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. 2022 Nov 16;7(47):43122–43129. doi: 10.1021/acsomega.2c05537

Artificial Neural Network Model for the Prediction of Thermal Conductivity of Saturated Liquid Refrigerants and n-Alkanes

Xiangsheng Meng †, Shangguo Yang †,*, Jianxiang Tian †,‡,*
PMCID: PMC9713888  PMID: 36467959

Abstract

graphic file with name ao2c05537_0010.jpg

In this paper, a feed-forward back-propagation artificial neural network (ANN) is proposed to correlate and predict the thermal conductivity from the triple point temperature up to 0.98 times critical temperature (Tc) for 23 refrigerants and 11 n-alkanes. It requires the temperature (T) as well as the molecular mass (M), acentric factor (ω), critical temperature, and critical pressure (Pc) as input variables. The optimal ANN model is obtained by a trial-and-error procedure and consists of the input layer and the output layer together with one hidden layer with seven neurons. This ANN model can not only correlate the thermal conductivity but also accurately predict the thermal conductivity of refrigerants and n-alkanes. The correlation coefficients (R) in the training and testing phases are 0.9994 and 0.9993, respectively. Furthermore, the average absolute deviation (AAD) values are less than 1% for 14 out of 34 fluids, less than 2% for 28 fluids, and less than 4.5% for all the considered fluids.

1. Introduction

Thermal conductivity is the ability to transfer heat through conductivity as defined by the Fourier’s law. It is one of the most important transport properties. The knowledge of liquid thermal conductivity is essential in chemical engineering design. Over the years, thermal conductivity data of many liquids have been experimentally measured and compiled. Although experimental data are accurate and reliable, such measurements are often expensive and time-consuming. As a result, many researchers have tried to employ different methods to reproduce and predict the thermal conductivity for many kinds of liquids.1

The method proposed by Bridgman2 is based on the theoretical calculation considering molecular motion and interaction, but there is not both enough accuracy and simple expression.1,3,4 Several methods use group contribution theory.1,5−8 Moreover, some empirical and semiempirical methods such as corresponding-state principle and multiparameter correlation have also been used to predict the thermal conductivity.9−18

Recently, many researchers have employed artificial neural networks (ANN) to correlate the thermal properties, such as surface tension,19−24 density,25,26 and in particular thermal conductivity.3,4,27−32 Karabulut and Koyuncu32 exploited the feed-forward ANN model to develop thermal conductivity correlations of propane for the first time. Later, Eslamloueyan and Khademi31 developed an ANN model to reproduce and predict thermal conductivity at atmospheric pressure for various pure gases. This model requires the temperature, molecular weight, critical pressure and critical temperature as input variables with an overall AAD of 5.42%. Pierantozzi et al.29 presented a multilayer perceptron ANN model to reproduce the thermal conductivity of alcohols with an overall AAD less than 0.0016%. Meanwhile, Lashkarbolooki et al.3 proposed an ANN based model to correlate the thermal conductivity for the normal and aromatic liquid hydrocarbons with the AAD of 0.20%. In this model, the input variables include the temperature, acentric factor, critical pressure, and critical temperature.

Subsequently, Pierantozzi and Petrucci,28 Ghaderi et al.,30 Ghalem et al.,4 and Wang et al.27 developed ANN models to correlate and predict thermal conductivity for various refrigerants, respectively. However, in the case of the model in ref (28), the temperature range covered is not wide enough for some refrigerants. In the case of the other three models, the number of refrigerant types involved is a little small. In view of the fact that some n-alkanes such as methane and ethane, etc. can be used as natural refrigerants, some n-alkanes are taken into account along with refrigerants in this paper. For the reasons above, in this work an ANN model is utilized to correlate and predict thermal conductivity over a very wide range of temperatures for 23 refrigerants and 11 n-alkanes liquids.

The paper is organized as follows. In Section 2, a feed-forward neural network is constructed and the network parameters are determined. Section 3 presents the discussions of some main results in the training and testing phases. Finally, this work is concluded in Section 4.

