Review on the Theoretical and Practical Applications of Symmetry in Thermal Sciences, Fluid Dynamics, and Energy

This literature review explores the role of symmetry in thermal sciences, fluid dynamics, and energy applications, emphasizing the theoretical and practical implications. Symmetry is a fundamental tool for simplifying complex problems, enhancing computational efficiency, and improving system design across multiple engineering and physics domains. Thermal and fluid processes are applied in several modern energy use technologies, essentially involving the complex, multidimensional interaction of fluid mechanics and thermodynamics, such as renewable energy applications, combustion diagnostics, or Computational Fluid Dynamics (CFD)-based optimization, where symmetry is highly considered to simplify geometric parameters. Indeed, the interconnection between experimental analysis and the numerical simulation of processes is an important field. Symmetry operates as a unifying principle, its presence determining everything from the stability of turbulent flows to the efficiency of nuclear reactors, revealing hidden patterns that transcend scales and disciplines. Rotational invariance in pipelines; rotors of hydraulic, thermal, and wind turbines, and in many other cases, for instance, not only lowers computational cost but also guarantees that solutions validated in the laboratory can be effectively scaled up to industrial applications, demonstrating its crucial role in bridging theoretical concepts and real-world implementation. Thus, a wide range of symmetry solutions is exhibited in this research area, the results of which contribute to the development of science and fast information for decision making in industry. In this review, essential findings from prominent research were synthesized, highlighting how symmetry has been conceptualized and applied in these contexts.