Forecasting of saturated boiling heat transfer inside smooth helically coiled tubes using conventional and machine learning techniquesPrévision du transfert de chaleur en ébullition saturée à l'intérieur de tubes lisses enroulés en hélice à l'aide de techniques conventionnelles et d'apprentissage automatique

https://doi.org/10.1016/j.ijrefrig.2022.06.036Get rights and content

Abstract

This study concerns to model the flow boiling heat transfer coefficient (HTC) in smooth helically coiled tubes. A dataset including 1035 samples was collected from 13 independent studies, enveloping a broad range of geometrical and operating conditions. The predictive capability of the earlier models was assessed for straight and coiled tubes by the analyzed database that they were not precise enough. Accordingly, a new empirical model based on the least square fitting method (LSFM) was constructed using seven input effective dimensionless factors. It was found that LSFM was not able to describe the complex and nonlinear nature of HTC in smooth helically coiled tubes. Furthermore, the intelligent method of genetic programming (GP) was utilized to obtain more accurate explicit correlation for HTC, which produced an acceptable average absolute relative error (AARE) of 17.35%. Finally, the machine learning approaches of multilayer perceptron (MLP), Gaussian process regression (GPR), radial basis function (RBF) was also implemented to model HTC in smooth coiled tubes. Although all intelligent based models provided excellent results, the GPR model outperformed the others with an average absolute relative error (AARE) of 5.93% for the tested dataset. In addition to the proposed models’ performance, the most influential factors in controlling the boiling HTC in coiled tubes were also detected.

Section snippets

Abbreviations

    AARE

    Average absolute relative error

    GPR

    Gaussian process regression

    HTC

    Heat transfer coefficient

    LSFM

    Least square fitting method

    MLP

    Multilayer perceptron

    RBF

    Radial basis function

    RRMSE

    Relative root mean squared error

GPR

The gaussian process regression (GPR) is known as a non-parametric and supervised machine learning algorithm which uses the concept of probability. It should be noted that this method provides reasonable outcomes even for limited numbers of data samples. Accordingly, it is utilized for a broad range of problems with nonlinear behaviors. GPR includes a collection of random variables which they have the multivariate normal distributions (Hosseini et al., 2019). If the outputs of h(x) are

Assessment of the earlier models

As mentioned before, several researchers have developed empirical models for HTC inside coiled tubes based on their own limited data. In contrast, some others have suggested the use of straight tubes’ models for flow boiling HTC in helical coils. A summary of earlier models for predicting HTC during flow boiling inside straight and coiled tube is presented in Table 3.

The accuracy of the various models listed in Table 3 are examined with the collected data points and the results are presented in

Conclusions

This study dealt with modeling of the HTC during saturated flow boiling in coiled tubes. In addition to conventional modeling approach of LSFM, three well-known machine learning algorithms, i.e., GPR, MLP and RBF as well as the intelligent method of GP were implemented to development of comprehensive and reliable models. The models were validated by an extensive set of 1035 experimental data collected from 13 published sources. The main findings of this study are listed as follows:

  • By a

Data availability statements

The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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