Genetic optimization of heat transfer correlations for evaporator tube flows Matheus P. Porto a,b , Hugo T.C. Pedro b , Luiz Machado a , Ricardo N.N. Koury a , Carlos U.S. Lima c , Carlos F.M. Coimbra b,⇑ a Programa de Pós Graduação em Engenharia Mecânica, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil b Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, Center of Excellence in Renewable Energy Integration, Center for Energy Research University of California San Diego, La Jolla, CA, USA c Departamento de Engenharia Mecânica, Universidade Federal do Pará, Belém, PA, Brazil article info Article history: Received 6 June 2013 Received in revised form 4 November 2013 Accepted 5 November 2013 Available online 30 November 2013 Keywords: Heat transfer coefficient Internal flows Genetic algorithms Artificial neural networks abstract Two-phase heat transfer coefficients for internal flows play a critical role in the design and analysis of evaporators and condensers. Previous studies propose empirical relations that combine the effects of nucleate and convective boiling onto the overall heat transfer coefficient. Although these relatively sim- ple empirical relations offer physical insight on the nucleation, boiling and flow processes, they come at the expense of some computational accuracy. In this work, we explored new techniques to determine two-phase heat transfer coefficients for refrigerants R-22, R-134a and R-404a. We used multiple func- tional forms for the heat transfer coefficients and considered multiple dimensionless parameters as inputs to the algebraic relations. We used genetic algorithms to search the solution space that consists of the input parameters plus the different functional forms, and obtained optimal empirical correlations that cover a wide range of heat transfer regimes. Then, we combined genetic algorithm and artificial neu- ral networks to obtain a more universal correlation. Two versions were developed for each correlation: one that assumes a priori knowledge of the local heat flux and another that does not. Several error met- rics were computed for all the correlations developed and compared against correlations from the liter- ature. We conclude that substantial improvements can be achieved in both accuracy and robustness of the correlations by using advanced optimization techniques. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction The determination of the heat transfer coefficients (HTC) in phase-changing conditions is critical to the optimal design of refrigeration systems. The current level of computational technol- ogy allows for the use of computationally intensive tools to solve heat transfer problems that were beyond reach just a few decades ago. Two optimization tools that are particularly relevant to the optimal determination of two-phase flow coefficients are genetic algorithms (GAs) and artificial neural networks (ANNs). Recent works employing GAs for the solution of heat transfer problems are reviewed by Gosselin et al. [1]. Mojaraj et al.[2] reviewed the application of ANNs for refrigeration, air conditioning and heat pump systems (RACHP), highlighting the ANN ability to model and solve multivariable nonlinear problems. Considering the deter- mination of HTC in particular, both ANNs and GAs have proven to offer substantial advantages over conventional methods for correlating experimental data [3–7]. Mohanraj et al. [2] conclude that there are substantial gains to be explored in the following areas:  development of simplified correlations for predicting the per- formance of RACHP systems;  hybridization of ANN with other expert systems;  phase change behavior of newly developed refrigerant mixtures. The present work introduces four different methodologies for obtaining two-phase flow HTC correlations, and these methodolo- gies combine all three areas mentioned above. The first two are based on the optimization of strictly empirical algebraic expres- sions, the third results from the optimization of an HTC functional form currently in use (based on the asymptotic behavior of nonlin- ear superposition effects), and the last one is based on the ability of ANNs to function as a universal nonlinear approximator. With the exception of the third methodology, the other methodologies are applied to two distinct cases: (1) assuming that the heat flux is known, and (2) assuming that the heat flux is unknown. The sec- ond scenario has especial relevance in design applications for which both the heat fluxes and the wall temperatures are 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.11.011 ⇑ Corresponding author. Tel.: +1 (858) 534 4285; fax: +1 (858) 534 7599. E-mail address: ccoimbra@ucsd.edu (C.F.M. Coimbra). International Journal of Heat and Mass Transfer 70 (2014) 330–339 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt