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Comparison of different correlating methods for the single-phase heat transfer data in laminar and turbulent flow regions

English Abstract

Experimental approach is one of the methods in heat transfer engineering research. The experimental heat transfer results, typically expressed as Nusselt number, are usually put in the form of an empirical correlation. Different correlating methods can be used to establish the correlation, such as the traditional least-squares method, artificial neural networks (ANN), and symbolic regression, to name a few. Ghajar and his co-workers (1994) have applied the three-layer ANN for the complicated heat transfer problem. The ANN-type correlation can predict the heat transfer data in good accuracy. However, the relationship between the input and output variables cannot be visually inspected from the martix-form correlation. In recent studies of Tam and Ghajar (2008), the optimized correlation form was found out by the symbolic regression. The global combination of input variables was determined by the genetic programming of Tam and Ghajar (2006). The symbolic-type correlation may give out not only the accurate predictive power, but also the explicit correlation format. Therefore, the input-output relationship, such as the importance of input variables, can be seen directly from the correlation. In this study, the traditional least-squares method, ANN and symbolic regression will be compared. Correlations for the basic single-phase heat transfer data of Tam and Ghajar (2004) (546 data poins for laminar region and 604 v data points turbulent region) were developed with these methods. The traditional correlation predicts the laminar data with a deviation range of -16.9% and +15.4% and the turbulent data with a deviation range of -10.3% and +10.5%. Majority of the experimental data (86% of the laminar data and 93% of the turublent data) were predicted within the ±10% range. For developing the new correlations, 90% of the total data were used for training. The new correlations developed by ANN and symbolic regression can both predict all of the heat transfer data in laminar and turbulent regions within ±15% range. Over 90% of the data points, which includes the unused data, can be predicted by those correlations within the ±10% deviation. The accuracy of those new correlations are comparable to that of the traditional least-squares method. For visual inspection of the symbolic-type correlation, the importance of each term can be examined directly. Therefore, the symbolic regression is more superior to the ANN method. Keywords: Heat Transfer Correlation, Laminar Flow, Turbulent Flow, Artificial Neural Networks (ANN), Symbolic Regression

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Lei, Chan Un


Faculty of Science and Technology


Department of Electromechanical Engineering




Heat -- Transmission

Mechanical engineering


Tam, Lap Mou

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