Analysis of the radiated ternary hybrid nanofluid flow containing TiO₂, CoFe₂O₄ and MgO nanoparticles past a bi-directional extending sheet using thermal convective and velocity slip conditions

We examined ternary hybrid Carreau nanofluid flow on a porous bi-directional elongating sheet. The nanoparticles of TiO₂, CoFe₂O₄, and MgO were mixed with water to get a ternary hybrid nanofluid. The flow was influenced by slip conditions of velocities along the x- and y-axes. The impacts of thermal- and space-dependent heat sources, thermal radiation, viscous dissipation, and Joule heating were used in this study. Moreover, magnetic effects were used along the z-axis, which was normal to the flow direction. The major equations were solved using the homotopy analysis method (HAM) in dimensionless form. As an outcome of this study, we discovered that with progression in velocity slip factors along x- and y-axes, magnetic factor, porosity factor, and local Weissenberg number, there was a reduction in primary and secondary velocities. With an upsurge in the stretching ratio factor, there was a reduction in primary flow and augmentation in secondary flow. Thermal distribution was augmented with the surge in thermal Biot number, thermal-dependent heat source factor, magnetic factor, space-dependent heat source parameter, radiation factor, and Eckert numbers along primary and secondary directions. The skin friction coefficients have augmented with growth in magnetic factor, porosity factor, and velocity slip factors along the x- and y-axes. The Nusselt number escalated with a surge in radiation factor, space-dependent heat source factor, thermal-dependent heat source factor, and Eckert numbers along x- and y-axes. Our results were validated through comparative analysis by matching our results with established data. A fine agreement was noticed among all the results. Our findings benefit aerospace, biomedical, and electronics industries by improving thermal management in porous media. Magnetic and slip conditions aid in advanced manufacturing, while enhanced Nusselt numbers support efficient heat exchanger design.