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

Abstract 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 ( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>S</m:mi> </m:math> 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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>S</m:mi> </m:math> S . When <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>λ</m:mi> <m:mo>&gt;</m:mo> <m:mo>−</m:mo> <m:mn>3.23</m:mn> </m:math> \lambda \gt -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.