thermoeconomic optimization of subcooled and superheated

ARTICLE IN PRESS

0360-5442/$ - se

doi:10.1016/j.en

�CorrespondE-mail addr

Energy 31 (2006) 2108–2128

www.elsevier.com/locate/energy

Thermoeconomic optimization of subcooled and superheatedvapor compression refrigeration cycle

Res-at Selbas-, Onder Kızılkan�, Arzu S-encan

Technical Education Faculty, Department of Mechanical Education, Suleyman Demirel University, Isparta 32260, Turkey

Received 20 July 2004

Abstract

An exergy-based thermoeconomic optimization application is applied to a subcooled and superheated vapor

compression refrigeration system. The advantage of using the exergy method of thermoeconomic optimization is that

various elements of the system—i.e., condenser, evaporator, subcooling and superheating heat exchangers—can be

optimized on their own. The application consists of determining the optimum heat exchanger areas with the corresponding

optimum subcooling and superheating temperatures. A cost function is specified for the optimum conditions. All

calculations are made for three refrigerants: R22, R134a, and R407c. Thermodynamic properties of refrigerants are

formulated using the Artificial Neural Network methodology.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Thermoeconomic optimization; Subcooling; Superheating; Heat exchangers; Refrigeration

1. Introduction

Refrigeration systems transfer heat from a low-temperature medium to a high-temperature medium.Refrigeration systems are cyclic processes that employ refrigerants to absorb heat from one place and move itto another. Mainly, a refrigeration system consists of a condenser, an evaporator, a compressor, and anexpansion valve. In a refrigeration system, the refrigerant vapor leaves the evaporator and enters thecompressor as a saturated vapor at the vaporizing temperature and pressure and the liquid leaves thecondenser and enters the expansion valve as a saturated liquid at the condensing temperature and pressure [1].

The design of a vapor compression refrigeration system is often done by a conventional method, based onexperimental work and experience. Therefore, most refrigeration systems operate over capacity, which meansa loss of money both for the producer and the customer. To prevent this, a thermoeconomic optimizationapproach was developed as an advanced tool for such energy systems. This approach combinesthermodynamic analysis by the first and second laws with principles of economics [2].

Several studies of exergy-based thermoeconomic optimization are available. For example, Wall [3] andD’Accadia and Rossi [4] used the exergetic-costing method for thermoeconomic optimization. Usta and Ileri [5]

e front matter r 2005 Elsevier Ltd. All rights reserved.

ergy.2005.10.015

ing author. Tel.: +90 246 2111428; fax: +90 246 2371283.

ess: [email protected] (O. Kızılkan).

www.elsevier.com/locate/energy

ARTICLE IN PRESS

Nomenclature

A area (m2)aC capital recovery factorbC the part of the annual cost which is not affected by the optimizationCe

IN unit cost of input exergyCC

l capital cost of the lth element of the systemCI

k,I local unit cost of irreversibilitycp specific heat capacity (J/kgK)E exergy (kW)g gravitational acceleration (m/s2)h specific enthalpy (kj/kg)I rate of irreversibility (W)In normalized input valueK overall heat transfer coefficient (kW/m2K)LMTD logarithmic mean temperature difference (1C)_m mass flow rate (kg/s)NET sum of net collected dataQ heat transfer rate (kJ)Sgen rate of entropy generation (kW/K)s specific entropy (kj/kgK)T temperature (1C)tOP period of operation per yearW work (kJ)Wn weightsV bulk velocity of the stream (m/s)xn inputsy outputZ altitude of the stream from sea level (m)

Greek letters

sk,i coefficient of structural bondszk,I capital cost coefficiente specific exergy (kJ/kg)S summation functionF(S) activation function

Subscripts

C condenserCI condenser first regionCII condenser second regionCOM compressorE evaporatorEV expansion valveIN inletOUT exitR refrigerantSH superheatingSC subcooling

R. Selbas- et al. / Energy 31 (2006) 2108–2128 2109

ARTICLE IN PRESS

T total0 environmental conditions1, 2, reference conditions

R. Selbas- et al. / Energy 31 (2006) 2108–21282110

have determined the economic optimum values of the design parameters of refrigeration systems withoutsubcooled and superheated effects. Evaporator and condenser temperature, water inlet and outlet temperatureof the cooling tower, interstage pressure and insulation thickness were chosen as the optimization variables. Theeffects of yearly operating hours, real interest rate, cooling capacity, outside design dry and wet bulbtemperatures, system life and price of electricity on the optimization variables were examined. Dingec- and Ileri[2] have carried out the optimization of a domestic R-12 refrigerator without subcooled and superheated effects.The structural coefficient method was used in this optimization procedure. Their objective was to minimizethe total life cycle cost, which includes both the electricity and capital costs, for a given cooling demand andsystem life.

