# Modeling Liquid Thermal Conductivity of Low-GWP Refrigerants Using Neural Networks
###### Abstract  
The thermal conductivity of refrigerants is needed to optimize and design the main components of HVAC&R systems. Consequently, it is crucial to have reliable models that are able to accurately calculate the temperature and pressure dependence of the thermal conductivity of refrigerants. For the first time, this study presents a neural network specifically developed to calculate the liquid thermal conductivity of various low-GWP-based refrigerants. In detail, a feed-forward network algorithm with 5 input parameters (i.e., the reduced temperature, the critical pressure, the acentric factor, the molecular weight, and the reduced pressure) and 1 hidden layer was applied to a large dataset of 3404 experimental points for 7 halogenated alkene refrigerants. The results provided by the neural network algorithm were very satisfactory, achieving an absolute average relative deviation of 0.389% with a maximum absolute relative deviation of 6.074% over the entire dataset. In addition, the neural network ensured lower deviations between the experimental and calculated data than that produced using different literature models, proving its accuracy for the liquid thermal conductivity of the studied refrigerants. HFO; thermal conductivity; ANN; multi-layers perceptron; k-fold cross-validation +
Footnote †: journal: Applied Sciences  
In addition, complex models based on artificial neural networks (ANNs) were also proposed for calculating the \(\lambda\) of refrigerants [24; 25; 26]. In fact, since ANNs are powerful tools that have shown the ability to accurately address complex and non-linear problems in different scientific fields [27; 28], ANNs have been widely used to ensure very reliable descriptions of the thermophysical properties of several families of fluids. Some examples are as follows: the thermal conductivity of alkanes, ketones, and silanes [29], the surface tension of alcohols [30], and the viscosity of fatty acid esters [31]. Some literature models have been specifically developed to describe the liquid thermal conductivity of low-GWP refrigerants, such as HFOs and HCFOs [13; 16; 22; 23; 26]. For example, modified versions of the [PERSON] et al. [19] correlation and the Latini and Sotte [18] correlation to calculate their liquid thermal conductivity dependence on temperature and pressure were proposed by [PERSON] et al. [22]. The modified [PERSON] et al. [21] correlation has the following expression:  
\[\frac{\lambda_{L}}{\lambda_{0}}=\left\lfloor\mathbf{aT_{r}}+\mathbf{bp_{c}}+c\mathbf{ \omega}+\left(\frac{1}{M}\right)^{d}\right\rfloor\left[\mathbf{1}+\left(f_{0}+f \mathbf{T_{r}}^{2}\right)\mathbf{p}_{s}^{\prime}\right] \tag{1}\]  
where \(\lambda_{L}\) is the liquid thermal conductivity in W m\({}^{-1}\) K\({}^{-1}\), \(T_{r}=T\ T_{c}{}^{-1}\) is the reduced temperature, \(T_{c}\) is the critical temperature in K, \(p_{r}=p\ p_{c}{}^{-1}\) is the reduced pressure, \(p_{c}\) is the critical pressure in bar, \(\omega\) is the acentric factor, and \(M\) is the molecular mass in kg kmol\({}^{-1}\). The following values of the coefficients \(\lambda_{0}\), \(a\), \(b\), \(c\), \(d\), \(f_{0}\), \(f_{\sigma}\) and \(g\) were obtained from the regression of the experimental \(\lambda_{L}\) data for six refrigerants: \(\lambda_{0}=0.43693\) W m\({}^{-1}\) K\({}^{-1}\), \(a=-0.28725\), \(b=0.00372\) bar\({}^{-1}\), \(c=0.26967\), \(d=0.36436\), \(f_{0}=-0.00135\), \(f=0.05484\), and \(g=0.88049\). The results showed that the new version of the [PERSON] et al. [21] correlation provided a more accurate description of \(\lambda_{L}\) for the studied refrigerants than the modified [PERSON] [20] correlation, ensuring an average absolute relative deviation of 1.45% for the complete dataset. [PERSON] et al.