Finite-time thermodynamics optimization of an irreversible parallel flow double-effect absorption refrigerator

Accepted Manuscript Title: Finite-time thermodynamics optimization of an irreversible parallel flow double-effect absorption refrigerator Author: Brigitte Astrid Medjo Nouadje, Paiguy Armand Ngouateu Wouagfack, Réné Tchinda PII: DOI: Reference:

S0140-7007(16)00046-3 http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.02.014 JIJR 3269

To appear in:

International Journal of Refrigeration

Received date: Revised date: Accepted date:

3-9-2015 11-2-2016 12-2-2016

Please cite this article as: Brigitte Astrid Medjo Nouadje, Paiguy Armand Ngouateu Wouagfack, Réné Tchinda, Finite-time thermodynamics optimization of an irreversible parallel flow doubleeffect absorption refrigerator, International Journal of Refrigeration (2016), http://dx.doi.org/doi: 10.1016/j.ijrefrig.2016.02.014. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Finite-time thermodynamics optimization of an irreversible parallel flow double-effect absorption refrigerator MEDJO NOUADJE Brigitte Astrid1,

3(*)

, NGOUATEU WOUAGFACK Paiguy Armand3,4,

TCHINDA Réné1,2,3

1

LESEE, Department of physics, University of Yaounde I, PO Box 812, Yaounde, Cameroon

2

L2MSP, Department of physics, University of Dschang, PO Box 67, Dschang, Cameroon

3

LISIE, University Institute of Technology Fotso Victor, University of Dschang, PO Box 134, Bandjoun,

Cameroon 4

Department of Renewable Energy, Higher Technical Teachers’ Training College, University of Buea, PO Box

249, Buea Road, Kumba, Cameroon

(*) Corresponding author: MEDJO NOUADJE Brigitte Astrid Tel.: +237 698 04 86 90 /673 97 57 75 Institut Supérieur des Sciences et Technologies, Université des Montagnes BP: 208 Bangangté-Cameroon E-mail address: [email protected]

1 Page 1 of 52

Highlights



Finite-time thermodynamics optimization of double-effect absorption refrigerator



Analytical and numerical ooptimization based on COP.



Numerical optimization based on the new thermo-ecological criterion.



We determine analytically the optimum parameters at maximum COP.



Working fluid temperatures, ECOP, specific cooling rate and entropy generation rate.

ABSTRACT Finite-time thermodynamics optimization analysis based on the coefficient of performance and the ecological coefficient of performance criteria has been carried out. This was done analytically and numerically for a double-effect parallel flow absorption refrigerator with losses of heat resistance, heat leakage and internal irreversibility. The maximum of the coefficient of performance and the corresponding optimal conditions have been derived analytically. The optimum performance parameters which maximize the coefficient of performance objective function have been investigated. The effects of irreversibility parameters on the general and optimal performances on the basis of COP and ECOP functions have been discussed. The results obtained may provide the basis for designing real doubleeffect parallel flow absorption refrigerators.

Keywords: Double-effect absorption refrigeration system, finite-time thermodynamic, optimization, coefficient of performance, ecological coefficient of performance.

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Nomenclature

A: total heat-transfer area (m2) COP: coefficient of performance ECOP: ecological coefficient of performance I: internal irreversibility parameter K: thermal conductance (kW K-1) : rate of heat transfer (kW) R: specific cooling load (kW m-2) S: specific entropy generation rate (kW K-1 m-2) T: temperature (K) U: overall heat-transfer coefficient (kW K-1 m-2) a : distribution rate of the total heat reject quantity between the condenser and the absorber b : ratio of the total heat between the HP generator and the LP generator

Symbol : entropy generation rate (kW K -1) : heat leakage coefficient (kW K-1 m-2) Subscripts 1: working fluid in the high generator 2: working fluid in the low generator 3: working fluid in evaporator 4: working fluid in absorber 5: working fluid in condenser A: absorber

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C: condenser E: evaporator G: generator HP: high pressure LP: low pressure env: environment conditions L: heat leakage max: maximum m: at maximum COP

