Dual solutions of ternary hybrid nanofluids stagnation point past a linearly shrinking sheet with second-order slip conditions

Purpose The purpose of this paper is to study the dual solutions of ternary hybrid nanofluids stagnation point past a linearly shrinking sheet with second-order slip conditions. The ternary nanofluid consists in alumina (Al_2 O_3), copper (Cu) and titanium dioxide (TiO_2) embedded as nanoparticles in water (H_2 O), as a base liquid. Design/methodology/approach The flow over a stretching/shrinking surface has wide range of applications in engineering and several technological purposes, such as, in the extrusion of a polymer in a melt-spinning process, the extrudate from the die is generally drawn and simultaneously stretched into a sheet which is then solidified through quenching or gradual cooling by direct contact with water, cooling of a large metallic plate in a bath, etc. Using appropriate transformations, the full partial differential equations, continuity, momentum and energy, were transformed into nonlinear ordinary differential equations that are, then, solved numerically using the bvp4c function in MATLAB software. Findings The effect of the governing parameters on the skin friction, heat transfer, velocity and temperature profiles has been analyzed by graphical and tabular reports. It is found that dual (upper and lower branch) solutions exist for some values of the governing parameters. From the stability analysis, it is found that the upper branch solution is stable and physically realizable in practice, while the lower branch solution is unstable and, therefore not realizable in practice. Both solution branches, reduced skin friction, reduced heat transfer and velocity and temperature profiles are graphically and in tables presented. It is found that the skin friction (or the surface shear stress), the surface heat transfer and the velocity and temperature profiles are substantially affected by the second-order slip. Originality/value The present results are original and new for the study of ternary hybrid nanofluids flow and heat transfer over a stretching/shrinking surface, as they successfully extend several problems from the open literature.