2. Modeling Thermal Conductivity with an ANN

2.1. Data Collection and Analysis

In this work, the REFPROP33 database is used as data source to study the ANN model for the thermal conductivity of refrigerants and n-alkanes. This program is developed by the National Institute of Standards and Technology (NIST). It is based on the most accurate pure fluids and fluid mixtures models currently available. In order to train and test the ANN model, we collected 19 113 data points of the thermal conductivity for 23 refrigerants and 11 n-alkanes from the REFPROP33 program. The thermal conductivity data from REFPROP are calculated using the correlation model and not experimental data. Correlation values may have higher errors than the assigned uncertainty level near the edges of the temperature range, especially near the critical point.33,34

A summary of these data is listed in Table 1 together with the physical properties required in the process of training and testing the ANN model. As can be seen, the data cover a very wide temperature range. The minimal temperature is the triple point temperature, while the highest temperature reaches about 0.98 times the critical point temperature for each fluid considered here. The data of the 29 fluids, which are carefully selected from all 34 fluids considered here and listed in the first 29 rows of Table 1, are used in the training phase to find the optimal structure and parameters of the ANN model, while the data of the other five fluids that were not used in the training phase are employed only in the testing phase to assess the predictive power of the optimal configuration model.

Table 1. Temperature Ranges, Number of Data Points (NP), and Physical Constants for 23 Refrigerants and 11 n-Alkanesa.

fluid T (K) λ (W/(m K)) Pc (MPa) M(g/mol) Tc (K) ω NP
dodecane 263.6–647.72 0.067991–0.14393 1.817 170.33 658.1 0.574 583
ethane 90.368–299.89 0.071493–0.25562 4.8722 30.069 305.32 0.0995 583
heptane 182.55–529.35 0.064359–0.15711 2.736 100.2 540.13 0.349 579
hexane 177.83–496.83 0.077499–0.16873 3.034 86.175 507.82 0.299 581
methane 90.864–187.42 0.076259–0.21099 4.5992 16.043 190.56 0.0114 569
octane 216.37–555.03 0.063591–0.15328 2.497 114.23 569.32 0.395 575
pentane 143.47–461.53 0.062577–0.17503 3.37 72.149 469.7 0.251 590
propane 85.525–363.3 0.067138–0.20792 4.2512 44.096 369.89 0.1521 592
R113 236.93–477.17 0.04007–0.085549 3.3922 187.38 487.21 0.2525 573
R115 173.75–345.35 0.039033–0.093819 3.129 154.47 353.1 0.248 573
R123 166–456.4 0.038918–0.11589 3.6618 152.93 456.83 0.2819 606
R124 120.44–386.66 0.044881–0.12476 3.6243 136.48 395.43 0.2881 494
R125 172.52–334.08 0.045807–0.11602 3.6177 120.02 339.17 0.3052 578
R134a 169.85–368.41 0.051448–0.14524 4.0593 102.03 374.21 0.3268 585
R13 92–295 0.044826–0.1349 3.879 104.46 302 0.1723 581
R141b 169.68–463.95 0.055423–0.12622 4.212 116.95 477.5 0.2195 578
R142b 142.72–402.82 0.049787–0.13891 4.055 100.5 410.26 0.2321 579
R143a 161.34–339.9 0.054416–0.13724 3.761 84.041 345.86 0.2615 577
R14 120.13–223.63 0.0437–0.11461 3.75 88.005 227.51 0.1785 451
R152a 154.56–379.2 0.065553–0.17633 4.5168 66.051 386.41 0.2752 577
R218 125.45–340.79 0.033449–0.085197 2.64 188.02 345.02 0.3172 583
R227ea 146.35–366.37 0.043666–0.094476 2.925 170.03 374.9 0.357 580
R236ea 242–403.6 0.048617–0.10352 3.42 152.04 412.44 0.369 405
R236fa 179.6–389.48 0.0486–0.10412 3.2 152.04 398.07 0.377 584
R245ca 203.97–438.75 0.059217–0.12865 3.9407 134.05 447.57 0.355 547
R245fa 171.05–418.3 0.053289–0.13556 3.651 134.05 427.16 0.3776 576
R32 136.34–346.58 0.09082–0.24291 5.782 52.024 351.26 0.2769 585
R41 129.82–314.58 0.092271–0.34698 5.897 34.033 317.28 0.2004 597
RC318 233.35–379.99 0.044076–0.079042 2.7775 200.03 388.38 0.3553 565
for predicting
butane 134.9–417.62 0.066699–0.17656 3.796 58.122 425.13 0.201 590
decane 243.5–602.48 0.07214–0.14408 2.103 142.28 617.7 0.4884 580
nonane 219.7–586.12 0.067149–0.15302 2.281 128.26 594.55 0.4433 592
R114 273.43–410.23 0.038431–0.066362 3.257 170.92 418.83 0.2523 343
R116 173.1–289.3 0.038056–0.086639 3.048 138.01 293.03 0.2566 582
total             19 113
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a

Data from the fluids for predicting are not used in the training phase. Data are from the REFPROP of NIST.