4 Page 4 of 52

1. Introduction Absorption refrigeration processes take place in finite-size devices in finite-time; therefore, it is impossible to meet reversibility conditions between the absorption refrigeration system and the surroundings. Thus, the classical thermodynamic performance bound couldn’t properly give the bound of absorption system (Bhardwaj et al., 2003; Kaushik et al., 2002; Ngouateu Wouagfack and Tchinda, 2013a). For this reason, the finite-time thermodynamics approach has been introduced to establish the performance bound of absorption system. The finite-time thermodynamics tends to model real system in a way closer to reality. It enables to distinguish the irreversibilities due to internal dissipation of the working fluid and that due to the finite-rate heat transfer between the system, the external heat reservoir and heat-sink. It tries to bridge the gap between thermodynamics and heat transfer. It deals with thermodynamic performance optimization of real finite-time and finite-size thermodynamic systems. The applications of finite-time thermodynamics include all the processes with thermal phenomena of all devices and systems operating with the constraints of finite-time and finite-size. The endoreversible cycle is the fundamental physical model adopted in finitetime thermodynamics. The finite-time thermodynamics has been first proposed by Henri B. Reitlinger in 1929 (Vaudrey et al., 2014) and later extended to nuclear energy by Chambadal and Novikov independently in 1957. This method has been popularized in many works including Curzon and Ahlborn (1975), Leff and Teeters (1978), Blanchard (1980), Bejan (1982, 1996, 1997), Andresen (1983), Feidt (1987), Sieniutycz and Salamon (1990), De Vos (1992, 1995), Radcenco (1994), Bejan et al. (1996), Chen et al. (1997), Bejan and Mamut (1999), Berry et al. (2000), Sieniutycz et al. (2002), Stitou et al. (2001, 2002), Zheng et al. (2003), Stitou, Feidt (2005),Chen et al. (2011), Li et al. (2013) and Feng et al. (2015a,b,c), in many review articles including Sieniutycz and Shiner (1994), Hoffmann et al. (1997), Chen et al. (1999), Durmayaz et al. (2004), Feidt (2013), Qin et al. (2013) and Ngouateu 5 Page 5 of 52

Wouagfack and Tchinda (2013b) and in books Wu et al. (1999) and Chen and Sun (2004). Significant results have been obtained and are provided in the literature. In the case of absorption refrigerators, the optimal operating region of endoreversible (Yan and Chen, 1989; Chen and Yan, 1993; Chen, 1995; Wijeysundera, 1996; Wu et al., 1997; Ng et al., 1997; Chen et al., 1997 a, b; Chen et al., 2004, 2011, 2013) and irreversible (Chen and Schouten, 1998; Chen, 1999; Chen et al., 2002; Zheng et al., 2003a,b, 2004; Chen et al., 2006; Qin et al., 2010; Ngouateu Wouagfack and Tchinda, 2011a; Ngouateu Wouagfack , 2012) single effect absorption refrigerator have been established.

For double-effect absorption refrigerator

systems, most of the theoretically work considers the mass and energy conversion approach to calculate the coefficient of performance of the system (Xu and Dait, 1997; Arun et al., 2000, 2001; Ezzine et al.,2004a,b, 2005; Kaushik et al., 2009; Torrella et al., 2009; Arona et al., 2009; Gebreslassie et al., 2010; Huicochea et al., 2011; Vasilescu et al., 2011; Sedigh and Saffari, 2011; Farshi et al., 2011, 2012; Shatata et al., 2012; Dominguez-Inzunza et al., 2014; Li et al., 2014) and the exergy efficiencies (Gomri and Hakimi, 2008; Arona et al., 2009; Kaushik et al., 2009; Gomri, 2010; Shahata et al., 2012; Farshi et al., 2013a,b). Chua et al. (2000) used the process average temperature to study the impact of the various dissipative mechanisms on the inverse of the coefficient of performance (COP-1) . Much work has yet to be done on the finite-time thermodynamics approach for double-effect absorption refrigerators except the work of Göktun and Er (2000). They used the finite-time thermodynamics approach to compare an irreversible double-effect absorption system affected by three internal irreversibilities parameters with an irreversible cascaded absorption refrigeration system. They did not establish the bound of the operating region of the system. In this paper, the finite-time performance of a parallel flow double-effect absorption refrigerator cycle with losses of heat resistance, heat leakage and internal irreversibility are

