# Modeling Liquid Thermal Conductivity of Low-GWP Refrigerants Using Neural Networks
###### Abstract
[16] developed a simple semi-empirical correlation based on the Modified Enskog Theory model to represent the \(\lambda_{L}\) of 14 refrigerants, including HFOs and HCFOs, defined as:  
\[\lambda_{L}=\lambda_{0}\mathbf{b}^{\prime}\rho\left(\frac{1}{\mathbf{b}^{\prime}\rho g (\sigma)}+\mathbf{A}+\mathbf{b}^{\prime}\rho\,g(\sigma)\right) \tag{2}\]  
where \(\lambda_{0}\) is the dilute gas thermal conductivity (calculated using the rigorous kinetic theory formulae in the original work), \(\rho\) is the molar density in mol m\({}^{-3}\), \(b^{\prime}\) is the covolume in m\({}^{3}\), \(g(\sigma)\) is the radial distribution function, \(\sigma\) is a characteristic distance parameter between colliding molecules, and \(A\) is a modified cross contribution term that has a specific value for each fluid. The values of \(b^{\prime}\rho\ g(\sigma)\) were obtained from the Peng Robison equation of state. It was found that the presented model generally produced better results than the analyzed literature models. Simple correlations to describe the temperature dependence of \(\lambda_{L}\) of HFOs and HCFOs were recently proposed by [PERSON] and [PERSON] [23]. One was developed to consider the different behavior of \(\lambda_{L}\) near the critical point and has the following form:  
\[\lambda_{L}=\lambda_{0}\left(C_{1}+C_{2}\tau+C_{3}\tau^{2}+C_{4}\tau^{-X}\right) \tag{3}\]  
where \(\chi=0.62\) is the critical index of heat conductivity, \(C_{1}=0.0441183554\), \(C_{2}=0.0362984013\), \(C_{3}=0.08788343\), and \(C_{4}=-0.00115567\) are regressed coefficients, and \(\tau=1-T_{r}\). Instead, \(\lambda_{0}\) is the critical unit, defined as:  
\[\lambda_{0}=\frac{p_{c}}{M^{1/5}T_{c}{}^{1/5}G\iota^{3}}+1.75\ \omega^{2.4} \tag{4}\]  
where \(G\iota=T_{c}\ T_{b}{}^{-1}\) is the Gulberg number, \(T_{b}\) is the normal boiling point temperature, and \(\omega\) is the acentric factor. Compared to other literature models, the present correlations generally ensured lower deviations between the calculated and experimental data. Finally, [PERSON] et al. [26] developed an ANN model for the thermal conductivity of different refrigerants, including three HFOs. The architecture of the proposed feed-forward ANN model consists of one input layer with four input variables (\(M\), \(T_{r}\), \(p_{r}\), \(\omega\)), one output layer with one neuron (\(\lambda\)), and one hidden-layer with eight neurons. The calculated thermal conductivity values showed a good agreement with the experimental data, giving an average absolute relative deviation of 1.00% for the complete dataset. This work presents a new neural network that has been specifically developed to predict the liquid thermal conductivity of various low-GWP synthetic alternative refrigerants for HVAC&R applications. The proposed ANN can describe the liquid thermal conductivity in large temperature and pressure ranges since it was trained on a large experimental dataset for seven alternative refrigerants. After explaining the neural network's nature, the feed-forward network architecture developed for the studied refrigerants is reported together with the obtained results.