- Email: [email protected]
Methods used for evaluation of actual power generating thermal cycles and comparing them
Electrical Power and Energy Systems 69 (2015) 85–89
Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Methods used for evaluation of actual power generating thermal cycles and comparing them Emin Açıkkalp ⇑ Department of Mechanical and Manufacturing Engineering, Engineering Faculty, Bilecik S.E. University, Bilecik, Turkey
a r t i c l e
i n f o
Article history: Received 29 August 2014 Received in revised form 1 January 2015 Accepted 3 January 2015
Keywords: Irreversibility Ecological function Ecological coefficient of performance Exergetic performance criteria Maximum available work
a b s t r a c t In this study, thermodynamic optimization criteria used for assessing thermal engines are investigated and compared. The Purpose of this is to determine the most advantageous criteria. An irreversible Carnot cycle is analyzed by using five different methods and results are compared. According to calculations, the ecological function criterion (ECF) is defined as the most convenient optimization method. Although, its work output is less than the maximum work criteria and maximum available work (MAW), it has advantageous in terms of entropy generation and first law efficiency. In addition, ecological coefficient of performance (ECOP) and exergetic performance criteria (EPC) values provide minimum entropy generation and maximum efficiency at their maximum, however, their work output is very small. ECF obtains its maximum values at x = 0.488 (377.175 kW) for endoreversible cycle and at x = 0.477 (329.812 kW) for irreversible cycle. For these reasons, ECF is suggested as the best optimization criteria. Ó 2015 Elsevier Ltd. All rights reserved.
Introduction Analysis of the irreversible thermodynamic systems has been gained importance especially after the petrol crisis happened in 1970s. This new thermodynamic branch was called as FiniteTime-Thermodynamics (FTT). First studies at this area are about the endoreversible power cycle that is external irreversible and internal reversible cycles. This engine is called as the Curzon-Ahlborn-Novikov (CAN) engine [1,2]. This engine provides us more realistic results than Carnot cycle that operates totally reversible. In addition to these studies, maximum work extracted from an irreversible system was investigated by the several authors [3–5]. Angulo-Brown proposed a criterion called as ecological function (ECF) [6]. Yan suggested to use To (heat sink temperature) instead of TL (heat sink temperature) [7]. Several papers can be found in literature about ecological optimization [8–39]. Another thermoecological criterion called as ecological coefficient of performance (ECOP) was presented and applied various thermodynamic cycles [40–49]. Similar performance coefficient in order to determine relationship between exergy and exergy destruction for a cycle presented so called exergetic performance criteria (EPC) [50–54]. Another effort are to obtain a method for application of exergy concept in FTT. A number of study were published by the several authors [55–66]. A new criteria for assessing actual thermal cycles
was submitted by Açıkkalp and Yamık [67]. This method is called as max available work (MAW) and it used for determining limits of real cycles. In this paper, all of these methods are applied to an irreversible Carnot cycle and compared. There are no study comparing these methods and determining the most advantageous one in the open literature. Methods mentioned above are applied to an irreversible Carnot like thermal engine and results are compared. Finally, the most advantageous method is suggested in the conclusion section. System description and thermodynamic analysis Carnot cycle presents thermodynamic upper bonds for a thermal cycle. This cycle is totally reversible and contains two isentropic and two adiabatic processes. There is no internal or external irreversibility in the cycle, in addition, it is a theoretical cycle. However, there is no reversible cycle in reality. All cycles includes irreversibilities based on heat transfer at the finite temperature difference, friction, fast expansion and compressing, mixing etc. In considered system, cycle is totally irreversible and it is illustrated in Fig. 1. Analysis is performed for infinite heat source and heat sink. Thermodynamic parameters are listed as following: Added heat to the system (kW):
Q_ H ¼ kH ðT H T FH Þ ⇑ Tel.: +90 (228) 2160061; fax: +90 (228) 216 05 88. E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.ijepes.2015.01.003 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.
