Entropy and Entransy Dissipation Analysis of a Basic Organic Rankine Cycles (ORCs) to Recover Low-Grade Waste Heat Using Mixture Working Fluids

Mixture working fluids can reduce effectively energy loss at heat sources and heat sinks, and therefore enhance the organic Rankine cycle (ORC) performance. The entropy and entransy dissipation analyses of a basic ORC system to recover low-grade waste heat using three mixture working fluids (R245fa/R227ea, R245fa/R152a and R245fa/pentane) have been investigated in this study. The basic ORC includes four components: an expander, a condenser, a pump and an evaporator. The heat source temperature is 120 °C while the condenser temperature is 20 °C. The effects of four operating parameters (evaporator outlet temperature, condenser temperature, pinch point temperature difference, degree of superheat), as well as the mass fraction, on entransy dissipation and entropy generation were examined. Results demonstrated that the entransy dissipation is insensitive to the mass fraction of R245fa. The entropy generation distributions at the evaporator for R245/pentane, R245fa/R152a and R245fa/R227ea are in ranges of 66–74%, 68–80% and 66–75%, respectively, with the corresponding entropy generation at the condenser ranges of 13–21%, 4–17% and 11–21%, respectively, while those at the expander for R245/pentane, R245fa/R152a and R245fa/R227ea are approaching 13%, 15% and 14%, respectively. The optimal mass fraction of R245fa for the minimum entropy generation is 0.6 using R245fa/R152a.


Introduction
With the increasing shortage of fossil energy and the escalating demand for energy, extensive attention has been paid to the renewable energy technologies. Several methods applicable to utilize renewable sources [1][2][3][4][5] have been studied, such as the organic Rankine cycle (ORC), Kalina cycle (using ammonia water) and trilateral cycle. Among them, ORC [6][7][8][9][10][11][12][13] is a promising method to convert low/medium-grade thermal energy into power. A large number of academic researches have been carried out, such as the choice of working fluids, the application of different configurations of ORC and economic analysis. In recent years, entropy generation has gradually played an important role in the research of ORC. Groniewsky et al. [14] used the Redlich-Kwong equation of state to predict the temperature-entropy saturation boundary of working fluids. They found that a limiting isochoric heat capacity may exist between dry and wet fluids. Li et al. [15] conducted an entropy generation analysis