In literature, available studies on thermoeconomic optimization of subcooling and superheating effects ofvapor compression refrigeration cycles are very limited. In this paper, thermoeconomic optimization wasapplied to subcooled and superheated vapor compression refrigeration system as different from literature. Thestructural coefficient method was used in this optimization procedure. Optimum heat exchanger areas andoptimum subcooling and superheating temperatures under various operating conditions of system wereobtained. In addition, the variation of cost function and irreversibility according to condenser, evaporator,subcooling and superheating temperatures was investigated. All calculations were made for alternativerefrigerants R-22, R-134a and R407c, which do not damage to ozone layer. In order to calculatethermodynamic properties of refrigerants, the new formulations were derived with Artificial Neural Networks(ANNs) because algorithms available in the literature are very complex. All analyses are performed usingMATLAB computer program.

2. Artificial neural networks

Although the concept of ANN analysis has been discovered nearly 50 years ago, it is only in the last twodecades that application software has been developed to handle practical problems. ANNs are good for sometasks while lacking in some others. Specifically, they are good for tasks involving incomplete data sets, fuzzy orincomplete information, and for highly complex and ill-defined problems, where humans usually decide on anintuitional basis.

ANNs differ from the traditional modeling approaches in that they are trained to learn solutions ratherthan being programmed to model a specific problem in the normal way. They are usually used to addressproblems that are intractable or cumbersome to solve with traditional methods. They can learn fromexamples, are fault tolerant in the sense that they are able to handle noisy and incomplete data, are able to dealwith non-linear problems, and once trained can perform predictions at very high speed. ANNs have been usedin many engineering applications such as in control systems, in classification, and in modeling complex processtransformations [6].

The advantages of ANN compared to classical methods are speed, simplicity and capacity to learn fromexamples. In the last decade, a number of papers have been published dealing with the use of ANN in energysystems [7–9]. This technique can be used in the modeling of complex physical phenomena. So, engineeringeffort can be reduced.

ANNs consist of a large number of computational units connected in a massively parallel structure andwork as a human brain [10]. Because of their simple and unlimited structure, they have a wide range ofapplications in artificial intelligence area. They have numerous advantages such as eliminating, estimating andlearning [11]. ANN is an alternative method that is used in solution of complex non-linear problems. Asshown in Fig. 1, an ANN basically consists of three layers: input layer, one or more hidden layers and outputlayer [10].

ARTICLE IN PRESS

Input Layer Hidden Layers Output Layer

Bias Bias

Fig. 1. Basic ANN architecture.

x1

x2

xn

W1

W2

Wn

yΣ F(Σ)

Fig. 2. Artificial neural unit [12].


An artificial neural unit is shown in Fig. 2. Each artificial neural unit consists of inputs (xn), weights (Wn),summation function (S), activation function (F(S)) and output (y).

Input layer feeds data to the network; therefore, it is not a computing layer since it has no weights andactivation function. Output layer represents the output response to a given input. Here, X is input vectorwhich can be expressed as XT ¼ ½X 1;X 2; . . . ;X n�. A vector which includes weights can be presented asWT ¼ ½W 1;W 2; . . . ;W n�. The node receives weighted activation of other nodes through its incomingconnections. First, these are added (summation function). The result is then passed through an activationfunction, the outcome of which is the activation of the node. For each of the outgoing connections, thisactivation value is multiplied with the specific weight and transferred to the next node.

Each data that transferred to a unit is obtained from the product of the input and connected weight data.The sum of net collected data in the unit is

NET ¼Xn

i¼1

xiW i ¼ x1W 1 þ x2W 2 þ � � � þ xnW n þ b, (1)

where b is the bias term. Output data y, for a tan–sig activation function is

y ¼2

1þ e�2�NET� 1. (2)

3. Modeling of the thermodynamic properties using ANN

In order to carry out thermodynamic analyses of subcooling and superheating effects of refrigerants,thermodynamic property equations are needed. There are a number of thermodynamic property equations ofsome refrigerants in the literature. In this study, thermodynamic data used to train network were obtainedfrom Dupont [13].

