<p>In manufacturing industries, the Casson fluid model is frequently used to describe fluids, with particular attention given to fluid flow across cylindrical surfaces due to its crucial role in shaping fluid dynamics and ensuring product quality in curved geometries. The objective of this study is to examine the heat transfer and the flow behaviour of Casson ternary nanofluids across flat plate and cylindrical surfaces with boundary convective heat flux. The ternary nanofluid (THF) is formed by suspending Graphene, Magnesium Oxide, and Zirconium Oxide into the base fluid ethylene glycol. The governing equations are initially simplified using similarity variables to reduce the complexity of the problem. Solutions are then obtained using the Homotopy Analysis Method (HAM). The effects of the Casson fluid parameter and convective heat flux on temperature, velocity distribution, skin friction, and Nusselt number are studied graphically. The results show that the rheological properties of Casson fluid lower the temperature and velocity profiles on the plate and cylinder surfaces. In comparison to the hybrid nanofluid (HNF), the THF has a greater temperature profile. The Nusselt number increases by approximately 46.86% for the THF and 46.90% for the HNF over a flat plate and by 46.63% for the THF and 46.52% for the HNF over a cylindrical surface under convective boundary conditions. These results provide valuable insights into different methods for selecting suitable materials and geometries to optimize, such as heat exchanger designs, which could lead to improved performance and efficiency in various manufacturing processes.</p>