Analysis of the ORC System
The schematic diagram of the basic ORC system to recover low-grade waste heat is shown in Figure 1, which includes an evaporator, an expander, a condenser, and a working fluid pump [35]. The thermodynamic process for the ORC system using mixture working fluids (showing the so-called dry characteristic) is illustrated on the temperature-entropy (T-s) diagram, as shown in Figure 2. It should be noted that the connecting points at a blue curve of 10, 9, 5 and 4 are the saturation points. The whole system is stable without leakages and heat losses. ORC is set to recover the waste heat, which is represented by a red line in Figure 2. Additionally, the working fluid and cooling water are represented by a blue line and a green line, respectively. A temperature of 120 • C and a mass flow rate of 0.33 kg/s are used for the simulated heat source, while the cooling water is used to condensate the working fluids with a condensate temperature of 20 • C. so-called dry characteristic) is illustrated on the temperature-entropy (T-s) diagram, as shown in Figure 2. It should be noted that the connecting points at a blue curve of 10, 9, 5 and 4 are the saturation points. The whole system is stable without leakages and heat losses. ORC is set to recover the waste heat, which is represented by a red line in Figure 2. Additionally, the working fluid and cooling water are represented by a blue line and a green line, respectively. A temperature of 120 °C and a mass flow rate of 0.33 kg/s are used for the simulated heat source, while the cooling water is used to condensate the working fluids with a condensate temperature of 20 °C.  In the evaporator, the working fluid is heated and vaporized by waste heat, and then the high pressure vapor (state 1) flows into the expander and its enthalpy is converted into work. The low-pressure vapor (state 2) exits the expander and is led to the condenser where it is liquefied by cooling water. Similarly, the liquid working fluid is available at the condenser outlet (state 6), and then it is pumped back to the evaporator, and a new cycle begins.
Compared to the pure working fluids, the main advantage of mixtures as ORC working fluids stems from their non-isothermal phase transitions during vaporization and condensation, and hence effectively matches the heat source and cooling water. The corresponding T-s diagram for the ORC system using mixture working fluids is shown in Figure 2.
The pump power ( p W  ) can be expressed as: so-called dry characteristic) is illustrated on the temperature-entropy (T-s) diagram, as shown in Figure 2. It should be noted that the connecting points at a blue curve of 10, 9, 5 and 4 are the saturation points. The whole system is stable without leakages and heat losses. ORC is set to recover the waste heat, which is represented by a red line in Figure 2. Additionally, the working fluid and cooling water are represented by a blue line and a green line, respectively. A temperature of 120 °C and a mass flow rate of 0.33 kg/s are used for the simulated heat source, while the cooling water is used to condensate the working fluids with a condensate temperature of 20 °C.  In the evaporator, the working fluid is heated and vaporized by waste heat, and then the high pressure vapor (state 1) flows into the expander and its enthalpy is converted into work. The low-pressure vapor (state 2) exits the expander and is led to the condenser where it is liquefied by cooling water. Similarly, the liquid working fluid is available at the condenser outlet (state 6), and then it is pumped back to the evaporator, and a new cycle begins.
Compared to the pure working fluids, the main advantage of mixtures as ORC working fluids stems from their non-isothermal phase transitions during vaporization and condensation, and hence effectively matches the heat source and cooling water. The corresponding T-s diagram for the ORC system using mixture working fluids is shown in Figure 2.
The pump power ( p W  ) can be expressed as: In the evaporator, the working fluid is heated and vaporized by waste heat, and then the high pressure vapor (state 1) flows into the expander and its enthalpy is converted into work. The low-pressure vapor (state 2) exits the expander and is led to the condenser where it is liquefied by cooling water. Similarly, the liquid working fluid is available at the condenser outlet (state 6), and then it is pumped back to the evaporator, and a new cycle begins. Compared to the pure working fluids, the main advantage of mixtures as ORC working fluids stems from their non-isothermal phase transitions during vaporization and condensation, and hence effectively matches the heat source and cooling water. The corresponding T-s diagram for the ORC system using mixture working fluids is shown in Figure 2.
The pump power ( . W p ) can be expressed as: where η p is the mechanical efficiency of pump.
Through the T-s plot, the ORC evaporator heat transfer rate ( . Q eva ) and the condenser heat transfer rate ( . Q con ) can be given as follows: .
where . m w f is the mass flow rate of mixture working fluids, which can be defined as: Since mixture working fluids have non-isothermal phase transitions in vaporization and condensation, the temperature glide of evaporator and condenser (as shown in Figure 2) can be expressed as: ∆T glide,eva = T 10 − T 9 (5) The temperature difference between the evaporator outlet temperature and saturation temperature corresponding to evaporator outlet pressure is superheat (∆T sup ), which can be given as: The PPTD in the ORC evaporator (∆T PP ) can be defined as:

Entropy Modeling
Based on previous research [12,19,22], the following equation of the entropy generation rate ( . S g ) can be obtained.
The entropy generation of evaporator and condenser can be expressed: .
In addition, entropy generation of expander and pump can be defined as: .

of 16
Based on Equations (14)- (16), the entropy generation of system can be given as: . S g,sys = .

Entransy Modeling
Based on the researches by Cheng and Liang [36], the entransy loss rate can be given as follows: .
G H is the entransy flows into the system, .
G L is the entransy flows out of the system, and they can be defined in ORC system as: .
The total entransy dissipation rate of the ORC system includes three parts. The first one is the entransy dissipation rate resulting from heat transfer between the hot stream and the working fluid: As the same principle goes, the second brace is the entransy dissipation rate due to heat transfer between the working fluid and the cold stream: The last part is the entransy dissipation rate due to dumping the used streams into the environment.

Working Fluid Selection
The selection of working fluid is crucial because working fluids have a great influence on the safety operation condition, economic efficiency and environmental impact. The primary fluid selection criteria for the ORC included: a high decomposition temperature to withstand the high-temperature exhaust gas and high boiling point under atmospheric pressure to easily release condensing heat to Entropy 2018, 20, 818 6 of 16 cooling water. Meantime, environmental protection, safety and economic characteristics still need to be taken into account. Considering the above criteria, proper working fluids were primarily selected and the basic thermodynamic properties of the fluids are listed in Table 1. Meanwhile, Feng et al. [22] investigated the thermoeconomic performance of mixture working fluids using R245fa/R227ea and R245fa/pentane. Wang et al. [37] presented an analysis of low-temperature solar ORC using R245fa/R152a. Therefore, three mixture working fluids, R245fa/R227ea, R245fa/R152a and R245fa/pentane, were selected in this study.

