Velocity slip effects on thermal transport in unsteady Maxwell trio-hybrid nanofluid flow over a variable geometry wedge for extrusion applications

Efficient thermal regulation in extrusion and heat exchanger systems remains a key challenge, particularly under unsteady conditions where conventional fluids fail to achieve optimal performance. This study investigates dual solutions in time-dependent Maxwell ternary hybrid nanofluid flow over a variable-geometry wedge with velocity slip, aiming to enhance boundary layer control and heat transfer. The governing equations, formulated for slit die extrusion, are solved using the bvp4c algorithm in MATLAB. Parametric analysis identifies regimes of no solution, unique solution, and dual solutions, emphasizing the effects of unsteadiness, wedge angle, velocity slip, suction/blowing, and elasticity. Results show that increased elasticity improves heat transfer in the shrinking regime, and all examined factors postpone boundary layer separation. Stability analysis reveals that only the first branch of dual solutions is temporally stable. At a stretching/shrinking parameter of − 3 . 7 , Al 2 O 3 –Cu– TiO 2 /EG exhibits a 0.89% higher heat transfer rate than Al 2 O 3 –Cu/EG and 4.47% higher than Al 2 O 3 /EG. The contribution lies in establishing a dual-solution and stability framework for an unsteady Maxwell fluid with ternary hybrid nanoparticles and velocity slip, offering new insights for industrial thermal optimization.