Entropy Scaling of Thermal Conductivity: Application to Refrigerants and Their Mixtures

Abstract

Residual entropy scaling (RES) of thermal conductivity was applied to pure refrigerants, including natural and halogenated refrigerants, and their mixtures. The reference equations of state and the mixture models implemented in the REFPROP software package were adopted to calculate the residual entropy, and the critical enhancement of thermal conductivity was taken into account with the RES approach for the first time. Experimental data of 39 pure fluids with more than 38,000 data points and of 31 mixtures with more than 7600 points were collected and analyzed. More than 95.4% of the data (within two standard deviations of the mean) of pure fluids collapse into a global dimensionless residual thermal conductivity versus scaled dimensionless residual entropy curve within 11.1% and those of mixtures are within 8.3%. This smooth, monotonically increasing curve was correlated with a polynomial function containing only four fitted parameters and one fluid-specific scaling factor. Each pure fluid has its individual scaling factor, and a simple mole-fraction-weighted mixing rule was applied for mixtures. The correlation function provides a reliable thermal conductivity prediction of pure fluids and, without any additional parameters, of mixtures. The proposed model yields a similar level of statistical agreement with the experimental data as the extended corresponding states model, which is the current state-of-the-art and has as many as four more parameters for each pair of components.

Thermal Conductivity of Binary Mixtures of 1,1,1,2-Tetrafluoroethane(R-134a), 2,3,3,3-Tetrafluoropropene (R-1234yf), and trans-1,3,3,3-Tetrafluoropropene (R-1234ze(E)) Refrigerants

“…The thermal conductivity data obtained in this study are used to test the residual entropy scaling model of Yang et al developed to calculate the thermal conductivity of refrigerants and their mixtures. The residual entropy defined as is the difference between the entropy, s ( T ,ρ), and the ideal gas entropy, s ig ( T ,ρ), at the same temperature and molar density.…”

“…Molar residual entropy values are calculated using pure component reference EoS for R-1234yf, R-134a, and R-1234ze­(E) and the applicable mixtures models using REFPROP interfaced with the Python package CoolProp 6.4.1 . In the approach utilized by Yang et al, the macroscopically scaled thermal conductivity, λ̃, given by is nondimensionalized using appropriate length, energy, and time dimensions. In eq , k B is the Boltzmann constant, ρ is the molar density, N A is Avogadro’s number, and m is the mass of the molecule in kilograms.…”

“…The data reported in the present work allow validation and improvement of available transport property models. The current mixture thermal conductivity model used in the REFPROP (version 10.0) program is the extended corresponding states model. , However, Yang et al recently reported a new entropy scaling model which is significantly less computationally complex than the current corresponding states model and may require less fitting of the data to calculate thermal conductivities over a wide range of conditions. The data reported in this study are compared to both the corresponding states and entropy scaling models, and the performance of both modeling approaches are evaluated.…”

Connecting Entropy Scaling and Density Scaling

“…The review of Dyre 1 in 2018 summarized the progress in this field up to that date. Since then, additional studies have considered the physical basis of this approach 2,7 , and applied the technique to different systems: the Lennard-Jones fluid 8 , refrigerants 9,10 , and alkanes 11,12 .…”

Searching for Sustainable Refrigerants by Bridging Molecular Modeling with Machine Learning

“…Mickoleit et al 43 examined the effect of the thermodynamic model on the accuracy of screening and designing refrigeration systems, examining models including classical cubic equations of state, COSMO-based models, and PCP-SAFT. Yang et al 44 applied entropy scaling with the REFPROP 45 reference EoS to model the thermal conductivity of several pure and mixed refrigerants. Wang et al 46 integrated a polar version of PC-SAFT with process modeling and optimization to determine optimal refrigerants based on technical evaluation.…”