Assumptions
In order to simplify the computing simulation study appropriately, general assumptions [38,39] should be used in this study: The main assumptions for the ORC system are listed in Table 2.

Results and Discussion
To better understand the effects of system parameters on entransy dissipation and entropy generation, three mixture working fluids (0.5R245fa/0.5R227ea, 0.5R245fa/0.5R152a and 0.5R245fa/0.5pentane) were chosen in Sections 5.1 and 5.2. It should be noted that the thermodynamic properties of mixture working fluids were obtained from the NIST Refprop [40]. According to the T-s plot, the operation parameters (PPTD, degree of superheat, evaporator outlet temperature and condenser temperature) have a significant influence on the system performance. Therefore, the effects of operation parameters on entransy dissipation and entropy generation were addressed in Sections 5.1 and 5.2, respectively. The effects of mass fraction on entransy dissipation and entropy generation were examined in Section 5.3.

Effects of Operation Parameters on Entransy Dissipation
The variations of entransy dissipation with PPTD and the degree of superheat using 0.5R245fa/0.5R227ea, 0.5R245fa/0.5R152a and 0.5R245fa/0.5pentane are displayed in Figure 3a. The evaporator outlet temperature and condenser temperature are set to be 60 and 30 • C, respectively. The PPTD varies from 5 • C to 20 • C, and the degree of superheat is in a range of 10-20 • C. thermodynamic properties of mixture working fluids were obtained from the NIST Refprop [40]. According to the T-s plot, the operation parameters (PPTD, degree of superheat, evaporator outlet temperature and condenser temperature) have a significant influence on the system performance. Therefore, the effects of operation parameters on entransy dissipation and entropy generation were addressed in Sections 5.1 and 5.2, respectively. The effects of mass fraction on entransy dissipation and entropy generation were examined in Section 5.3.

Effects of Operation Parameters on Entransy Dissipation
The variations of entransy dissipation with PPTD and the degree of superheat using 0.5R245fa/0.5R227ea, 0.5R245fa/0.5R152a and 0.5R245fa/0.5pentane are displayed in Figure 3a. The evaporator outlet temperature and condenser temperature are set to be 60 and 30 °C, respectively. The PPTD varies from 5 °C to 20 °C, and the degree of superheat is in a range of 10-20 °C.   is hardly affected by the changes in degree of superheat. As noted in Equation (20), when the PPTD increases, the temperature points (T 2 , T 4 , T 5 ,T 6 , T 8 , T 9 , T 10 and T 1 ) are unchanged, whereas the heat source outlet temperature deceases, resulting in the decline in the working fluid mass flow rate, and causing eventually the increase in entransy dissipation. Therefore, entransy dissipation presents an increasing trend with the PPTD. Moreover, it is worth mentioning that 0.5R245fa/0.5R227ea has a better performance than 0.5R245fa/0.5R152a. Figure 3b illustrates the effects of evaporator outlet temperature and condenser temperature on the entransy dissipation using 0.5R245fa/0.5R227ea, 0.5R245fa/0.5R152a and 0.5R245fa/0.5pentane. The PPTD and degree of superheat are set to be 5 • C and 10 • C, respectively. The evaporator outlet temperature varies from 60 • C to 90 • C and the condenser temperature varies from 30 • C to 40 • C.
The entransy dissipation for three mixture working fluids owns a similar behavior of an increase with the condenser temperature but has a nonlinear variation with the evaporator outlet temperature. As expressed in Equation (17), when the evaporator outlet temperature increases, the temperature points (T 8 , T 9 , T 10 and T 1 ) increase, whereas the working fluid mass flow rate declines, ensuring the decline in the heat transfer rate, and eventually causing the decrease in entransy dissipation at first. However, as the evaporator outlet temperature continues to rise, the decline of the mass flow rate gradually occupies a dominant position compared to the rise of temperature, and thus the entransy dissipation increases gradually. The evaporator outlet temperature corresponding to the lowest entransy is in a range of 70-80 • C.
It can also be found that the entransy dissipation keeps decreasing with the condenser temperature. The reason is that the temperature difference declines between the working fluid and cooling water, resulting in the decrease in the irreversible loss. In Equation (18), as the condenser temperature increases, the temperature points (T 2 , T 4 , T 5 and T 6 ) increase, while the mass flow rate has no change. Accordingly, the entransy dissipation represents a rising trend with the condenser temperature. Moreover, 0.5R245fa/0.5pentane yields the highest G dis , followed by 0.5R245fa/0.5R152a. In addition, 0.5R245fa/0.5R227ea owns the lowest G dis with the evaporator outlet temperature of 80 • C and the condenser temperature of 30 • C. Figure 4a reveals the variation of entropy generation with the PPTD and degree of superheat using 0.5R245fa/0.5R227ea, 0.5R245fa/0.5R152a and 0.5R245fa/0.5pentane. The evaporator outlet temperature is 60 • C and the condenser temperature is 30 • C. The PPTD varies from 5 • C to 20 • C, and the degree of superheat varies from 10 • C to 20 • C. The entropy generation for the three working fluids has a similar behavior to the degree of superheat and PPTD. At first, with the increase of PPTD, 0.5R245fa/0.5pentane has the highest entropy generation. However, as the point temperature difference further increases, 0.5R245fa/0.5pentane gradually highlights its advantages. 0.5R245fa/0.5R227ea presents the highest entropy generation, followed by 0.5R245fa/0.5pentane, and 0.5R245fa/0.5R152a has the lowest entropy generation. In Equation (4), the mass flow rate of heat source keeps constant and h 14 decreases with the increase of the PPTD, and therefore the mass flow rate of working fluids declines. As expressed in Equations (9)-(13), when the PPTD increases, the mass flow of working fluids decreases, and therefore the generated entropy at the evaporator, condenser, expander and pump decline.