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derived. The irreversibility parameters and heat leakage effects on the COP and on the ECOP of the irreversible cycle are investigated. 2. System description Figure 1 shows the schematic illustration of a parallel flow double-effect system. It is seen in this figure that the weak solution leaving the absorber is pumped to the low-temperature heat exchanger (LTHE) after which it is divided into two streams. One stream flows to the HPG through the high-temperature heat exchanger (HTHE) and the other to the low-pressure generator (LPG) via EV4. In the LPG, the vapour refrigerant from the high-pressure generator (HPG) is condensed and its latent heat is utilized to generate water vapour from the weak solution in the LPG. A high-temperature heat source is used to provide heat to the HPG for water vapour generation from the weak solution. The strong solution exiting the HPG passes to the mixing point (P1), where it mixes with the other strong solution from the LPG. The combined strong solution is passed to the absorber through LTHE and EV3. 3. Physical model A parallel flow double-effect absorption refrigerator system has five main components: a high pressure generator, a low pressure generator, an absorber, a condenser and an evaporator. The system is a five-temperature (temperature in LPG, temperature in HPG, evaporator temperature, condenser temperature, and absorber temperature) and threepressure levels (low pressure in the evaporator and absorber, medium pressure in the condenser and the low pressure generator, the high pressure in the high pressure generator). The diagram of a parallel flow double-effect absorption refrigerator system adapted by us is represented in Fig. 2.

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In this model, Q H P G is the rate of heat absorbed from the heat source at temperature T H P G to high pressure generator, Q L P G is the rate of heat absorbed from the heat source at

temperature T L P G to low pressure generator, Q C is the heat rejection rate from the condenser to the heat-sink at temperature TC , Q A is the heat rejection rate from the absorber to the heatsink at temperature T A and Q E is the heat input rate from the cooling space at temperature T E to the evaporator. The work input required by the solution pump is negligible compared to the energy input to the high and low pressure generator. According to the first law of thermodynamics, we have (Göktun and Er, 2000): Q LP G  Q E  Q C  Q A  0

(1)

The performances of an absorption refrigerator system closely depend on the irreversible factors. We have considered the cycle of the working fluid as a three-irreversible isothermal process and three-irreversible adiabatic process since the double-effect system is a triple thermal system. The temperatures of the working fluid in the isothermal processes are different from those of the external heat reservoirs such that the heat is transferred under a finite temperature difference. Fig. 3 presents a schematic diagram of an irreversible parallel flow double-effect absorption refrigerator. In this figure, T1 and T 2 are respectively the temperatures of the working fluid in the HP generator and LP generator. T 3 , T 4 and T5 are respectively the temperature of the working fluid in the absorber, evaporator and condenser. We also considered the existence of heat leakage from the heat sink to the cooled space denoted Q L . The heat exchanged between the working fluid and heat reservoirs obey a linear heat transfer law, such that the equation of heat transfer can be written as:

8 Page 8 of 52

Q H PG  U H PG AH PG  T H PG  T1 

(2)

Q LP G  U LP G ALP G  T 2  T LP G 

(3)

Q E  U E AE  T E  T 4 

(4)

Q A  U A A A  T3  T A 

(5)

Q C  U C AC  T5  TC 

(6)

Following the idea developed by Chen and Schouten (1998), the heat-leak of a parallel flow double-effect system is given by: .

Q L  K L  T A  T E  TC  T E  T LP G  T E



(7)

where Eqs. (1)-(6) are written like Göktun and Er (2000). In equations (2)-(6), ,

AE

AA

and

AC

AH P G

,

ALP G

,

are the heat-transfer areas of the HP generator, LP generator , evaporator ,

absorber and condenser respectively,

U HPG

,

U LP G

,

U E ,U A

and

UC

are the overall heat-

transfer coefficients of the HP generator, LP generator, evaporator, absorber and condenser respectively. The total area of heat transfer between the cycle system and the external heat reservoirs is given by the relationships: A  AH P G  ALP G  AE  A A  AC

(8)

the second law is written as: .

.

.

.

.

.

Q H P G T1  Q LP G T LP G  Q E T 4  Q A IT 3  Q LP G IT 2  Q C IT 5  0 .

where I 

.

.

Q A T 3  Q C T5  Q LP G T 2 .

(9)

.

.

 1 is the internal irreversibility parameter.

Q H P G T1  Q LP G T LP G  Q E T 4

Defining the parameter a as the distribution rate of the total heat reject quantity between the condenser and the absorber given as:

9 Page 9 of 52

.

