Fluids, containing gases and liquids, have a wide range of applications in daily life and play an important role in modern industrial processes. Since refrigerants are crucial in the refrigeration industry, we must have a scientific knowledge about their transport properties. Computational methods that allow for the prediction of transport properties serve as valuable tools due to their time efficiency when compared to the time it would take to conduct the work in a laboratory. The effect of microscopic motions and the interactions of molecules on the transport properties of gases are considered to form the basis of these methods.

The transport properties of refrigerants have been investigated in numerous studies. Kandlikar et al. (1975) predicted the transport properties of R₁₂ and R₂₂ (Kandlikar et al., 1975). Assael at al. performed the absolute thermal conductivity measurement of liquid refrigerants R₁₁ and R₁₂ at the temperature range of 250–340 K and pressures from saturation to 30 MPa (Assael et al., 1992). In another study, the thermal conductivity of R_134a, R_152a, and R₁₂₃ was evaluated using the transient hot-wire method (Gross et al., 1992). The viscosity coefficient of R₁₅₂ was investigated by Krauss et al. (1996). A practical representation for the transport coefficients of pure refrigerants R₃₂, R₁₂₅, R_134a, and R₁₂₅ + R₃₂ mixtures was presented by Kiselev et al. and was valid in the vapor-liquid critical region (Kiselev et al., 1999). Also, the transport properties of R14 have been examined in some studies (Smith and Pace, 1969; Rubio et al., 1985).

In 1917, Sydney Chapman and David Enskog solved the accurate equation for the transport properties of gases that had been presented by Maxwell and Boltzmann in 1860–1870 (Levine, 1995). Chapman-Enskog relations for monatomic gases and mixtures of these gases are expressed through the use of inter-atomic potential and temperature. In this theory, each coefficient of transport properties in gases is related to the collision integral (Ω) that depends on the value of potential, the nature of the interaction, and the reduced temperature (T^*). The basis of the calculation of (Ω) in this work was the expansion of corresponding states presented by Najafi et al. (1983).

The Chapman-Enskog theory relates the effect of local binary molecular collisions. Furthermore, the role of higher-order molecular collisions is considered in the regions of higher density in gases. The existence of the internal degree of freedom in polyatomic gases has a considerable influence on thermal conductivity (λ), and thus thermal conductivity cannot be definitely calculated by the Chapman-Enskog theory (Maitland et al., 1978). In 1980, Rainwater and Friend proposed a microscopic theoretical methodology for calculating the second transport virial coefficients of moderately dense gases (up to 2 mol.dm⁻³; Friend and Rainwater, 1984; Rainwater and Friend, 1987). In this theory, thermal conductivity is described according to the second thermal conductivity virial coefficient (Bλ) and depends on interatomic potential and temperature. Rainwater and Friend calculated Bλ by utilizing the Lennard-Jones potential (Rainwater and Friend, 1987). Bich and Vogel then presented correlation functions for B^*λ (reduced second virial coefficient of thermal conductivity; Millat et al., 1996). Since the Lennard-Jones potential is a rough approximation of reality, Najafi et al. (1998) calculated the thermal conductivity of some gases at moderate density by applying a highly accurate and realistic potential known as Aziz potential (Aziz and Slaman, 1990; Aziz, 1993).

Husseinnejad and Behnejad estimated the thermal conductivity of a number of refrigerants via Bich and Vogel potential scaling parameters (Hosseinnejad and Behnejad, 2008). In 2014, Geller et al. calculated the viscosity and thermal conductivity of refrigerant mixtures using a set of models. They utilized a corresponding states method to anticipate thermal conductivity in refrigerant mixtures (Geller et al., 2014). Huber and Assael used Chapman-Enskog method to predict the transport properties of (R1234yf) and [R1234ze(E)] as refrigerant replacements (Huber and Assael, 2016). Perkins et al. represented the thermal conductivity of (R245fa) as a sum of three contributions in a range of temperatures and pressures (Perkins et al., 2016).

At densities higher than the moderate range of the RF theory, new residual correction functions were offered by Najafi et al. (1998, 2000). These functions are density-dependent. However, at higher levels of density, these methods are defeated and, thus, an appropriate method is required to solve this problem.