Effects of Operation Parameters for Entropy Generation
The variation of entropy generation with the evaporator outlet temperature and condenser temperature are illustrated in Figure 4b. The PPTD is 5 • C and the degree of superheat is 10 • C. The evaporator outlet temperature varies from 60 • C to 90 • C, and the condenser temperature varies from 30 • C to 40 • C. The increase in the evaporator outlet temperature results in a decrease in entropy generation. However, with the condenser temperature increasing, entropy generation decreases slightly. As stated in Equation (4), when evaporator outlet temperature increases, the heat source mass flow rate has no change and the value of h 14 keeps rising, resulting in the decline in the mass flow rate. In Equations (9)- (12), the entropy generation of system declines with the working fluid mass flow rate. Furthermore, it can be found that 0.5R245fa/0.5R227ea presents the Entropy 2018, 20, 818 9 of 16 highest entropy generation, followed by 0.5R245fa/0.5pentane and 0.5R245fa/0.5R152a. For example, for a specified evaporator temperature of 65 • C and a condenser temperature of 30 • C, the entropy generation is 10.991 J/kg K for 0.5R245fa/0.5R227ea, 10.865 J/kg K for 0.5R245fa/0.5pentane, and 10.420 J/kg K for 0.5R245fa/0.5R152a.  The variation of entropy generation with the evaporator outlet temperature and condenser temperature are illustrated in Figure 4b. The PPTD is 5 °C and the degree of superheat is 10 °C. The evaporator outlet temperature varies from 60 °C to 90 °C, and the condenser temperature varies from 30 °C to 40 °C. The increase in the evaporator outlet temperature results in a decrease in

Effects of Mass Fraction on Entransy Dissipation and Entropy Generation
The variation of entransy dissipation for three working fluids with the mass fraction of R245fa is displayed in Figure 5a-c. The PPTD, degree of superheat, evaporator outlet temperature and condenser temperature are set to be 5, 10, 60 and 30 • C, respectively. source mass flow rate has no change and the value of 14 h keeps rising, resulting in the decline in the mass flow rate. In Equations (9)-(12), the entropy generation of system declines with the working fluid mass flow rate. Furthermore, it can be found that 0.5R245fa/0.5R227ea presents the highest entropy generation, followed by 0.5R245fa/0.5pentane and 0.5R245fa/0.5R152a. For example, for a specified evaporator temperature of 65 °C and a condenser temperature of 30 °C, the entropy generation is 10.991 J/kg K for 0.5R245fa/0.5R227ea, 10.865 J/kg K for 0.5R245fa/0.5pentane, and 10.420 J/kg K for 0.5R245fa/0.5R152a.