.

a  Q A / QC

(10)

and the parameter b as the ratio of the total heat between the HP generator and the LP generator given as: b

Q HPG

(11)

Q LPG

Using Eqs. (1)-(11), we obtain the coefficient of performance, the specific cooling load and the specific rate of entropy production of a parallel flow double-effect absorption refrigerator given by the following equations: .

COP 

.

Q E Q L .

Q HPG

. .  QE  QL  1 . .  Q HPG  Q E

.   QE .  bQ LPG 

.  Q  1 L .  QE 

   

(12)

where .

b  1  a T1   1  a   T LP G 1

QE



.

a  IT 3 

Q LP G .

QL .

QE



1

1

  1  a  IT 2 

  IT 5 

1

1

 a  IT 3 

  1  a T 4

1

  IT 5 

1

(13-a)

1

.

.

1  bQ LP G Q LP G    T A  T E  TC  T E  T LP G  T E     . . U T  T 4  E E Q E U H P G  T H P G  T1  Q E U LP G  T 2  T LP G 

. .      Q Q LPG  LPG     a 1 . 1 .      QE  QE        U A  T3  T A  1 a  U C  T5  TC  1 a     

and   K L .

R

.

Q E Q L A

A

(13-b)

is the heat leakage coefficient. .

.

1  bQ LP G Q LP G    . .  U E  T E  T4  Q U Q E U LP G  T 2  T LP G H P G  T H P G  T1  E



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. .      Q Q L P G    1 L P G  a  1 . .      QE  QE           T A  T E  TC  T E  T L P G  T E U A  T3  T A  1 a  U C  T5  TC  1 a     



(14)

and . . . . .  . 1  Q A  K L  T A  T E  Q C  K L  TC  T E  Q L P G  K L  T L P G  T E  Q H P G Q L P G Q E  K L  T A  T E  TC  T E  T L P G  T E S      TA TC TLPG TH PG TLPG TE A 

. .       Q Q  LPG  LPG     a 1 . 1 . .       QE  QE  bQ L P G 1        .    U T  T4  U A  T3  T A  1 a  U C  T5  TC  1 a    E  E Q E U H P G  T H P G  T1        

   T A  T E  TC  T E  T LP G  T E

 Q  . E   Q LP G .

   

1



 .  Q E  .    Q LP G 

1

  TC  1  aT A  1   b THPG    1 a 



1

  TC  1  aT A  1 1   TE   1 a   

 T  1  aT A  1 1    T A  T E  TC  T E  T LP G  T E   C  b THPG     1 a  

 T  1  aT A  1 1     T A  TE  C  T A     TC  T E   1 a  

 TC  1  aT A  1

 

1 a



 TC

1

     T LP G  T E 

 TC  1  aT A  1

  

1 a

 T LP G

1

  

(15) According to the definition of the general thermo-ecological criterion function (Ust and Sahin, 2007; Ust, 2009; Ngouateu Wouagfack and Tchinda, 2011a,b, 2013a,b; Ngouateu Wouagfack, 2012 and Medjo Nouadje et al., 2013, 2014) the new thermo-ecological objective function called ecological coefficient of performance (ECOP) of a parallel flow double-effect absorption refrigerator system is written as:

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

  

  . Q Q L 1   Q E ECOP  E   . . T env    T env   Q LP G  .

.

   

1

 1 1  TC  1  aT A  1  aT A  1  TC 1   b THPG    TE   1 a 1 a    

. .       Q LPG  Q LPG      a 1 . 1 . . .       QE  QE  b Q LPG Q LPG 1        .  .    U T  T4  U A  T3  T A  1 a  U C  T5  TC  1 a    E  E Q E U H P G  T H P G  T1  Q E U L P G  T 2  T L P G       



   T A  T E  TC  T E  T LP G  T E

  Q   E  Q  LP G

   

1  

 TC  1  aT A  1  TC  1  aT A  1 1  1   T  T  T   T  T  TC    C A E    A E  1 a 1 a      

1

 T  1  aT  1  T A  T E  TC  T E  T LP G  T E   C 1 a A  b  T H P G 



1

   TC  1  aT A  1 1      T  T  T     LP G E  LP G 1 a     

1

(16) For the sake of convenience, let





b1  b2  b3  b5   1  a   T L P G b  b 3  b5  b 4 

 b  b  b  b  1 a   T 2

3

,

b3  a  IT 3 

1

,

1

b 3  b5  b 4

1

1

and b5   IT5  . Then Eq. (12) may be written as:

b4   1  a  T 4  1

COP 

b2   1  a  IT 2 

b1   1 a  bT1 1 ,

5

LP G



b1  b2  b4   1  a   T LP G  b1  b2  b3  b5   1  a   T LP G 

1

1

1







1

   1    T A  T E  T C  T E  T L P G  T E   

  b   1 a  b U  HPG  THPG  b1  



  1    U  T  1 a   E E b4     

1

  1 a  T  U LP G   Ib2  LP G  

     a 1     1 a   U A  a  T A  U C  1  TC     Ib3   Ib5    

     

