Application of the ‘nusselt-equation simulated evolution method’ in forced convective heat transfer modeling

Abstract

Reliability of heat exchangers thermal analysis strongly depends on the equations selected to determine local convective heat transfer coefficients. Chosen analogy among momentum, heat and mass transfer also plays a remarkable role. Within this context, the aim of the study was to validate a novel approach to obtain mean forced convective film coefficients under single-phase non-laminar fluid flow conditions, inside tubes. It relied on a comprehensive Nusselt-number equation that is able to evolve into different functional forms according to Reynolds-Colburn, Prandtl and von Karman analogies. Parameters estimation was carried out through Genetic Algorithms. Applied experimental database was numerically obtained by Taler by solving the energy conservation equation for fully developed turbulent flow in tubes with constant wall heat flux. Application of the method provided a new correlation, valid for 0.1 ≤ Pr ≤ 103 and 3 × 103 ≤ Re ≤ 106 . Besides attaining a better fit to the experimental data as compared to benchmark expressions, it correlated very well with the results of reference models (Skupinski, Seban & Shimazaki, Gnielinski, Camaraza-Medina, Petukhov, and Sandall). The first assessment provided mean and maximum relative errors of 2.41% and 19.45%, respectively, while the second comparison resulted in deviations over the Nusselt number up to 20% in 92.59% of the data points. The implemented solution overcomes the drawbacks of non-linear and symbolic regression methods by allowing evolution of the regression function within a controlled mathematical environment. Future model improvements should investigate different fitting-intervals along with higher turbulence regions.