The 16 426 data points of the 29 fluids in the training phase are used as inputs to construct the ANN model and obtain the optimal weight and bias values of the model; 70%, 15%, and 15% of these data are randomly divided into the training data set, validation data set, and test data set, respectively. The 2687 data points of the other five liquids are employed to examine the predictive power of the trained model with optimal configuration. These data are unknown for the training phase.

2.2. Constructing the ANN Model

In this work, a feed-forward back-propagation ANN model to correlate and predict thermal conductivity is constructed through utilizing the neural network toolbox in MATLAB software. As illustrated in Figure 1, this model consists of three layers: one input layer, one hidden layer, and one output layer. Its input variables are the temperature (T) as well as the molecular mass (M), acentric factor (ω), critical temperature (Tc) and critical pressure (Pc), while the output variable is the thermal conductivity (λ) of each liquid. As is well-known to all, thermal conductivity is dependent on the temperature. Thus, the temperature is selected as one of the input variables. References (11, 13, 17, 35, and 36) have indicated that the thermal conductivity of the fluid is closely related to the molecular mass, acentric factor, critical temperature, and critical pressure. Furthermore, the four parameters are successfully used as inputs of the ANN model to differentiate the characteristic of the substances considered in ref (27). In this paper, the molecular mass, acentric factor, critical temperature, and critical pressure are employed to characterize the fluid types as in ref (27). Therefore, five neurons in the input layer are selected to receive the input signals and one neuron in the output layer is considered to transmit the output signal.

Figure 1.

Figure 1

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Structure of the ANN model for thermal conductivity.

The ANN model is like a black box. The parameters affecting its performance include the number of neurons in the hidden layer, transfer function and training algorithm. To evaluate the performance of the different ANN, we used some statistical parameters, such as the mean square error (MSE), correlation coefficient (R), percent deviation (PD), and average absolute deviation (AAD). They are defined as follows

2.2. 1
2.2. 2
2.2. 3
2.2. 4

where Cv represents the covariance, λdata is the thermal conductivity values from the REFPROP program, and λcal is the calculated thermal conductivity from the ANN model. Also, the adjust coefficient of determination (Radj2) is employed to compare the fit of regression models with different numbers of inputs. The Radj is defined as the following

2.2. 5

where k and N represent the number of input parameters and the number of data points, respectively.

Optimization of structure and parameters is the major and difficult task for the ANN model. In this study, the Levenberg–Marquardt back-propagation (trainlm) algorithm is employed as training algorithm, mainly because this algorithm appears to be the fastest and the most widely used method. With regard to the activity function or transfer function, by using trial-and-error method together with considering the aforementioned statistical parameters, the hyperbolic tangent sigmoid function (tansig) and linear function (purelin) are used in the hidden layer and output layer, respectively. They are defined as follows

2.2. 6
2.2. 7

Furthermore, the optimal number of the neurons in the hidden layer need to be found utilizing the trial-and-error method. Too few neurons can lead to underfitting, whereas too many neurons can lead to overfitting. The MSE in the training phase and AAD in the testing phase versus the number of neurons in the hidden layer are shown in Figure 2. As can be seen, MSE value decreases in the training phase with the increase of the neurons number in the hidden layer. When the number of neurons is more than seven, the MSE value tends to be stable. On the other hand, AAD value in the testing phase tends to increase when the number of neurons is greater than seven. In order to balance the performance in the training phase and AAD values in the testing phase, the number of neurons is selected as 7.

Figure 2.

Figure 2

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MSE in the training phase and AAD in the detection phase versus the number of neurons in the hidden layer.

The constructed ANN model with optimal configuration needs to be trained by using the Levenberg–Marquardt back-propagation algorithm so as to find the optimum weight and bias matrixes. The optimized weight and bias values in the hidden layer and output layer are obtained and shown in Table 2. Furthermore, performances of the ANN model with seven neurons in the hidden layer are tested for several combinations of inputs (T, M, Pc, Tc, and ω). These results are listed in Table 3. According to the MSE, as can be seen, in the training phase the critical temperature is the most important while the critical pressure is the least important. However, the critical pressure is of relative importance for the predictive power of the model.