(17)

12 Page 12 of 52

We obtain the following optimal temperature of the working fluid in the HP generator ( T1 m ), LP generator ( T 2 m ), evaporator ( T 4 m ), absorber ( T3 m ) and condenser ( T 5 m ) that maximize the COP: T1m  T H P G 1 x  1 B  

(18)

T 2 m  T LP G 1 y  1 B  

(19)

T 3 m  T A 1 z  1 B  

(20)

T 4 m  T E 1 w  1 B  

(21)

T 5 m  TC B

(22)

where x  U C IU H P G 

1 2

1 2

, z  U C U A 

1 2

, w  U C IU E 

1 2

1

 T A  T E  TC  T E  T LP G  T E   w 1 a 1 w T E  1  1 2 1 2 1 1 Iw TC  1  a T E  z aTC T A   1  a TC U C   T A  T E  TC  T E  T LP G  T E   1

az  1  z  I T A   1  a U C I 1

B

, y  U C U LP G 

1

1 1



B1

B1  1  a  aI  1  w  z  T E  1T A  1  I  1T E 1T C 1 1  a  w  1   a 1  z  T C  1T A  1 2



U C  1  a  I  1  1  T A  T E  TC  T E  T L P G  T E

2



1

  aI

1

1

TA  I

2

T C   1  a T E

1

1

1



(23)

Substituting Eqs. (18)-(22) into Eqs. (12) and (14)-(16) give the maximum coefficient of performance ( C O Pm ax ), the corresponding ecological coefficient of performance ( E C O Pm ), the specific cooling load ( R m ) and the specific entropy generation rate ( S m ). 4. Results and discussion Numerical calculations are carried out by employing the relevant values U HPG=173500 W m-2 K-1, ULPG=171900 W m-2 K-1, UE=449000 W m-2 K-1, UA=379700 W m-2 K-1, UC=278200 W m-2 K-1 taken from refs. (Chua et al., 2000) and THPG=443 K, TLPG=363 K TC=303 K, TA=305 K, Tenv=300 K, TE=285 K. Maple software is used to carry out derivation

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and to solve polynomial equation. MATLAB software is used for numerical calculations and to plot the curves. 4.1 Optimization based on the coefficient of performance Fig.4 presents the variation of the coefficient of performance with respect to the specific cooling load for different values of internal irreversibility. We obtained a similar curve that obtained in the case of the single effect by Chen and Yan (1989). It can also be observed that when the internal irreversibility increases, both the maximum coefficient of performance and the maximum specific cooling load decrease. Fig. 5 presents the effect of the heat leakage coefficient on the maximum coefficient of performance for different values of the internal irreversibility parameter. We can observe that the COPmax decreases with an increase in the heat leakage coefficient. It can also be seen that when ξ = 0, that is there is no loss due to heat leakage and when I = 1, the system is endoreversible and COPmax ≈ 1.32. This value is closer to 1.28 obtained by Chua et al. (2000). Fig. 6 presents the effect of the parameter a on the maximum coefficient of performance for different values of the internal irreversibility parameter. We observe that the COPmax decreases slightly with an increase in the parameter a, and tends to an asymptotic value when the parameter a is large. We can conclude that the effect of the parameter a on the maximum coefficient of performance could then be neglected. Fig. 7 presents the effect of the parameter b on the maximum coefficient of performance for different value of the internal irreversibility parameter. We observe that the COPmax decreases when the parameter b increases. So, when b 1 the maximum of the COP is very high and this result does not reflect the reality. And when b 1 , the maximum of the COP tends to reasonable value.