Effects of Mass Fraction on Entransy Dissipation and Entropy Generation
The variation of entransy dissipation for three working fluids with the mass fraction of R245fa is displayed in Figure 5a-c. The PPTD, degree of superheat, evaporator outlet temperature and condenser temperature are set to be 5, 10, 60 and 30 °C, respectively. As noted in Equations (21)-(24), the entransy dissipation of system is affected mainly by Gdiss,env, Gdiss,con and Gdiss,eva. Figure 5a-c reveals that the evaporator owns the largest proportion of entransy dissipation in the ORC system. It can also be found that the entransy dissipation for the three mixture working fluids have a similar trend. As for R245fa/pentane, the proportions of evaporator, condenser and environment are 58%, 14%, and 28%, respectively, which are approaching the values for R245fa/R152a. Meanwhile, the proportions of evaporator, condenser and environment for R245fa/R227ea are 60%, 15%, and 15%, respectively, indicating that the entransy dissipation is insensitive to the working fluid type. Moreover, the entransy dissipation almost has no change with the mass fraction of R245fa, representing that the mass fraction of mixture working fluids has a small impact on the entransy dissipation. Figure 5d shows the trend of the entransy dissipation of the three mixture working fluids with the variation of the mass fraction of R245fa. Obviously, the entransy dissipations of the R245fa/R227ea and R245fa/R152a keep rising, whereas that of R245fa/pentane yields a reverse trend with the mass fraction of R245fa. As noted in Equations (21)-(24), the entransy dissipation of system is affected mainly by G diss,env , G diss,con and G diss,eva . Figure 5a-c reveals that the evaporator owns the largest proportion of entransy dissipation in the ORC system. It can also be found that the entransy dissipation for the three mixture working fluids have a similar trend. As for R245fa/pentane, the proportions of evaporator, condenser and environment are 58%, 14%, and 28%, respectively, which are approaching the values for R245fa/R152a. Meanwhile, the proportions of evaporator, condenser and environment for R245fa/R227ea are 60%, 15%, and 15%, respectively, indicating that the entransy dissipation is insensitive to the working fluid type. Moreover, the entransy dissipation almost has no change with the mass fraction of R245fa, representing that the mass fraction of mixture working fluids has a small impact on the entransy dissipation. Figure 5d shows the trend of the entransy dissipation of the three mixture working fluids with the variation of the mass fraction of R245fa. Obviously, the entransy dissipations of the R245fa/R227ea and R245fa/R152a keep rising, whereas that of R245fa/pentane yields a reverse trend with the mass fraction of R245fa. Figure 6a-c reveals the variation of entransy dissipation with mass fraction of R245fa. The entropy generation of system is determined mainly by four parts, including S g,evp , S g,con , S g,p and S g,exp .
It should be noted that the S g,p is relatively smaller than the others. Taking R245fa/pentane as an example and for a specified mass of fraction of 0.2, S g,evp is 8.497 J/(kg·K), S g,exp is 2.026 J/(kg·K) and S g,con = 1.566 J/(kg·K), while S g,p is 0.012 J/(kg·K). Therefore, S g,p can be ignored and the residual data are plotted in Figure 6. The entropy generation distributions at the expander for R245/pentane, R245fa/R152a and R245fa/R227ea are approaching 13%, 15% and 14%, respectively. Meanwhile, for the three working fluids, the entropy generation at the expander increases first and then decreases, whereas that at the condenser presents a reverse trend with the mass fraction of R245fa. The entropy generation distributions at the evaporator for R245/pentane, R245fa/R152a and R245fa/R227ea are in ranges of 66-74%, 68-80% and 66-75%, respectively, with the corresponding entropy generation distribution ranges at the condenser of 13-21%, 4-17% and 11-21%, respectively, which is shown in Figure 6a-c. Moreover, the maximum entropy generation at the expander appears for the mass fraction of 0.5 using R245, corresponding to the minimum entropy generation at the condenser. This indicates that the mass fraction has a significant influence on the entropy generation. As observed in Figure 6d, when the mass fraction of R245fa is 0.1, R245fa/R227ea owns the highest entropy generation, whereas R245f/R152a and R245fa/pentane yield a similar entropy generation. As the mass fraction of R245fa rises, the entropy generation variations for R245fa/R227ea and R245fa/R152a have a similar trend, that is, the entropy generation decreases first and then increases. Meanwhile, R245fa/pentane exhibits a slight variation with the mass fraction of R245fa. For a specified mass fraction of R245fa, R245fa/R227ea owns the highest entropy generation, whereas the lowest entropy generation is obtained by R245fa/R152a. It can also be found that the optimal mass fraction of R245fa for the minimum entropy generation is 0.6 using R245fa/R152a. Figure 6a-c reveals the variation of entransy dissipation with mass fraction of R245fa. The entropy generation of system is determined mainly by four parts, including Sg,evp, Sg,con, Sg,p and Sg,exp. It should be noted that the Sg,p is relatively smaller than the others. Taking R245fa/pentane as an example and for a specified mass of fraction of 0.2, Sg,evp is 8.497 J/(kg·K), Sg,exp is 2.026 J/(kg·K) and Sg,con = 1.566 J/(kg·K), while Sg,p is 0.012 J/(kg·K). Therefore, Sg,p can be ignored and the residual data are plotted in Figure 6. The entropy generation distributions at the expander for R245/pentane, R245fa/R152a and R245fa/R227ea are approaching 13%, 15% and 14%, respectively. Meanwhile, for the three working fluids, the entropy generation at the expander increases first and then decreases, whereas that at the condenser presents a reverse trend with the mass fraction of R245fa. The entropy generation distributions at the evaporator for R245/pentane, R245fa/R152a and R245fa/R227ea are in ranges of 66-74%, 68-80% and 66-75%, respectively, with the corresponding entropy generation distribution ranges at the condenser of 13-21%, 4-17% and 11-21%, respectively, which is shown in Figure 6a-c. Moreover, the maximum entropy generation at the expander appears for the mass fraction of 0.5 using R245, corresponding to the minimum entropy generation at the condenser. This indicates that the mass fraction has a significant influence on the entropy generation. As observed in Figure 6d, when the mass fraction of R245fa is 0.1, R245fa/R227ea owns the highest entropy generation, whereas R245f/R152a and R245fa/pentane yield a similar entropy generation. As the mass fraction of R245fa rises, the entropy generation variations for R245fa/R227ea and R245fa/R152a have a similar trend, that is, the entropy generation decreases first and then increases. Meanwhile, R245fa/pentane exhibits a slight variation with the mass fraction of R245fa. For a specified mass fraction of R245fa, R245fa/R227ea owns the highest entropy generation, whereas the lowest entropy generation is obtained by R245fa/R152a. It can also be found that the optimal mass fraction of R245fa for the minimum entropy generation is 0.6 using R245fa/R152a.