Table 2. Weight and Bias Values of the ANN Model for Thermal Conductivity.

  hidden layer weight
      
neuron T Pc M Tc ω hidden layer bias output layer weight output layer bias
1 2.9284 3.1977 –1.0803 6.6785 –6.7831 6.6343 0.0533 0.5625
2 0.4269 0.452 0.0091 –1.478 0.0591 –2.9088 –12.9359
3 –0.4807 0.2525 –0.2578 0.6324 0.2577 –0.9434 1.2995
4 –1.2319 1.0717 0.8516 –0.2914 0.3142 –1.3103 2.4064
5 1.0868 –0.2992 –0.0711 0.163 –0.0805 1.324 –5.913
6 –1.0054 1.7473 –0.3851 –0.0234 –0.8597 –4.7474 13.9369
7 1.1082 –0.539 –0.3278 0.1197 –0.1398 1.3766 8.8979
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Table 3. Performances for Several Cases with Seven Neurons in the Hidden Layer.

  training set (29 fluids)
 testing set (5 fluids)
inputs MSE (×106) R R2 Radj2 MSE (×106) R R2 Radj2
(T, M, Pc, Tc, ω) 2.8192 0.9994 0.9988 0.9988 2.1724 0.9993 0.9986 0.9986
(T, Pc, Tc, ω) 3.8501 0.9991 0.9982 0.9982 23.9109 0.9908 0.9817 0.9817
(T, M, Tc, ω) 2.0588 0.9995 0.9990 0.9990 28.5217 0.9906 0.9813 0.9813
(T, M, Pc, ω) 4.7282 0.9989 0.9978 0.9978 18.3671 0.9936 0.9872 0.9872
(T, M, Pc, Tc) 3.9719 0.9991 0.9982 0.9982 78.7035 0.9960 0.9920 0.9920
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3. Results and Discussions

In the training phase, a plot of predicted thermal conductivity values, the outputs, versus the targets with respect to the ANN model of the optimal configuration is illustrated in Figure 3. As can be seen, the outputs of the ANN model keep close agreement with the targets, namely, the thermal conductivity values from REFPROP program. In the training stage, the MSE, R, and Radj2 of the presented ANN model are 2.8192 × 10–6, 0.9994, and 0.9988, respectively. Then, the trained ANN model with the optimum structure, parameters as well as optimum weight and bias values is applied in the testing phase to examine the predictive ability. In this case, the thermal conductivity values of the five unknown liquids are used which is not used in the training phase. A comparison of the output values, i.e., the predicted thermal conductivity values, and the target ones is depicted in Figure 4. As can be seen in Figure 4, in the testing stage, the MSE, R, and Radj of this ANN model are 2.1724 × 10–6, 0.9993, and 0.9986, respectively. As shown, the trained ANN model with the optimum configuration and parameters reveals the powerful predictive ability for the thermal conductivity of the unknown fluids.

Figure 3.

Figure 3

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Calculated thermal conductivity values with the proposed model versus the target values in the training phase. The perfect fit is indicated by the solid red line. Thermal conductivity is in W/(m K).

Figure 4.

Figure 4

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Calculated thermal conductivity values with the proposed model versus the target values in the testing phase. The perfect fit is indicated by the solid red line. Thermal conductivity is in W/(m K).

Additionally, the PD and AAD values of the ANN model are given in Figure 5 and Table 4 with regard to all 34 fluids considered here. From Table 4, the mean AAD values are 1.34%, 1.46%, and 1.36% in the training phase, testing phase and both phases, respectively. The accuracy of output varies with the substance for the proposed ANN model. AAD values vary from 0.18% to 4.5%. Also, AAD values are less than 1% for 14 out of 34 fluids, and less than 2% for 28 fluids. AAD value is higher than 3% for only hexane.

Figure 5.

Figure 5

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PD values with the proposed model versus thermal conductivity values for all 34 fluids considered here.

Table 4. Deviations of the ANN Model for Thermal Conductivity.