ð1Þ
where TH and TFH are the heat source temperature and hot working fluid temperature respectively (K) and kH is the heat conductance
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E. Açıkkalp / Electrical Power and Energy Systems 69 (2015) 85–89
In this study, a methodology that was submitted by Chen et al. [23,24] is applied. Optimization parameter is chosen as ratio of hot fluid temperature TFL to TFH (x). In addition, parameter of the heat FL and the sum of heat conductance rate conductance rate y ¼ kkFH ðz ¼ kFL þ kFH Þ is defined. According to second law of the thermodynamics:
Q_ L Q_ H 60 T FL T FH
ð10Þ
This inequality can be converted to an equality by describing an internal irreversibility parameter (I):
Q_ L Q_ H I ¼0 T FL T FH
ð11Þ
According to all Eqs. (1)–(11): Added heat to the system:
Q_ H ¼ Fig. 1. Schematic of irreversible Carnot cycle.
z yðT H x T L Þ 1 þ y ðy þ IÞx
Rejected heat from the system:
Q_ L ¼ IQ_ H x (kW/K) between the hot temperature heat source and working fluid. Rejected heat from the system (kW):
Q_ L ¼ kL ðT FL T L Þ
ð2Þ
where TL and TFL are the heat sink temperature and cool working fluid temperature (K) respectively and kL is the heat conductance (kW/K) between the low temperature heat sink and working fluid. Work output of the system (kW):
_ ¼ Q_ H Q_ L W
ð3Þ
Q_ L Q_ H TL TH
! ð4Þ
ð14Þ
Entropy generation in the system:
Sgen ¼
ðT L T H xÞðT L IT H xÞyz T L T H xð1 þ yÞðI þ yÞ
ð15Þ
First law efficiency:
ð16Þ
Ecological function criteria:
ðT L T H xÞðT H ðIT o x þ T L ðIx 1ÞÞ T L T o Þyz T L T H xð1 þ yÞðI þ yÞ
ð17Þ
Ecological coefficient of performance:
_ W
g¼ _ QH
ð5Þ
Criteria to evaluate actual thermal cycles are ECF, ECOP, EPC and MAW. ECF and ECOP are aimed to determine the maximum power output while the exergy destruction is the minimum. EPC and MAW, similarly, try to the optimum point between exergy output and the exergy destruction. Ecological function criteria (kW):
_ T o ðSgen Þ ECF ¼ W
To T o ðSgen Þ MAW ¼ Q_ H 1 TH
ð7Þ
Ecological coefficient of performance:
_ W ECOP ¼ T o ðSgen Þ
ð8Þ
Exergetic performance criteria:
Q_ H 1 TTHo T o ðSgen Þ
ECOP ¼
ð9Þ
T H T L ðIx 1Þ T o ðT L IT H xÞ
ð18Þ
Exergetic performance criteria:
EPC ¼
T L ðT o T H Þ T o ðT L IT H xÞ
ð19Þ
Maximum available work:
ð6Þ
where To is environment temperature (K). Maximum available work (kW):
EPC ¼
_ ¼ ðT L T H xÞðIx 1Þyz W xð1 þ yÞðI þ yÞ
ECF ¼
First law efficiency of the system:
ð13Þ
Work output of the system:
g ¼ 1 Ix
Entropy generation in the system (kW/K):
Sgen ¼
ð12Þ
MAW ¼
ðT H x T L ÞðT L IT o xÞyz T L xð1 þ yÞðI þ yÞ
ð20Þ
Results and discussion In this section, thermodynamics methods presented previous sections are searched in detail and compared to each other. Firstly, analyses is performed for classical thermodynamics parameters including the entropy production, work output, optimum (maximum) function value and first law efficiency. Secondly, other criteria are investigated and then, all results are compared to each other. According to calculations, system cannot be operated under the point x that is equal to 0.34, because of thermodynamic limitations. Fixed parameters used in the calculations listed in Table 1.