Conclusions
In this study, the entropy and entransy dissipation analyses of a basic ORC system using three mixture working fluids (R245fa/R227ea, R245fa/R152a and R245fa/pentane) have been investigated. The effects of the four operation parameters (evaporator outlet temperature, condenser temperature, PPTD, degree of superheat), as well as the mass fraction, on entransy dissipation and entropy generation, were examined. The main results are summarized as follows: (1) The entransy dissipations for the three mixture working fluids keep increasing with the condenser temperature, but have a nonlinear variation with the evaporator outlet temperature. The entropy generation for the three working fluids has a similar behavior of an increase with the degree of superheat and PPTD.
(2) The entransy dissipations of the R245fa/R227ea and R245fa/R152a keep rising, whereas that of R245fa/pentane yields a reverse trend with the mass fraction of R245fa. Meanwhile, the entropy generation of expander increases first and then decreases, whereas that of condenser presents a reverse trend with the mass fraction of R245fa.

Conclusions
In this study, the entropy and entransy dissipation analyses of a basic ORC system using three mixture working fluids (R245fa/R227ea, R245fa/R152a and R245fa/pentane) have been investigated. The effects of the four operation parameters (evaporator outlet temperature, condenser temperature, PPTD, degree of superheat), as well as the mass fraction, on entransy dissipation and entropy generation, were examined. The main results are summarized as follows: (1) The entransy dissipations for the three mixture working fluids keep increasing with the condenser temperature, but have a nonlinear variation with the evaporator outlet temperature. The entropy generation for the three working fluids has a similar behavior of an increase with the degree of superheat and PPTD.
(2) The entransy dissipations of the R245fa/R227ea and R245fa/R152a keep rising, whereas that of R245fa/pentane yields a reverse trend with the mass fraction of R245fa. Meanwhile, the entropy generation of expander increases first and then decreases, whereas that of condenser presents a reverse trend with the mass fraction of R245fa.