  PD
  
fluids maximum (%) minimum (%) mean (%) AAD (%)
dodecane 0.2 –1.62 –0.42 0.47
ethane 1.01 –2.82 –0.24 0.37
heptane 4.38 –0.2 0.91 0.99
hexane –0.88 –13.48 –4.5 4.5
methane 0.92 –1.1 0.04 0.18
octane 6.77 –1.58 2.2 2.37
pentane 7.5 0.11 2.57 2.57
propane 2.18 –1.35 0.39 0.71
R113 0.43 –1.29 –0.3 0.38
R115 0.73 –6.6 –1.12 1.46
R123 11.89 –4.4 1.79 2.58
R124 2.23 –1.17 1.21 1.22
R125 1.78 –0.98 0.66 0.80
R134a 7.02 –4.23 0.66 1.66
R13 1.62 –12.52 –0.29 1.63
R141b 1.88 –3.58 0.01 0.50
R142b 2.05 –2.1 –0.74 1.28
R143a 0.59 –2.62 –0.53 0.81
R14 1.73 –10.35 –0.15 1.59
R152a 1.45 –2.81 0.13 0.84
R218 7.17 –0.7 0.9 1.24
R227ea 0.89 –4.25 –1.13 1.26
R236ea 2.24 –5.58 –0.25 1.87
R236fa 3.04 –4.4 –0.55 1.78
R245ca 1.61 –5.03 –1.33 2.18
R245fa 2.73 –2.78 1.19 1.35
R32 1.57 –4.48 –0.19 0.75
R41 6.65 –1.31 0.18 0.90
RC318 1.86 –0.46 0.18 0.63
mean-train - - - 1.34
butane 2.89 0.11 1.57 1.57
decane 1.48 –6.44 0.06 1.49
nonane 1.56 –3.37 –0.64 1.54
R114 1.92 –4.05 –1.74 2.14
R116 2.11 –1.53 0.28 0.56
mean-predicted       1.46
mean-all       1.36
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As seen in Figure 5, the PD values are affected by the thermal conductivity values, and most of the PD values are between −5% and 5% for all the fluids considered here. The PD values are relatively small when the thermal conductivity values are great, whereas the PD values are often comparatively high when the thermal conductivity values are very small. Moreover, considering Table 4 as well, all the absolute PD values are all less than 13.48%. The maximum absolute PD values are more than 10% only in case of hexane, R13, R14 and R123. The maximum absolute PD value, 13.48%, is also obtained from hexane. The mean PD values are between −1% and 1% for 23 fluids, between −2% and 2% for 31 fluids, outside −3% to 3% for only hexane.

However, the performance of the proposed ANN model is slightly different for each family of fluids. The calculated thermal conductivity values versus the target values with respect to the ANN model for each family in the training and testing phase are shown in Figures 6 and 7, respectively. As can be seen in Figure 6, the MSE and R of this model are 1.7898 × 10–6 and 0.9996, respectively, for refrigerants in the training stage, while the MSE and R of this model are 5.4246 × 10–6 and 0.9984, respectively, for n-alkanes in the training stage. Obviously, the performance of this model for refrigerants is slightly better than for n-alkanes, which can also be seen in Figure 7.

Figure 6.

Figure 6

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Calculated thermal conductivity values versus the target values for refrigerants and n-alkanes in the training phase. Thermal conductivity is in W/(m K).

Figure 7.

Figure 7

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Calculated thermal conductivity values versus the target values for refrigerants and n-alkanes in the testing phase. Thermal conductivity is in W/(m K).

To finish this section, the results obtained for hexane are considered. For this fluid, the AAD, absolute maximum PD, and mean PD are 4.5%, −13.48%, and −4.5%, respectively. Any of the three deviations is the highest among all the 34 fluids considered here. A plot of the PD values versus correlation values for hexane from REFPROP illustrated in Figure 8. As seen, the absolute PD value increases with the increase of temperature in the intermediate and high temperatures. The maximum value is found at the highest temperature considered, namely, near the critical temperature. As denoted in REFPROP,33 for hexane, “the overall uncertainty is estimated to be less than 4.2%, and larger uncertainties are in the critical region”. The predicted results from the ANN model basically agree with the specified information in REFPROP. Evidently, for hexane, the ANN model underestimates the correlation values from REFPROP. For this reason, experimental data of hexane are collected from some literature,37−39 as listed in Table 5. For these experimental data, PD values with respect to the proposed ANN model are calculated. A plot of the PD values versus the experimental data is shown in Figure 9. It can be seen that the predicted values from the ANN model keep agreement with the experimental data for hexane. Obviously, the correlation model from REFPROP overestimates thermal conductivity values for hexane. Unfortunately, experimental data near the critical temperature is not found in previous literature. Therefore, experimental data near the critical temperature are needed in order to obtain a clear conclusion about whether the ANN model is adequate or not for hexane near the critical temperature.

Figure 8.

Figure 8

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PD values versus thermal conductivity values from REFPROP for hexane.

Table 5. Experimental Thermal Conductivity Data of Hexane from Refs (37−39).

T (K) λ (W/(m K)) uncertainty (%) NP ref
183.15–303.15 0.1182–0.1597 1 13 (37)
297.35–324.77 0.1123–0.1209 1 12 (38)
298.15–333.15 0.1083–0.1215 1 4 (39)
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Figure 9.

Figure 9

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PD values versus experimental thermal conductivity data from ref (37−39) for hexane.

