Analyzing heat transfer and fluid dynamics of ternary hybrid nanomaterials in confined cavities is vital for improving thermal performance in wide-ranging engineering applications. The current investigation employs finite element technique to explore natural convection and thermal transport of ternary hybrid nanomaterials \((Fe_{3} O_{4} - Cu - TiO_{2 } - H_{2} O)\) inside an undulant-wall enclosure enclosing a heated fin. The integration of fins in confined cavities emerged as a highly effective strategy for enhancing the efficiency of thermal systems. Impacts of heat generation and horizontal magnetic field are invoked. The finite element technique is utilized to solve coupled nonlinear PDE’s governing fluid motion and heat transport under steady and laminar flow conditions. Key variables, such as Rayleigh number, heat generation parameter and Hartmann number, are systematically varied to analyze their impacts on fluid flow patterns and thermal performance. Results reveal that enhancing Rayleigh number and heat generation parameter significantly improves heat transfer rate up to 58% and 25%, respectively. Furthermore, invoking magnetic field within the enclosure influences the heat distribution up to 18%, leading to a suppression of convective flow. Enhancement of fin’s length in the enclosure leads to a notable enhancement in thermal transport up to 20% due to increased surface area for convective flow. Nusselt numbers are computed to evaluate heat transfer performance. Temperature and velocity profiles are found to increase with high Rayleigh numbers and heat generation parameter. This analysis provides valuable insights into optimizing enclosure design using ternary hybrid nanomaterials for improved thermal system performance.