Saturated liquid and saturated vapor properties of refrigerants used in vapor compression refrigerationsystems are formulated using ANN method. Furthermore, properties such as superheated vapor enthalpy andsuperheated vapor temperature are also formulated using ANN. For the training of the ANN,

ARTICLE IN PRESSR. Selbas- et al. / Energy 31 (2006) 2108–21282112

Levenberg–Marquardt feed forward back-propagation algorithm and sigmoid activation functions were used.In feed forward algorithm, the units are arranged as layers and the output data of a unit are transported to thenext layer as inputs over the weights. The input layer transports the data with no change to units of hiddenlayers. Data processing is performed in hidden and output layer forming the network output. With thisstructure feed forward networks carry out a non-linear static function. Feed forward ANNs are trained withback-propagation algorithm [14].

For the thermodynamic properties of refrigerants, data from Dupont [13] were used. The number of datapatterns available are given in Table 1.

For each refrigerant, 80% of data were used for training and 20% of data were used for testing the neuralnetwork. Tan–sig activation function was used and for this reason all data were normalized between �1 and 1.The input and output parameters of each neural network are given in Table 2.

Different network structures, sizes and learning parameters have been tried. The best network that wasultimately selected has one hidden layer and eight neurons. After training with the best network architecture,thermodynamic property equations were derived using weights and biases of network for each property. Theaverage percentage deviation between the ANN predicted and actual values is given in Table 3.

In order to determine thermodynamic properties of refrigerations, the following equations are used derivedfrom the ANN methodology:

En ¼ Inwn þ bn, (3)

Fn ¼2

ð1þ expð�2EnÞÞ� 1. (4)

In the above equations for En the first two values are the multiplication of the input parameters with theirweights at location n and the last constant value (bn) represents the bias term. In the case of eight neurons usedin this study, above equations are E1–E8 and F1–F8 and represent summation and activation functions of eachneuron of the hidden layer, respectively. The coefficients of Eqs. (3) and (5) were given by Kızılkan [11] and

Table 1

Number of data patterns available

Type of refrigerant properties Data patterns available

R22 R134a R407c

Saturated region properties 245 203 181

Superheated region properties 2728 2479 2477

Table 2

Input and output parameters

Neural network number Input parameters Output parameters

Neural network #1 Saturation temperature Saturation pressure

Neural network #2 Saturated liquid temperature Saturated liquid enthalpy

Saturated liquid pressure

Neural network #3 Saturated vapor temperature Saturated vapor enthalpy

Saturated vapor pressure

Neural network #4 Saturated vapor temperature Saturated vapor entropy

Saturated vapor pressure

Neural network #5 Superheated vapor pressure Superheated vapor enthalpy

Superheated vapor entropy

Neural network #6 Superheated vapor pressure Superheated vapor temperature

Superheated vapor enthalpy

ARTICLE IN PRESS

6

2

1

5

Evaporator

Condenser

CompressorExpansionValve

SuperheatingRegion

SubcoolingRegion

WC

Heatingfluid in

Heatingfluid out

Coolingfluid in

Coolingfluid out

7

34

Fig. 3. Subcooled and superheated refrigeration cycle.

Table 3

Average percentage deviation of ANN predicted values from real values

Output values Average % deviation

R22 R134a R407c

Saturation pressure 1.05658 1.649458 1.149994

Saturated liquid enthalpy 0.02935 0.017341 0.028242

Saturated vapor enthalpy 0.006785 0.006884 0.005745

Saturated vapor entropy 0.000451 0.000949 0.003902

Superheated vapor enthalpy 0.053451 0.066446 0.051517

Superheated vapor temperature 0.091252 0.07106 0.106338


S-encan et al. [6].Additionally, the actual input data of the various parameters need to be normalized in the range [�1 to 1].

