Stability analysis of unsteady ternary nanofluid flow past a stretching/shrinking wedge

Slit die extrusion depends highly on fluid temperature and flow properties, which play a crucial role in determining material quality. This research aims to enhance product quality in extrusion processes by deriving a mathematical model from the extrusion process, ensuring practical relevance to industrial applications. The study focuses on the stability analysis of unsteady ternary nanofluid flow past a stretching/shrinking wedge, incorporating viscous dissipation and Joule heating. A key novelty of this work lies in identifying the critical values for the existence of dual solutions and conducting a comprehensive stability analysis. The findings reveal that the first solution is stable, whereas the second is unstable. Critical values are determined using the boundary value problem solver using 4th-order collocation method function in Matlab, and the effects of key parameters - such as the wedge parameter, Eckert number, suction/injection parameter ( S ), and hybridity - are analyzed through graphical representations. Results show that for a shrinking wedge, the skin friction coefficient and Nusselt number increase with higher values of the unsteadiness parameter, nanoparticle volume fraction, and S . When lambda > -3.23 (shrinking wedge), the ternary nanofluid demonstrates superior thermal transfer compared to binary and mono nanofluids. This study provides a critical foundation for validating advanced models and optimizing heat transfer performance in industrial processes, paving the way for enhanced applications in extrusion and thermal management systems.