In sum, in a very wide temperature range, the proposed ANN model not only can accurately correlate the thermal conductivity, but also has the strong power to predict the thermal conductivity of unknown fluids, that is, it can extrapolate the thermal conductivity very well.

4. Conclusions

In this work, a feed-forward back-propagation ANN model is developed to correlate and predict the thermal conductivity of 23 refrigerants and 11 n-alkanes from the triple point temperature up to 0.98Tc. The input variables are the temperature, molecular weight, acentric factor, together with the critical temperature and pressure. This ANN model is composed of the input layer, the output layer, and one hidden layer with seven neurons. The activity functions in the hidden layer and output layer are selected as “tansig” and “purelin” functions, respectively. Also, the ANN model is trained by using the “trainlm” algorithm, and the optimum weight and bias values are obtained. The calculated thermal conductivity values by the trained ANN with the optimum parameters agree well with the data from the REFPROP program in both the training and testing stages. The R values in both stages are 0.9994 and 0.9993, respectively. Moreover, AAD values less than 1% are found for 14 out of 34 fluids, less than 2% for 28 fluids, and less than 4.5% for all the considered fluids. The maximum absolute PD value is 13.48%, corresponding to hexane. The ANN model performs slightly better for refrigerants than for n-alkanes. However, some disagreements can be found near the critical temperature for some fluids. In conclusion, the developed ANN model demonstrates a powerful predictive ability in addition to the correlative power in the very wide temperature range.

Acknowledgments

Special thanks to the anonymous reviewer for his/her helpful comments and suggestions. The National Natural Science Foundation of China under Grant 11274200, the Natural Science Foundation of Shandong Province under Grant ZR2022MA055, and the foundations of QFNU have supported this work.

The authors declare no competing financial interest.

