The heat transport analysis in the three-dimensional unsteady flow of non-Newtonian nanofluid is studied in this research communication. Comparison of water-based ternary hybrid nanofluid conveying three various shaped nanoparticles (titanium spherical-carbon nanotube (CNT) cylindrical-graphene platelet) and Zinc Oxide-Society of Automotive Engineers 50 nanolubricant (ZnO-SAE50Nanolubricant) is emphasized with two different models. Also, this paper is mainly focused on an electrically non-conducting and incompressible magnetic liquid with moderate saturation magnetization and low Curie temperature. An infinitely long, straight wire delivering an electric current generates a magnetic field that affects the fluid. To study heat transfer characteristics thermal radiation is taken into account. Pertinent flow expressions are reduced into ordinary differential equations (ODEs) through appropriate transformations. The obtained ODEs are solved by means of the numerical method Runge–Kutta–Fehlberg’s fourth-fifth order method (RKF-45) with shooting technique. Results reveals that the ZnO-SAE50Nanolubricant flow shows maximum heat transport followed by titanium spherical-CNT cylindrical-graphene platelet-water hybrid nanofluid flow for increased values of radiation parameter. Further in this scenario, it is found that the heat transfer rate in ternary hybrid nanofluid increases about 2–5% whereas in Nanolubricant it is about 3–8% for the gradual increasing values of the ferromagnetic interaction parameter.