For this purpose, the actual values of each parameter are divided with the coefficients given by Kızılkan [11]and S-encan et al. [6]. Finally, the output values of refrigerants depending on input values given in Table 2 canbe computed from

E9 ¼ F1W 1 þ F 2W 2 þ F 3W 3 þ F 4W 4 þ F 5W 5 þ F6W 6 þ F7W 7 þ F8W 8 þ b2, (5)

F9 ¼ 2=ð1þ expð�2E9ÞÞ � 1. (6)

4. Subcooled and superheated vapor compression refrigeration system

In the simple saturated refrigeration cycle, the refrigerant vapor is assumed to reach the inlet (suction) of thecompressor as a saturated vapor and refrigerant liquid is assumed to be a saturated liquid before the inlet ofthe expansion valve. If evaporator dimensions are enlarged a little, saturated vapor usually will continue toabsorb heat and thereby become superheated before it reaches the compressor. In practice, this is controlledby the expansion valve. In the same manner, if condenser dimensions are enlarged a little, saturated liquid willcontinue to remove heat and so become subcooled before the expansion valve inlet as shown in Fig. 3 [15–18].

4.1. Effects of superheating

In most cases, superheating and subcooling procedures are applied for improving the system efficiency. Ifthe simple refrigeration system is compared to subcooled and superheated refrigeration system, as shown inFig. 4, then the refrigerating effect per unit mass is greater by an amount equal to the amount of superheat [1].

ARTICLE IN PRESS

h

1

234

5

67

P P

h

1

234

5

Actual

Ideal

(a) (b)

Fig. 4. P� h diagrams of (a) typical refrigeration cycle, (b) subcooled and superheated refrigeration cycle.


Since the refrigerating effect per unit mass is greater for the superheated cycle than for the saturated cycle,the mass flow rate of refrigerant per unit capacity is less for the superheated cycle than for the saturated cycle.

Even though the specific volume of the suction vapor and the heat of compression per unit mass are bothgreater for the superheated cycle than for the saturated cycle, the volume of vapor compressed per unitcapacity and the power required per unit capacity are both lower for the superheated cycle than for thesaturated cycle. This is because of the reduction in the mass flow rate.

For the superheated cycle, both the refrigerating effect per unit mass of refrigerant and the heat ofcompression per unit mass of refrigerant are greater than for the saturated cycle. However, since the increasein the refrigerating effect is proportionally greater than the increase in the heat of compression, the COP forthe superheated cycle is higher than that of the saturated cycle.

The superheating of the suction vapor in an actual cycle usually occurs in such a way that part of the heattaken by the vapor in becoming superheated is absorbed from the refrigerated space and produces usefulcooling. The portion of the superheat that produces useful cooling will depend on the individual application,and the effect of the superheating on the cycle will vary approximately in proportion to the useful coolingaccomplished.

Regardless of the effect on capacity, except in some special cases, a certain amount of superheating isusually unavoidable and, in most cases desirable. When the suction vapor is drawn directly from theevaporator into the suction inlet of the compressor without at least a small amount of superheating, there is agood possibility that small particles of unvaporized liquid will be entrained in the vapor. Such a vapor is calleda wet vapor. Wet suction vapor drawn into the cylinder of the compressor adversely affects the capacity of thecompressor. Furthermore, since refrigeration compressors are designed as vapor pumps, if any appreciableamount of unvaporized liquid is allowed to enter the compressor from the suction line, serious mechanicaldamage to the compressor may result. Since superheating the suction vapor eliminates the possibility of wetsuction vapor reaching the compressor inlet, a certain amount of superheating is usually desirable. Again, theextent to which the suction vapor should be allowed to become superheated in any particular instance dependson where and how the superheating occurs and on the refrigerant used.

Superheating of the suction vapor may take place in any one or in any combination of the following places:

1.
at the end of the evaporator, 2. at the suction piping installed inside the refrigerated space (usually referred to as a drier loop), 3. at the suction piping located outside the refrigerated space, 4. at the liquid-suction heat exchanger.
4.2. Effects of subcooling

On the P2h diagram in Fig. 4, a simple saturated cycle is compared with one in which the liquid issubcooled. When the liquid is subcooled before it reaches the expansion valve, the refrigerating effect per unit

ARTICLE IN PRESSR. Selbas- et al. / Energy 31 (2006) 2108–2128 2115

mass is increased. Because of the greater refrigerating effect per unit mass, the mass flow rate of refrigerant perunit capacity is less for the subcooled cycle than for the saturated cycle.