References

  1. Poling B. E.; Prausnitz J. M.; O’Connell J. P.. The Properties of Gases and Liquids; 5th ed.; McGraw-Hill: New York, 2001. [Google Scholar]
  2. Bridgman P. W. conductivity of liquids under pressure. Proc. Am. Acad. Art Sci. 1923, 59, 141–169. 10.2307/20026073. [DOI] [Google Scholar]
  3. Lashkarbolooki M.; Hezave A. Z.; Bayat M. Correlating thermal conductivity of pure hydrocarbons and aromatics via perceptron artificial neural network (PANN) method. Chin. J. Chem. Eng. 2017, 25 (5), 547–554. 10.1016/j.cjche.2016.08.025. [DOI] [Google Scholar]
  4. Ghalem N.; Hanini S.; Naceur M. W.; Laidi M.; Amrane A. Prediction of thermal conductivity of liquid and vapor refrigerants for pure and their binary, ternary mixtures using artificial neural network. Thermophys. and Aeromech. 2019, 26 (4), 561–579. 10.1134/S0869864319040085. [DOI] [Google Scholar]
  5. Gharagheizi F.; Ilani-Kashkouli P.; Sattari M.; Mohammadi A. H.; Ramjugernath D.; Richon D. Development of a quantitative structure-liquid thermal conductivity relationship for pure chemical compounds. Fluid Phase Equilib. 2013, 355, 52–80. 10.1016/j.fluid.2013.06.043. [DOI] [Google Scholar]
  6. Nagvekar M.; Daubert T. E. A group contribution method for liquid thermal conductivity. Ind. Eng. Chem. Res. 1987, 26 (7), 1362–1365. 10.1021/ie00067a017. [DOI] [Google Scholar]
  7. Lazzús J. A. A group contribution method to predict the thermal conductivity lambda(T,P) of ionic liquids. Fluid Phase Equilib. 2015, 405, 141–149. 10.1016/j.fluid.2015.07.015. [DOI] [Google Scholar]
  8. Wu K. J.; Zhao C. X.; He C. H. Development of a group contribution method for determination of thermal conductivity of ionic liquids. Fluid Phase Equilib. 2013, 339, 10–14. 10.1016/j.fluid.2012.11.024. [DOI] [Google Scholar]
  9. Yang S.; Tian J.; Jiang H. Corresponding state principle based correlation for the thermal conductivity of saturated refrigerants liquids from Ttr to 0.90Tc. Fluid Phase Equilib. 2020, 509, 112459. 10.1016/j.fluid.2020.112459. [DOI] [Google Scholar]
  10. Lv Y. M.; Tian J. X.; Jiang H. Three-parameter correlation for the temperature dependent thermal conductivity of saturated liquids. Fluid Phase Equilib. 2020, 514, 112563. 10.1016/j.fluid.2020.112563. [DOI] [Google Scholar]
  11. Latini G.; Di Nicola G.; Pierantozzi M. Liquid thermal conductivity prediction for alkanes, ketones and silanes. Phys. Chem. Liq. 2017, 55 (6), 747–765. 10.1080/00319104.2016.1277720. [DOI] [Google Scholar]
  12. Latini G.; Di Nicola G.; Pierantozzi M. A method to estimate the thermal conductivity of organic alcohols in the liquid phase at atmospheric pressure or along the saturation line. Fluid Phase Equilib. 2016, 427, 488–497. 10.1016/j.fluid.2016.08.010. [DOI] [Google Scholar]
  13. Di Nicola G.; Ciarrocchi E.; Pierantozzi M.; Stryjek R. A new equation for the thermal conductivity of organic compounds. J. Therm. Anal. Calorim. 2014, 116 (1), 135–140. 10.1007/s10973-013-3422-7. [DOI] [Google Scholar]
  14. Latini G., Thermal conductivity of refrigerant fluids: A new correlation for the compounds of methane and ethane series in the liquid phase along the saturation line. In 3rd Conference on Thermophysical Properties and Transfer Processes of Refrigerants;Boulder, CO; International Institute of Refrigeration: Paris, 2009.
  15. Latini G.An estimation method for the thermal conductivity of the refrigerants in the liquid state. In International Refrigeration and Air Conditioning Conference; Purdue University Libraries: West Lafayette, IN, 2008.
  16. Di Nicola G.; Coccia G.; Tomassetti S. A modified Kardos equation for the thermal conductivity of refrigerants. J. Theor. Comput. Chem. 2018, 17 (2), 1850012. 10.1142/S0219633618500128. [DOI] [Google Scholar]
  17. Gharagheizi F.; Ilani-Kashkouli P.; Sattari M.; Mohammadi A. H.; Ramjugernath D.; Richon D. Development of a General Model for Determination of Thermal Conductivity of Liquid Chemical Compounds at Atmospheric Pressure. AIChE J. 2013, 59 (5), 1702–1708. 10.1002/aic.13938. [DOI] [Google Scholar]
  18. Latini G.; Sotte M. Refrigerants of the methane, ethane and propane series: the thermal conductivity calculation along the saturation line. Int. J. Air-Cond. Refri. 2011, 19 (1), 37–43. 10.1142/S2010132511000387. [DOI] [Google Scholar]
  19. Sattari M.; Bakare B. F. Artificial neural network for the correlation and prediction of surface tension of refrigerants. Fluid Phase Equilib. 2018, 465, 107–116. 10.1016/j.fluid.2018.02.023. [DOI] [Google Scholar]
  20. Mulero A.; Pierantozzi M.; Cachadiña I.; Di Nicola G. An artificial neural network for the surface tension of alcohols. Fluid Phase Equilib. 2017, 449, 28–40. 10.1016/j.fluid.2017.06.003. [DOI] [Google Scholar]