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E. Açıkkalp / Electrical Power and Energy Systems 69 (2015) 85–89
Results for I = 1 (endoreversible cycle)
160 140 120
ECOP, EPC
Changes of the parameters can be shown in Figs. 2–4 and all of the investigated criteria changes logarithmically except for first law efficiency. ECF, W and MAW increased until the optimum (maximum point), in contrast to this, ECOP and EPC criteria reduces with x. In this condition, maximum work is obtained at x = 0.577 (535.898 kW). At the optimum point for maximum work criteria, entropy generation is equal to 0.777 kW/K, first law efficiency gets the value of 0.222. Ecological criteria reaches its optimum value at x = 0.488 (377.175 kW). At this point, work, entropy generation and first law efficiency values are (489.184 kW, 0.368 kW/K, 0.522) respectively. Maximum available work criteria has optimum point at x = 0.669 (754.639 kW). In the maximum available work point, work output is equal to (498.232 kW), entropy generation and first law efficiency are equal to (1.263 kW/K) and (0.331) respectively. Ecological coefficient of performance and exergetic coefficient performance has not optimum point. They reduce with x. However, at x = 0.34 (beginning point) they acquire their maximum (132.819, 151.241 respectively), work output is only (38.824 kW) and entropy generation is the minimum (0.00098 kW/K), first law efficiency is maximum (0.66) at this value.
100 ECOP EPC
80 60 40 20 0 -20 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Fig. 3. Variations of ECOP and EPC with x (I = 1).
4 0.7 0.6
Results for I = 1.05 (totally irreversible cycle)
3
0.5 2
η
0.4 0.3
1
0.2 0.1
η
sgen (kW/K)
Variations of the parameters can be shown in Figs. 5–7 and all parameters’ changes are same with endoreversible engine generally. Maximum work criteria has optimum point at x = 0.563 (488.148 kW). At this point, entropy generation is 0.770 kW/K and first law efficiency value is 0.409. Investigating ecological criteria, it can be seen that the optimum point is obtained at x = 0.477 (329.812 kW). At this point, work is equal to (436.288 kW), entropy generation is (0.369 kW/K) and first efficiency value is equal to (0.499). For the maximum available work criteria, optimum point is obtained at x = 0.653 (700.349 kW). Work output is (450.397 kW), entropy generation is (1.262 kW/K) and first law
0
Sgen
0.0 -0.1
-1 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x Fig. 4. Variations of Sgen and g with x (I = 1).
Table 1 Parameters used in calculations. Unit
Value
y z TH TL To
– (W/m2 K) K K K
1 10 1200 400 298.15
750 500
W, ECF, MAW (kW)
Parameter
750 500
W, ECF, MAW (kW)
1.1
x
250
250 0 -250 W ECF MAW
-500 -750
0 -1000 -250 W ECF MAW
-500
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x
-750
Fig. 5. Variations of ECF, W and MAW with x (I = 1.05).
-1000 0.3
0.4
0.5
0.6
0.7
0.8
0.9
x Fig. 2. Variations of ECF, W and MAW with x (I = 1).
1.0
1.1
efficiency is equal to (0.314). Finally, trends of ECOP and EPC criteria are same with the endoreversible cycle. In these conditions, maximum values of these are obtained at x = 0.34 (0.3645 and 42.301 respectively). Work, entropy generation and first law
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E. Açıkkalp / Electrical Power and Energy Systems 69 (2015) 85–89
optimization should be made by using ECF method. Also it should be remembered that MAW is used to determine the limits for irreversible cycles. In the present world, energy demands are continuously increasing. Thus, efficiency and entropy generation parameters have become more important. For determining optimum values between work output, entropy generation and first law efficiency the most convenient methods should be defined.
ECOP, EPC
40
ECOP EPC
20
References
0 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x Fig. 6. Variations of ECOP and EPC with x (I = 1.05).
4 0.7 0.6
3
0.5
η
0.3 1
0.2 η Sgen
0.1
sgen (kW/K)
2
0.4
0
0.0 -0.1
-1 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x Fig. 7. Variations of Sgen and g with x (I = 1.05).
efficiency values respectively).