It should be noted that the refrigerant vapor entering the suction inlet of the compressor is the same for bothcycles. For this reason, the specific volume of the vapor entering the compressor will be the same for both thesaturated and subcooled cycles and, since the mass flow rate per unit capacity is less for the subcooled cyclethan for the saturated cycle, it follows that the volume of vapor that the compressor must handle per unitcapacity will also be less for the subcooled cycle than for the saturated cycle.

Because the volume of vapor compressed per unit capacity is less for the subcooled cycle, thecompressor displacement required for the subcooled cycle is smaller than that required for the saturatedcycle.

It should also be noted that the heat of compression per unit mass is the same for both the saturated andsubcooled cycles. This means that the increase in refrigerating effect per unit mass resulting from thesubcooling is accomplished without increasing the energy input to the compressor. Any change in therefrigerating cycle that increases the quantity of heat absorbed in the refrigerated space without causing anincrease in the energy input to the compressor will increase the COP of the cycle and reduce the powerrequired per unit capacity.

Subcooling of the liquid refrigerant can and does occur in several places and in several ways. Very often theliquid refrigerant becomes subcooled while stored in the liquid receiver tank or while passing through theliquid line by giving off heat to the surrounding air. The gain in system capacity and efficiency resulting fromthe liquid subcooling is very often more than sufficient to offset the additional cost of the subcooler,particularly for low-temperature applications [1].

5. Exergy analysis

Exergy is that part of energy which can be transformed completely into other kinds of energy, especially intowork under thermodynamic conditions. The standard conditions of the earth atmosphere are considered asthe thermodynamic state of the environment [19].

Exergy is defined as maximum amount of work which can be produced by a system when it comes toequilibrium with a reference environment. Exergy analysis is a method that uses the conservation of mass andconservation of energy together with the second law of thermodynamics for the design and analysis of energysystems [20].

An exergy analysis usually aims to determine the maximum performance of the system and identify theequipment in which exergy destruction occurs. Exergy analysis of a complex system can be performed byanalyzing each component of the system separately. Identifying the equipment in which the main exergydestruction occurs, shows the direction for potential improvements [18].

The amount of work that can be extracted from heat is

EQ ¼ QT � T0

T

� �. (7)

Work is equal to exergy:

EW ¼W , (8)

where T is the temperature of the system and T0 is the temperature of the environment. Specific exergy can bedefined as [21]

e ¼ ðh� T0sÞ þ12

V 2 þ gZ � ðh0 � T0s0Þ. (9)

Ignoring kinetic and potential terms in Eq. (9):

e ¼ ðh� T0sÞ � ðh0 � T0s0Þ. (10)

ARTICLE IN PRESS

Table 4

Design parameters and assumptions

Cooling capacity (QE) 2 kW

Condenser temperature (TC) 35–60 1C

Evaporator temperature (TE) �10–12 1C

Subcooling temperature (DTSC) 1–12 1C

Superheating temperature (DTSH) 1–15 1C

Compressor efficiency (ZC) 0.78–0.92


For determining the irrversibilities of each component of vapor compression refrigeration system, the amountof entering and exiting exergies of each component must be estimated. Therefore [21]:

W ¼X

EQ þXin

me�Xout

me� I , (11)

where I is the total irreversibility, i.e., the loss of work.The design parameters of the vapor compression refrigeration system considered in the present analysis are

given in Table 4. The ranges were selected according to working range of the various parameters of vaporcompression cycles. Also, condenser cooling fluid entering temperature and evaporator heating fluid enteringtemperature are assumed to be 20 1C. Heat exchanger type is considered as pipe-in-pipe, counter-flow heatexchanger and pipe diameter is assumed to be 13.5mm [6,11].

After calculation of irreversibilities of each component of the refrigeration system, the total irreversibilitycan be written as

IT ¼X

I system components. (12)

If the calculated irreversibilities of each component are entered into Eq. (12), then

IT ¼ T0 mCðsC2 � sC1Þ þmCðsC3 � sC2Þ½ þmCðsC4 � sC3Þ þmEðsE2 � sE1ÞþmEðsE3 � sE2Þ�. (13)

By rearranging Eq. (13):

IT ¼ T0 mC sC4 � sC1ð Þ �mE sE3 � sE1ð Þ½ �. (14)

In Eq. (14), the term s2–s1 for liquids can be approximated as [22]

s2 � s1 ¼ cp lnT2

T1(15)

as the effect of the pressure is small compared to the temperature.

