This study investigates the influence of an axial magnetic field on the flow and Heat Transfer (HT) of a Ternary Hybrid Nanofluid in a rotating horizontal annulus between two coaxial tubes, considering the impact of viscous dissipation and thermal radiation. The study examines the use of spherical aluminum oxide (Al2O3) nanoparticles, platelet-shaped graphene and Cylindrical Carbon Nanotubes (CNTs). The velocity and temperature fields were transformed to get a system of Ordinary Differential Equations (ODEs) representing the flow and HT governing equations. A dataset is produced by systematically varying key parameters using the bvp4c function in MATLAB. Following this, two advanced artificial intelligence techniques, Artificial Neural Networks (ANNs) and Fuzzy Particle Swarm Optimization (FPSO), are utilized to forecast the Nusselt number. The effects of various parameters, including the radiation parameter, Reynolds number and Hartmann number on HT and flow characteristics were analyzed. Analysis of data presents that the Nusselt number increases with higher radiation parameter and falls with higher Hartmann number (Ha), Reynolds number and Eckert number. Furthermore, Nusselt number achieves higher values for Quadratic Thermal Radiation (QTR) case in comparison to Linear Thermal Radiation (LTR). It is observed that when value of radiation parameter is increased from 5.5 to 11.5, the Nusselt number values rises by 216.19% (when Ha=4), 231.34% (when Ha=4.5) and 249.82% (when Ha=5) for LTR, whereas the Nusselt number values rises by 153.68% (when Ha=4), 157.01% (when Ha=4.5) and 160.70% (when Ha=5) for QTR. The applications of the nanofluid flow inside a rotating horizontal annulus are seen in heat exchangers, gas turbines, rotating machinery, cylindrical solar collectors, medical devices like centrifuge and rotating drum dryers in food processing.