Recently, some nonlinear methods have been presented to classify and predict the behavior of nonlinear systems. One of the most famous approaches in these contexts is the artificial neural network (ANN). The ANN prediction method is employed in many areas including climate (Ghaderi and Darooneh, 2012; Abdellatif et al., 2015) and economy (Aydin et al., 2015) as well as in thermodynamic and thermophysics applications (Di Nicola et al., 2016; Rostamian et al., 2016).

The thermodynamic characteristics of an alternative refrigerant (R_407c) have been examined by Sozen et al. They used an ANN to determine the specific volume, enthalpy, entropy, viscosity, and thermal conductivity of R_407c. Promising results were obtained from the thermodynamic specifications of this refrigerant in acceptable error (Sozen et al., 2009).

The determination of thermophysical properties in the case of refrigerants was accomplished by Sencan et al. using ANN. R_413A, R_417a, R_422a, R_422d, and R_423a were considered while the liquid and vapor thermophysical properties of refrigerants were obtained by ANN (Sencan et al., 2011). The thermodynamic analyses of R₁₂, R₂₂, and R₅₀₂ using ANNs were performed by Arcaklioglu et al. (2004). In some studies, ANN has been used for predicting the viscosity of refrigerants (Cristofoli et al., 2002; Ghaderi et al., 2013). Thermodynamic properties such as enthalpy, entropy, and specific volume of R_413a, R_417a, R_422d, and R_423a were predicted using ANN and the adaptive neuro-fuzzy approach by Sahin et al. (2012). Furthermore, Sozen et al. utilized ANN method for estimating the thermodynamic properties of an environmentally friendly refrigerant (R_404a) in both superheated vapor region and saturated liquid-vapor region (wet vapor) as numerical equations. In this study, the calculated thermodynamic properties had an acceptable uncertainty (Sozen et al., 2010). A three-layer feed-forward neural network was employed to predict the thermal conductivity of pure gases, and the performance of ANN was compared with those of several commonly used models. The results indicated that the commonly used regular conductivity correlations are used for a limited range of temperatures and components, while the network method can cover a wide range of temperatures and substances (Eslamloueyan and Khademi, 2009). In the case of refrigerants, the viscosity of six refrigerants was predicted by ANN and computational methods. The ANN method shows a very good accuracy at high levels of density, while computational methods are defeated in the case of density levels higher than 8 (Ghaderi et al., 2013).

In the present study, the thermal conductivity of six refrigerants containing R12 (dichlorodifluoromethane), R14 (carbontetrafluoride), R32 (diflouromethane), R143a (1, 1, 1trifluoroethane), R115 (chloropentafluoroethane), and R152a (1, 1difluoroethane) was calculated by the RF method at low and moderate levels of density. For higher ranges of density, a modified RF theory was applied which stretched beyond the validity range of the RF theory and allowed for the development of corresponding states correction functions. Residual thermal conductivity was also computed. Then, the graphs of Δλ vs. ρ were drawn. The principle of corresponding states was used to confirm the graphs. The parameters λ^* and ρ^* of refrigerants were also found.

The results of thermal conductivity calculation were compared with the existing experimental data (Keyes, 1954; Oshen et al., 1967; Rosenbaum and Thodos, 1967; Rodgers et al., 1974; Makita et al., 1981; Yata et al., 1984; Imaishi et al., 1985; Millat et al., 1988; Hahne and Song, 1989; Tanaka et al., 1991; Assael et al., 1992, 2000; Gross et al., 1992; Assael and Karagiannidis, 1993; Kim et al., 1993; Papadaki and Wakeham, 1993; Vargaftik, 1994; Gao et al., 1995; Hammerschmidt, 1995; Ro et al., 1995; Zaporozhan and Geller, 1995; Gross and Song, 1996; Krauss et al., 1996; Tsvetkov et al., 1996; McLinden et al., 2000; Le and Garrabos, 2001). After that, a feed forward ANN was used to predict the thermal conductivity of six refrigerants in the entire range of densities. The ANN training data were collected from the National Institute of Standards and Technology (NIST) (http://webbook.nist.gov/chemistry/). The NIST Chemistry Web Book has provided a great online database of chemical and physical properties for chemical species. The NIST also introduces many useful references and experiments that contain practical and experimental data.

