DIMENSIONLESS PHYSICAL-MATHEMATICAL MODELING OF TURBULENT NATURAL CONVECTION

Abstract

Natural convection heat transfer is present in the most diverse applications of Thermal Engineering, such as in electronic equipment, transmission lines, cooling coils, biological systems, etc. The correct physical-mathematical modeling of this phenomenon is crucial in the applied understanding of its fundamentals and the design of thermal systems and related technologies. Dimensionless analyses can be applied in the study of flows to reduce geometric and experimental dependence and facilitate the modeling process and understanding of the main influence physical parameters; besides being used in creating models and prototypes. This work presents a methodology for dimensionless physical-mathematical modeling of natural convection turbulent flows over isothermal plates, located in an “infinite” open environment. A consolidated dimensionless physical-mathematical model was defined for the studied problem situation. The physical influence of the dimensionless numbers of Grashof, Prandtl, and Turbulent Prandtl was demonstrated. The use of the Theory of Dimensional Analysis and Similarity and its application as a tool and numerical device in the process of building and simplifying CFD simulations were discussed.