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Figs. 8 and 9 present the effect of the internal irreversibility on the specific entropy generation rate and the specific cooling load at the maximum coefficient of performance respectively. As expected, the specific entropy generation rate increases with the increase in the internal irreversibility while the specific cooling decreases. 4.2 Optimization based on the ecological coefficient of performance The variations of the normalized ecop (ecop = ECOP/ECOPm) and cop (cop = COP/COPmax) with respect to the normalized specific entropy generation rate and the normalized specific cooling load have been plotted in Figs. 10 and 11 respectively. From these figures, we can observe that unlike the maximum ECOP and COP for mechanical compression refrigeration systems (Ust and Sahin, 2007; Ust, 2009) and single effect absorption refrigeration systems (Ngouateu Wouagfack and Tchinda, 2011a, 2013b) the maxima ecop and cop for the parallel flow double-effect absorption refrigeration systems do not occur for the same value of normalized specific entropy generation rate and normalized specific cooling load. Another result from the interpretation of these figures is that there also exists a specific T1, T2, T3, T4 and T5 that maximize the ECOP function of parallel flow double-effect absorption refrigerators for given I and ξ values. Therefore Eq. (16) can be maximized with respect to T1, T2, T3, T4 and T5. This optimization was done numerically. The variations of the ecological coefficient of performance function for the parallel flow double-effect absorption refrigerator with respect to the specific cooling load for different values of a, b, ξ and I is given in Fig. 12. This figure reveals the optimal operating region of an irreversible parallel flow double-effect absorption refrigerator system. Like in the case of the single-effect absorption refrigerator, the ECOP-R characteristic curve is loopshape passing through the origin and divided into three parts. In positive slope part, the 15 Page 15 of 52

ecological coefficient of performance increases with the increase of the specific cooling load. In the negative slope part, the ecological coefficient of performance increases with a decrease in the cooling load. This is normal since the main goal of the ecological optimization consists of maximizing the ecological coefficient of performance in order to produce a certain amount of cooling load for a lower entropy generation (Ngouateu Wouagfack and Tchinda, 2011b). The variations of the ecological coefficient of performance function for the parallel flow double-effect absorption refrigerator with respect to the specific entropy generation rate for different values of a, b, ξ and I is given in Fig. 13. It can be observed in this figure that the ecological coefficient of performance increases with low value of the specific entropy generation rate and when reached it optimal value it decreases with an increase in the specific entropy generation rate. The variations of the ecological coefficient of performance function for the parallel flow double-effect absorption refrigerator with respect to the coefficient of performance have been plotted in Fig.14 for different values of a, b, ξ and I. There, we observed that the ecological coefficient of performance increases with an increase in the coefficient of performance. In Fig.12A, Fig.13A and Fig.14A, the ECOP decreases slightly with an increase in a. Hence, we can see that when the parameter a tends toward infinity, its effect on the performance of the system is negligible. We also observed that the specific cooling load (fig. 12A) and the coefficient of performance (fig. 14A) decrease slightly with an increase in a. These relevant optimization parameters do not increase any longer when the parameter a takes a high value. We can say that as much as the heat release at the absorber is higher than the heat release at the condenser, the performance of the system is not influenced.

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In Figs. 12B, 13B and 14B, when the parameter b increases the maximum of the ecological coefficient of performance decreases. This result is also observed in the case of the specific cooling load (Fig. 12B) and the coefficient of performance (Fig. 14B) which decrease with an increase in parameter b. We notice that the value of the parameter b should be near 1.23 in order to have a higher value of the system performance. For instance, when b=1.4 in fig. 14B, the maximum of the coefficient of performance is less than 0.5 compared to the value of 1.2 given in literature. In Figs.12C, 13C, 14C, 12D, 13D and 14D, the ECOP objective function decreases when both heat leakage and internal irreversibility increase. Similar observations have been made in the case of single effect absorption refrigerators (Ngouateu Wouagfack and Tchinda, 2011a,b, 2013b). The higher value of the ECOP is obtained in the endoreversible case (Figs.12D, 13D and 14D). We also observe that as the heat-leak coefficient and the internal irreversibility parameter increase the specific cooling load (figs. 12C and 12D) and the coefficient of performance (figs. 14C and 14D) decreases. 5. Conclusion The finite-time performance optimization for a parallel flow double-effect irreversible absorption refrigerator system with the losses of heat resistance, heat leakage, and internal irreversibility by considering the coefficient of performance (COP) and the ecological coefficient of performance (ECOP) as objective functions has been investigated in this paper. The five optimal temperatures of the working fluids in the main components of the system that maximize the COP function and the corresponding ecological coefficient of performance, specific cooling load and specific entropy production rate are investigated. Then, it has been shown that the maxima COP and ECOP do not occur for the same operating conditions. The effects of internal irreversibility, heat leakage, distribution rate of the total heat reject quantity between the condenser and the absorber and ratio of the total heat between the HP generator 17 Page 17 of 52

and the LP generator on the general and optimal COP and ECOP have been investigated and discussed.

