slit die extrusion engineering and heat exchanger applications.