  21. Mulero A.; Cachadiña I.; Valderrama J. O. Artificial neural network for the correlation and prediction of surface tension of refrigerants. Fluid Phase Equilib. 2017, 451, 60–67. 10.1016/j.fluid.2017.07.022. [DOI] [Google Scholar]
  22. Zhang J. Y.; Feng Q. H.; Zhang X. M.; Zhang X. L.; Yuan N.; Wen S. M.; Wang S. L.; Zhang A. G. The use of an artificial neural network to estimate natural gas/water interfacial tension. Fuel 2015, 157, 28–36. 10.1016/j.fuel.2015.04.057. [DOI] [Google Scholar]
  23. Di Nicola G.; Pierantozzi M. Surface tension of alcohols: A scaled equation and an artificial neural network. Fluid Phase Equilib. 2015, 389, 16–27. 10.1016/j.fluid.2015.01.014. [DOI] [Google Scholar]
  24. Gharagheizi F.; Eslamimanesh A.; Mohammadi A. H.; Richon D. Use of artificial neural network-group contribution method to determine surface tension of pure compounds. J. Chem. Eng. Data 2011, 56 (5), 2587–2601. 10.1021/je2001045. [DOI] [Google Scholar]
  25. Sabzevari S.; Moosavi M. Density prediction of liquid alkali metals and their mixtures using an artificial neural network method over the whole liquid range. Fluid Phase Equilib. 2014, 361, 135–142. 10.1016/j.fluid.2013.10.044. [DOI] [Google Scholar]
  26. Moosavi M.; Sedghamiz E.; Abareshi M. Liquid density prediction of five different classes of refrigerant systems (HCFCs, HFCs, HFEs, PFAs and PFAAs) using the artificial neural network-group contribution method. Int. J. Refrig. 2014, 48, 188–200. 10.1016/j.ijrefrig.2014.09.007. [DOI] [Google Scholar]
  27. Wang X.; Li Y.; Yan Y.; Wright E.; Gao N.; Chen G. Prediction on the viscosity and thermal conductivity of hfc/hfo refrigerants with artificial neural network models. Int. J. Refrig. 2020, 119, 316–325. 10.1016/j.ijrefrig.2020.07.006. [DOI] [Google Scholar]
  28. Pierantozzi M.; Petrucci G. Modeling thermal conductivity in refrigerants through neural networks. Fluid Phase Equilib. 2018, 460, 36–44. 10.1016/j.fluid.2017.12.027. [DOI] [Google Scholar]
  29. Pierantozzi M.; Di Nicola G.; Latini G.; Coccia G. Artificial neural network modelling of liquid thermal conductivity for alcohols. Phys. Chem. Liq. 2018, 56 (3), 363–380. 10.1080/00319104.2017.1341980. [DOI] [Google Scholar]
  30. Ghaderi F.; Ghaderi A. H.; Ghaderi N.; Najafi B. Prediction of the Thermal Conductivity of Refrigerants by computational Methods and Artificial Neural Network. Front. Chem. 2017, 5, 99. 10.3389/fchem.2017.00099. [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Eslamloueyan R.; Khademi M. H. Estimation of thermal conductivity of pure gases by using artificial neural networks. Int. J. Therm. Sci. 2009, 48 (6), 1094–1101. 10.1016/j.ijthermalsci.2008.08.013. [DOI] [Google Scholar]
  32. Karabulut E. Ö.; Koyuncu M. Neural network-based correlations for the thermal conductivity of propane. Fluid Phase Equilib. 2007, 257 (1), 6–17. 10.1016/j.fluid.2007.04.024. [DOI] [Google Scholar]
  33. Lemmon E. W.; Huber M. L.; McLinden M. O.. REFPROP: Reference Fluid Thermodynamic and Transport Properties, NIST Standard Reference Database, Version 9.1; National Institute of Standards and Technology: Gaithersburg, MD, 2018.
  34. Bloxham J. C.; Redd M. E.; Giles N. F.; Knotts T. A.; Wilding W. V. Proper Use of the DIPPR 801 Database for Creation of Models, Methods, and Processes. J. Chem. Eng. Data 2021, 66 (1), 3–10. 10.1021/acs.jced.0c00641. [DOI] [Google Scholar]
  35. Di Nicola G.; Pierantozzi M.; Petrucci G.; Stryjek R. Equation for the Thermal Conductivity of Liquids and an Artificial Neural Network. J. Thermophys. Heat Tr. 2016, 30 (3), 651–660. 10.2514/1.T4863. [DOI] [Google Scholar]
  36. Latini G.; Sotte M. Thermal conductivity of refrigerants in the liquid state: A comparison of estimation methods. Int. J. Refrig. 2012, 35 (5), 1377–1383. 10.1016/j.ijrefrig.2012.04.009. [DOI] [Google Scholar]
  37. Brykov V. P.; Mukhamedzyanov G. K.; Usnaanov A. G. Experimental Investigation of the Thermal Conductivity of Organic Fluids at Low Temperatures. Inzh.-Fiz. 1970, 18 (1), 62–66. 10.1007/BF00828364. [DOI] [Google Scholar]
  38. Assael M. J.; Charitidou E.; Nieto de Castro C. A.; Wakeham W. A. The Thermal Conductivity of n-Hexane, n-Heptane, and n-Decane by the Transient Hot-wire Method. Int. J. Thermophys. 1987, 8 (6), 663–670. 10.1007/BF00500786. [DOI] [Google Scholar]
  39. Kashiwagi H.; Oishi M.; Tanaka Y.; Kubota H.; Makita T. Thermal Conductivity of Fourteen Liquids in the Temperature Range 298–373 K. Int. J. Thermophys. 1982, 3 (2), 101–116. 10.1007/BF00503634. [DOI] [Google Scholar]

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Data Citations

  1. Lemmon E. W.; Huber M. L.; McLinden M. O.. REFPROP: Reference Fluid Thermodynamic and Transport Properties, NIST Standard Reference Database, Version 9.1; National Institute of Standards and Technology: Gaithersburg, MD, 2018.

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