are
(36.901 kW,
0.0034 kW/K
and
0.643
Interpretation of the obtained results Comparing all methods for using evaluate the irreversible Carnot cycle converting heat to power according to thermodynamically parameters that consists of different criteria, it can be seen that ECF provides the most reasonable results. Although, work output of ECF is less than maximum work criteria naturally, it has second big work output value compared it with the other methods. Investigating entropy generation values of all methods at optimum points, it can be seen that ECF has advantage apparently because of having smaller value. Although, ECOP and EPC criteria have small entropy generation when they values are maximum, their work output values are very small too. Similar result are true for the first law efficiency, ECF has advantage within optimum parameters of methods. Conclusions In this study, methods using to assess an irreversible thermal engine are submitted and compared. As it is shown in results and discussion section, ECF has advantages compared with other evaluation methods. In addition to that, it can be said that
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Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Methods used for evaluation of actual power generating thermal cycles and comparing them Emin Açıkkalp ⇑ Department of Mechanical and Manufacturing Engineering, Engineering Faculty, Bilecik S.E. University, Bilecik, Turkey
a r t i c l e
i n f o
Article history: Received 29 August 2014 Received in revised form 1 January 2015 Accepted 3 January 2015
Keywords: Irreversibility Ecological function Ecological coefficient of performance Exergetic performance criteria Maximum available work
a b s t r a c t In this study, thermodynamic optimization criteria used for assessing thermal engines are investigated and compared. The Purpose of this is to determine the most advantageous criteria. An irreversible Carnot cycle is analyzed by using five different methods and results are compared. According to calculations, the ecological function criterion (ECF) is defined as the most convenient optimization method. Although, its work output is less than the maximum work criteria and maximum available work (MAW), it has advantageous in terms of entropy generation and first law efficiency. In addition, ecological coefficient of performance (ECOP) and exergetic performance criteria (EPC) values provide minimum entropy generation and maximum efficiency at their maximum, however, their work output is very small. ECF obtains its maximum values at x = 0.488 (377.175 kW) for endoreversible cycle and at x = 0.477 (329.812 kW) for irreversible cycle. For these reasons, ECF is suggested as the best optimization criteria. Ó 2015 Elsevier Ltd. All rights reserved.
Introduction Analysis of the irreversible thermodynamic systems has been gained importance especially after the petrol crisis happened in 1970s. This new thermodynamic branch was called as FiniteTime-Thermodynamics (FTT). First studies at this area are about the endoreversible power cycle that is external irreversible and internal reversible cycles. This engine is called as the Curzon-Ahlborn-Novikov (CAN) engine [1,2]. This engine provides us more realistic results than Carnot cycle that operates totally reversible. In addition to these studies, maximum work extracted from an irreversible system was investigated by the several authors [3–5]. Angulo-Brown proposed a criterion called as ecological function (ECF) [6]. Yan suggested to use To (heat sink temperature) instead of TL (heat sink temperature) [7]. Several papers can be found in literature about ecological optimization [8–39]. Another thermoecological criterion called as ecological coefficient of performance (ECOP) was presented and applied various thermodynamic cycles [40–49]. Similar performance coefficient in order to determine relationship between exergy and exergy destruction for a cycle presented so called exergetic performance criteria (EPC) [50–54]. Another effort are to obtain a method for application of exergy concept in FTT. A number of study were published by the several authors [55–66]. A new criteria for assessing actual thermal cycles
was submitted by Açıkkalp and Yamık [67]. This method is called as max available work (MAW) and it used for determining limits of real cycles. In this paper, all of these methods are applied to an irreversible Carnot cycle and compared. There are no study comparing these methods and determining the most advantageous one in the open literature. Methods mentioned above are applied to an irreversible Carnot like thermal engine and results are compared. Finally, the most advantageous method is suggested in the conclusion section. System description and thermodynamic analysis Carnot cycle presents thermodynamic upper bonds for a thermal cycle. This cycle is totally reversible and contains two isentropic and two adiabatic processes. There is no internal or external irreversibility in the cycle, in addition, it is a theoretical cycle. However, there is no reversible cycle in reality. All cycles includes irreversibilities based on heat transfer at the finite temperature difference, friction, fast expansion and compressing, mixing etc. In considered system, cycle is totally irreversible and it is illustrated in Fig. 1. Analysis is performed for infinite heat source and heat sink. Thermodynamic parameters are listed as following: Added heat to the system (kW):
Q_ H ¼ kH ðT H T FH Þ ⇑ Tel.: +90 (228) 2160061; fax: +90 (228) 216 05 88. E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.ijepes.2015.01.003 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.