6. Thermoeconomic optimization

Thermoeconomy is a discipline which combines concept of exergy method with those belonging to economicanalysis. The purpose of thermoeconomic optimization is to achieve, within a given system structure, abalance between expenditure on capital costs and exergy costs which will give a minimum cost of the plantproduct. The advantage of using the exergy method of thermoeconomic optimization is that various elementsof the system can be optimized on their own; the effect of the interaction between the given element and thewhole system being taken into account by local unit costs of exergy flows or those of exergy loses.

There are basically two different methods which make use of exergy concept. The method developed byTribus and Evans uses local unitary cost of exergy entering or leaving and is called autonomous method. Theother method developed by Beyer, uses the unitary costs of exergy loses and is called structural method [23].The advantage of Beyer’s methods is that, all systems elements and parts can be optimized individually interms of economics and exergy loses. Thus the whole system can be optimized in their elements. But in theother method, the whole system can be optimized, not separately. In this article the Beyer’s method is used in


order to optimize the system components. Optimization procedure applied each element of the system to findoptimum system structure.

Beyer originally put the concept of structural coefficients forward. Structural coefficients are used in thestudy of system structure, optimization of plant components and product pricing in multi-product plants. Thecoefficient of structural bonds (CSB) is defined by [23]

sk;i ¼qIT

qxi

� ��qIk

qxi

� �, (16)

where Ik is the irreversibility rate of the kth component of the system under consideration and xi the parameterof the system which produces the changes.

The effect of a change in xi on the system would be to alter the rate of exergy input while leaving the outputconstant. This acceptation conforms with the usual practice of specifying a plant in terms of its output ratherthan its input. From the exergy balance of the system:

_EIN ¼ _EOUT þ _IT; _EOUT ¼ constant; (17)

D _EIN ¼ D _IT. (18)

As seen in Eq. (18), changes in the irreversibility of the system are equivalent to changes in the input.

6.1. Coefficient of structural bonds method for thermoeconomic optimization

The purpose of the optimization of a selected component is to determine the capital cost corresponding tothe minimum annual operating cost of the system for a given system output with minimum unit cost of theproduct.

The exergy balance of the system can be written as [23]

_ITðxiÞ ¼ _EINðxiÞ � _EOUT. (19)

As can be seen from Eq. (19) both _EINEIN and _IT are functions of parameter xi. For the optimization, theobjective function is taken as the annual cost of system operation, given by

CTðxiÞ ¼ tOPCeINEINðxiÞ þ aC

Xn

l¼1

CCl ðxiÞ þ bC. (20)

When the exergy balance equation and objective function are differentiated with respect to xi:

qEIN

qxi

¼qIT

qxi

(21)

and

qCT

qxi

¼ tOPCeIN

qEIN

qxi

þ aCXn

l¼1

qCC1

qxi

. (22)

Rearranging Eqs. (21) and (22):

qCT

qxi

¼ tOPCeIN

qIT

qxi

þ aCXn

l¼1

qCCl

qxi

. (23)

The second term on the right-hand side of Eq. (23) may be rearranged conveniently as

aCXn

m¼1

qCC1

qxi

¼ aCXn

m¼1

qCCm

qxi

þ aC qCCk

qxi

, (24)

where mak, i.e., m subscript denotes any element of the system except the element that was applied tooptimization. It is also convenient to make the following rearrangement for the first term on the right-hand


side of Eq. (24):

Xn

m¼1

qCCm

qxi

¼qIk

qxi

Xn

m¼1

qCCm

qIk

. (25)

The term on the right-hand side of Eq. (25) is called the capital cost coefficient and can be denoted as

zk;i ¼Xn

m¼1

qCCm

qIk

. (26)

When Eqs. (24)–(26) are put into Eq. (23):

qCT

qxi

¼ topCeIN

qIT

qxi

þ aC qIk

qxi

zk;i þ aC qCCk

qxi

. (27)

Then, from Eq. (16):

qIT

qxi

¼ sk;iqIk

qxi

. (28)

Putting Eq (28) into Eq. (27):

qCT

qxi

¼ topCeINsk;i

qIk

qxi

þ aC qIk

qxi

zk;i þ aC qCCk

qxi

. (29)

Rearranging Eq. (29) will result in the following form:

qCT

qxi

¼ top CeINsk;i þ

aC

topzk;i

� �qIk

qxi

þ aC qCCk

qxi

. (30)

From which the following equation is obtained:

qCT

qxi

¼ topCIk;i

qIk

qxi

þ aC qCCk

qxi

, (31)

where the CIk;i term is defined as

CIk;i ¼ Ce

INsk;i þaC

topzk;i. (32)

The term CIk,i is local unit cost of irreversibility.

