<p>The ternary hybrid nanofluids are in high demand in the context of engineering systems such as compact heat exchangers, rotating chemical reactors, and high-performance cooling of electronics engineering devices, which are seeking far more advanced thermal management solutions. This research provides an extensive computational model of a ternary hybrid nanofluid flow (molybdenum disulfide (MoS₂), graphene oxide (GO) and copper (Cu) in acetic acid–water base) between two turns comprising of concentric cylinders. The model has a unique combination of the influence of chemical reaction, thermal radiation, and the shape fracture of nanoparticles (spherical, cylindrical, platelet) to fill a considerable gap in the literature. The main aim is to create a strong mathematical model of this complicated system, define the heat generated in the system, and determine the effect of shape fracture on the thermal conductivity and fluid dynamics. The resulting governing nonlinear partial differential equations are then reduced to ordinary differential equations and solved through the use of the Adomian Decomposition Method (ADM) with the validation of the results by the Homotopy Analysis Method (HAM)-package, which reveals very good agreement (e.g., velocity profiles within 3% of benchmark studies). The most important quantitative results are that the flow velocity is increased with an increase in the Grashof number by half, and the radiation parameter may drop the temperature of the fluid by 20%. Moreover, nanoparticles in the form of plates produce approximately 8% more entropy than the spheres. These outcome proves that the forces of buoyancy, Brownian motion, and thermo-phoresis severely affect the flow and heat transfer. The findings present the critical information toward the optimisation of the thermal efficiency and design of advanced energy systems, which have a great contribution to the thermal engineering and sustainable energy technology.</p>