ð1Þ
where TH and TFH are the heat source temperature and hot working fluid temperature respectively (K) and kH is the heat conductance
86
E. Açıkkalp / Electrical Power and Energy Systems 69 (2015) 85–89
In this study, a methodology that was submitted by Chen et al. [23,24] is applied. Optimization parameter is chosen as ratio of hot fluid temperature TFL to TFH (x). In addition, parameter of the heat FL and the sum of heat conductance rate conductance rate y ¼ kkFH ðz ¼ kFL þ kFH Þ is defined. According to second law of the thermodynamics:
Q_ L Q_ H 60 T FL T FH
ð10Þ
This inequality can be converted to an equality by describing an internal irreversibility parameter (I):
Q_ L Q_ H I ¼0 T FL T FH
ð11Þ
According to all Eqs. (1)–(11): Added heat to the system:
Q_ H ¼ Fig. 1. Schematic of irreversible Carnot cycle.
z yðT H x T L Þ 1 þ y ðy þ IÞx
Rejected heat from the system:
Q_ L ¼ IQ_ H x (kW/K) between the hot temperature heat source and working fluid. Rejected heat from the system (kW):
Q_ L ¼ kL ðT FL T L Þ
ð2Þ
where TL and TFL are the heat sink temperature and cool working fluid temperature (K) respectively and kL is the heat conductance (kW/K) between the low temperature heat sink and working fluid. Work output of the system (kW):
_ ¼ Q_ H Q_ L W
ð3Þ
Q_ L Q_ H TL TH
! ð4Þ
ð14Þ
Entropy generation in the system:
Sgen ¼
ðT L T H xÞðT L IT H xÞyz T L T H xð1 þ yÞðI þ yÞ
ð15Þ
First law efficiency:
ð16Þ
Ecological function criteria:
ðT L T H xÞðT H ðIT o x þ T L ðIx 1ÞÞ T L T o Þyz T L T H xð1 þ yÞðI þ yÞ
ð17Þ
Ecological coefficient of performance:
_ W
g¼ _ QH
ð5Þ
Criteria to evaluate actual thermal cycles are ECF, ECOP, EPC and MAW. ECF and ECOP are aimed to determine the maximum power output while the exergy destruction is the minimum. EPC and MAW, similarly, try to the optimum point between exergy output and the exergy destruction. Ecological function criteria (kW):
_ T o ðSgen Þ ECF ¼ W
To T o ðSgen Þ MAW ¼ Q_ H 1 TH
ð7Þ
Ecological coefficient of performance:
_ W ECOP ¼ T o ðSgen Þ
ð8Þ
Exergetic performance criteria:
Q_ H 1 TTHo T o ðSgen Þ
ECOP ¼
ð9Þ
T H T L ðIx 1Þ T o ðT L IT H xÞ
ð18Þ
Exergetic performance criteria:
EPC ¼
T L ðT o T H Þ T o ðT L IT H xÞ
ð19Þ
Maximum available work:
ð6Þ
where To is environment temperature (K). Maximum available work (kW):
EPC ¼
_ ¼ ðT L T H xÞðIx 1Þyz W xð1 þ yÞðI þ yÞ
ECF ¼
First law efficiency of the system:
ð13Þ
Work output of the system:
g ¼ 1 Ix
Entropy generation in the system (kW/K):
Sgen ¼
ð12Þ
MAW ¼
ðT H x T L ÞðT L IT o xÞyz T L xð1 þ yÞðI þ yÞ
ð20Þ
Results and discussion In this section, thermodynamics methods presented previous sections are searched in detail and compared to each other. Firstly, analyses is performed for classical thermodynamics parameters including the entropy production, work output, optimum (maximum) function value and first law efficiency. Secondly, other criteria are investigated and then, all results are compared to each other. According to calculations, system cannot be operated under the point x that is equal to 0.34, because of thermodynamic limitations. Fixed parameters used in the calculations listed in Table 1.