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Acknowledgments The present research work was carried out in LISIE and LESEE. All the senior researchers of these laboratories are gratefully acknowledged for their helpful comments. We also thank the administrators of these laboratories for the opportunity.

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efficiency at maximum power formula for heat engines. J. Non-Equilibrium Thermodynamics39(4): 199-204. Vasilescu, C., Hera, D., Infante Ferreira, C., 2011. Model for double-effect absorption refrigeration cycle. Termotehnica 2. Wijeysundera, N.E., 1996. Performance limits of absorption cycles with external heatirreversibilities. Appl. Therm. Eng., vol 16, No 2, pp 175-181. Wu, C., Chen, L., Sun, F., 1997. Optimization of solar absorption refrigerator. Appl. Therm. Eng., 17(2), 203-208. Wu, C., Chen, L., Chen, J. (eds.)., 1999. Recent Advances in Finite Time Thermodynamics. New York: Nova Science Publishers. Xu, G. P., Dait, Y. Q., 1997. Theoretical analysis and optimization of a double-effect parallelflow-type absorption chiller. Appl. Therm. Eng., Vol. 17, No. 2. pp. 157-1 70. Zheng, T., Chen, L., Sun, F., Wu, C., 2003a. Performance optimization of an irreversible four-heat–reservoir absorption refrigerator. Appl. Energy, 391-414. Zheng, T., Chen, L., Sun, F., Wu, C., 2003b. Performance of a four-heat-reservoir absorption refrigerator with heat resistance and heat leak. Int. J. Ambient Energy, 24(3), 157-168 Zheng, T., Chen, L., Sun, F., Wu, C., 2004. The influence of heat resistance and heat leak on the performance of a four-heat-reservoir absorption refrigerator with heat transfer law of Q   (T

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Figure 1: parallel flow double-effect absorption refrigerator (Farshi et al., 2012).

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Figure 2: Schematic diagram of a parallel flow double-effect absorption refrigerator

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Figure 3: Schematic diagram of an irreversible parallel flow double-effect absorption refrigerator

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Figure 4: Variations of COP function with respect to the specific cooling load for different values of I (a=2.5, b=1.23, =0.7).

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Figure 5: Effect of the heat leakage coefficient on COPmax for different values of I (a=2.5, b=1.23).

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Figure 6: Effect of the parameter a on COPmax for different values of I ( =0.7, b=1.23).

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Figure 7: Effect of the parameter b on COPmax for different values of I ( =0.7, a=2.5).

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Figure 8: Variations of Sm with respect to the internal irreversibility I (b=1.23, a=2.5, =0.7).

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Figure 9: Variations of Rm with respect to the internal irreversibility I (b=1.23, a=2.5, =0.7).

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Figure 10: Variations of the normalized ECOP and COP with respect to the normalized specific entropy generation rate (I=1.01, b=1.23, =0.7)

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Figure 11: Variations of the normalized ECOP and COP with respect to the normalized specific cooling load (I=1.01, b=1.23, =0.7)

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Figure 12: Variations of ECOP function with respect to the specific cooling load for different values of (A) a (I=1.01, b=1.23, =0.7), (B) b (I=1.01, a=2.5, =0.7), (C) (I=1.01, a=2.5, b=1.23) and (D) I (b=1.23, a=2.5, =0.7).

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Figure 13: Variations of ECOP function with respect to the specific entropy generation rate for different values of A) a (I=1.01, b=1.23, =0.7), (B) b (I=1.01, a=2.5, =0.7), (C) (I=1.01, a=2.5, b=1.23) and (D) I (b=1.23, a=2.5, =0.7).

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Figure 14: Variations of ECOP function with respect to the coefficient of performance for different values of A) a (I=1.01, b=1.23, =0.7), (B) b (I=1.01, a=2.5, =0.7), (C) (I=1.01, a=2.5, b=1.23) and (D) I (b=1.23, a=2.5, =0.7).

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