Since there is no established method for determining the thermal conductivity of refrigerants in a wide range of densities, the ANN's efficiency was investigated. It is proposed that ANN as a nonlinear approach can successfully predict thermal conductivity. Finally, the two methods were compared. According to the results, the computational method is a reliable method only at low levels of density, while ANN is a valuable method at moderate and high levels of density where the computational method fails.

This paper is organized as follows: Computational methods for predicting thermal conductivity are described in first section. The feed-forward ANN and the learning algorithm are explained in second section. Applications of the computational method and the ANN approach for predicting thermal conductivity are stated in third and fourth sections. Finally, fifth and sixth sections are devoted to the expression of results, discussion, and conclusions.

In the case of calculating the thermal conductivity of the six refrigerants, the efficiency of the two methods (ANN and the computational approach) was compared. The RF theory is a statistical method for predicting the thermal conductivity of refrigerants in low densities (Rainwater, 1981; Rainwater and Friend, 1987). Nevertheless, this model fails at higher levels of density. To predict thermal conductivity at higher densities, the RF theory can be used (Najafi et al., 2000).

On the other hand, the ANN approach is a nonlinear method which can be applied for predicting thermal conductivity in all ranges of density (Sencan et al., 2011; Ghaderi et al., 2013). The performances of the ANN approach and the computational method were compared at low, mid, and high levels of density, with the results presented in Tables 4–6, respectively. At the low densities (<2), the two methods were reliable. However, the ANN approach had better results (Table 4). These results show that, in the case of R14, R32, R115, R143, R153, all of the three ANNs represented slightly better predictions than the computational method. In the moderate range of density, (Tables 1, 5 and Figures 4–9), the computational method could be used only for R₃₂ and was defeated in other cases. In another study, however, the computational method showed reliable results in this range of density for predicting the viscosity of the same fluids (Ghaderi et al., 2013). Furthermore, the thermal conductivity of the six refrigerants was precisely predicted by ANN in the mid-density range.

In the high range of density, the computational method was invalid for the six refrigerants, while the ANN approach proved to be a reliable method for predicting thermal conductivity at density levels up to 27. These results are consistent with the results of another study on viscosity prediction (Ghaderi et al., 2013).

The number of hidden neurons in the ANN structure is selected as 10, 20, and 30. Based on the results, a network with 30 hidden neurons has the best prediction at higher levels of density. On the other hand, the results of the computational method indicate that the regular dependence between thermal conductivity and density at higher densities is eliminated. It can develop a nonlinear problem. Therefore more nodes in hidden layer are needed to solve the nonlinearity problem.

The ANN approach proved to be a reliable method for predicting thermal conductivity in all ranges of density, while the computational method was restricted to low densities (Figures 4–9 and Tables 1, 4–6). In the low levels of density (ρ < 2), the computational method based on RF theory was usable (R > 0.92) (Tables 1, 4 and Figures 4–9). However, in the moderate and high levels of density (ρ > 2), this model often failed.

On the other hand, the results showed that, in the case of R32, this model succeeded at moderate levels of density (R = 0.98372). Thus, according to the results, we concluded that the computational method is an accurate model at low levels of density for predicting thermal conductivity prediction. Nevertheless, since the accuracy of computational method based on RF theory is reduced at higher levels of density, the ANN with MLPs as a nonlinear method is proposed for solving this problem. There is a nonlinear relationship between the thermal conductivity and other thermodynamical properties such as, pressure and density. As a result, analytical approaches are unable to predict thermal conductivity in a wide range of densities. Instead, a nonlinear approach such as, ANN is a valuable method for this purpose.

Other thermodynamic properties may be predicted by the ANN approach and the accuracy of predictions can be compared with those of computational methods. Moreover, other nonlinear methods may be used for prediction in this context.

FG worked on theoretical concept of chemical aspects and computational method and wrote a considerable volume of manuscript. AG worked on artificial neural network model, compared results of two methods, and wrote a part of manuscript. NG wrote a part of manuscript and helped in data analyzing. BN conducted group in all procedures.