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Results for I = 1 (endoreversible cycle)
160 140 120
ECOP, EPC
Changes of the parameters can be shown in Figs. 2–4 and all of the investigated criteria changes logarithmically except for first law efficiency. ECF, W and MAW increased until the optimum (maximum point), in contrast to this, ECOP and EPC criteria reduces with x. In this condition, maximum work is obtained at x = 0.577 (535.898 kW). At the optimum point for maximum work criteria, entropy generation is equal to 0.777 kW/K, first law efficiency gets the value of 0.222. Ecological criteria reaches its optimum value at x = 0.488 (377.175 kW). At this point, work, entropy generation and first law efficiency values are (489.184 kW, 0.368 kW/K, 0.522) respectively. Maximum available work criteria has optimum point at x = 0.669 (754.639 kW). In the maximum available work point, work output is equal to (498.232 kW), entropy generation and first law efficiency are equal to (1.263 kW/K) and (0.331) respectively. Ecological coefficient of performance and exergetic coefficient performance has not optimum point. They reduce with x. However, at x = 0.34 (beginning point) they acquire their maximum (132.819, 151.241 respectively), work output is only (38.824 kW) and entropy generation is the minimum (0.00098 kW/K), first law efficiency is maximum (0.66) at this value.
100 ECOP EPC
80 60 40 20 0 -20 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Fig. 3. Variations of ECOP and EPC with x (I = 1).
4 0.7 0.6
Results for I = 1.05 (totally irreversible cycle)
3
0.5 2
η
0.4 0.3
1
0.2 0.1
η
sgen (kW/K)
Variations of the parameters can be shown in Figs. 5–7 and all parameters’ changes are same with endoreversible engine generally. Maximum work criteria has optimum point at x = 0.563 (488.148 kW). At this point, entropy generation is 0.770 kW/K and first law efficiency value is 0.409. Investigating ecological criteria, it can be seen that the optimum point is obtained at x = 0.477 (329.812 kW). At this point, work is equal to (436.288 kW), entropy generation is (0.369 kW/K) and first efficiency value is equal to (0.499). For the maximum available work criteria, optimum point is obtained at x = 0.653 (700.349 kW). Work output is (450.397 kW), entropy generation is (1.262 kW/K) and first law
0
Sgen
0.0 -0.1
-1 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x Fig. 4. Variations of Sgen and g with x (I = 1).
Table 1 Parameters used in calculations. Unit
Value
y z TH TL To
– (W/m2 K) K K K
1 10 1200 400 298.15
750 500
W, ECF, MAW (kW)
Parameter
750 500
W, ECF, MAW (kW)
1.1
x
250
250 0 -250 W ECF MAW
-500 -750
0 -1000 -250 W ECF MAW
-500
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x
-750
Fig. 5. Variations of ECF, W and MAW with x (I = 1.05).
-1000 0.3
0.4
0.5
0.6
0.7
0.8
0.9
x Fig. 2. Variations of ECF, W and MAW with x (I = 1).
1.0
1.1
efficiency is equal to (0.314). Finally, trends of ECOP and EPC criteria are same with the endoreversible cycle. In these conditions, maximum values of these are obtained at x = 0.34 (0.3645 and 42.301 respectively). Work, entropy generation and first law
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optimization should be made by using ECF method. Also it should be remembered that MAW is used to determine the limits for irreversible cycles. In the present world, energy demands are continuously increasing. Thus, efficiency and entropy generation parameters have become more important. For determining optimum values between work output, entropy generation and first law efficiency the most convenient methods should be defined.
ECOP, EPC
40
ECOP EPC
20
References
0 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x Fig. 6. Variations of ECOP and EPC with x (I = 1.05).
4 0.7 0.6
3
0.5
η
0.3 1
0.2 η Sgen
0.1
sgen (kW/K)
2
0.4
0
0.0 -0.1
-1 0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
x Fig. 7. Variations of Sgen and g with x (I = 1.05).
efficiency values respectively).
are
(36.901 kW,
0.0034 kW/K
and
0.643
Interpretation of the obtained results Comparing all methods for using evaluate the irreversible Carnot cycle converting heat to power according to thermodynamically parameters that consists of different criteria, it can be seen that ECF provides the most reasonable results. Although, work output of ECF is less than maximum work criteria naturally, it has second big work output value compared it with the other methods. Investigating entropy generation values of all methods at optimum points, it can be seen that ECF has advantage apparently because of having smaller value. Although, ECOP and EPC criteria have small entropy generation when they values are maximum, their work output values are very small too. Similar result are true for the first law efficiency, ECF has advantage within optimum parameters of methods. Conclusions In this study, methods using to assess an irreversible thermal engine are submitted and compared. As it is shown in results and discussion section, ECF has advantages compared with other evaluation methods. In addition to that, it can be said that
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