For the thermoeconomic optimization, Eq. (31) is set equal to zero. Thus

qIk

qxi

� �opt

¼ �aC

topCIk;i

qCCk

qxi

. (33)

This equation is the general optimization equation.

6.2. Thermoeconomic optimization of subcooled and superheated vapor compression refrigeration cycle

To obtain the general optimization equations of the refrigeration system components, the structural methodwill be applied to each component. Components to be optimized are condenser, evaporator, subcooling andsuperheating heat exchangers. For the optimization procedure the equations developed in the previous sectionare used. For the optimization of the condenser first region, Eq. (33) can be written as

qICI

qACI

� �Opt

¼ �aC

topCICI

@CCCI

@ACI. (34)


The terms in Eq. (34) can be written asFrom Eq. (32):

CICI ¼ Ce

INsCI þaC

topzCI. (35)

From Eq. (16):

sCI ¼ðqIT=qACIÞ

ðqICI=qACIÞ(36)

and, from Eq. (26):

zCI ¼qCC

CII

qICIþ

qCCSC

qICIþ

qCCE

qICIþ

qCCSH

qICI. (37)

The terms at the right-hand side of Eq. (37) can be separately written as

qCCCII

qICI¼

qCCCII

qIT

� �qIT

qICI

� �¼

qCCCII

qACII

� �qITqACII

� � qITqACI

� �qICIqACI

� � ¼qCC

CII

qACII

� �qITqACII

� � sCI, (38)

qCCSC

qICI¼

qCCSC

qIT

� �qIT

qICI

� �¼

qCCSC

qASC

� �qITqASC

� � qITqACI

� �qICIqACI

� � ¼qCC

SC

qASC

� �qITqASC

� � sCI, (39)

qCCE

qICI¼

qCCE

qIT

� �qIT

qICI

� �¼

qCCE

qAE

� �qITqAE

� � qITqACI

� �qICIqACI

� � ¼qCC

E

qAE

� �qITqAE

� � sCI, (40)

qCCSH

qICI¼

qCCSH

qIT

� �qIT

qICI

� �¼

qCCSH

qASH

� �qITqASH

� � qITqACI

� �qICIqACI

� � ¼qCC

SH

qASH

� �qITqASH

� � sCI. (41)

Therefore, Eq. (37) becomes

zCI ¼qCC

CII

qACII

qITqACII

þ

qCCSC

qASC

qITqASC

þ

qCCE

qAE

qITqAE

þ

qCCSH

qASH

qITqASH

0@

1AsCI. (42)

When Eqs. (35)–(42) are put in Eq. (34), the optimization equation for the condenser first region can beobtained as

qICI

qACI

� �Opt

¼ �1

tOP

aCCe

INsSH þqCC

CIIqACIIqIT

qACII

þ

qCCSC

qASCqITqASC

þ

qCCE

qAEqITqAE

þ

qCCSH

qASHqITqASH

!sCI

qCCCI

qACI. (43)

By following a similar procedure, the following formulations of optimization equations for the other heatexchangers of the refrigeration system can be obtained:

For the condenser second region:

qICII

qACII

� �Opt

¼ �1

tOP

aCCe

INsCII þqCC

CIqACIqITqACI

þ

qCCSC

qASCqITqASC

þ

qCCE

qAEqITqAE

þ

qCCSH

qASHqITqASH

!sCII

qCCCII

qACII. (44)


For the subcooling heat exchanger:

qISC

qASC

� �Opt

¼ �1

tOP

aCCe

INsSC þqCC

CIqACIqITqACI

þ

qCCCII

qACIIqIT

qACII

þ

qCCE

qAEqITqAE

þ

qCCSH

qASHqITqASH

!sSC

qCCSC

qASC. (45)

For the evaporator:

qIE

qAE

� �Opt

¼ �1

tOP

aCCe

INsA þ

qCCCI

qACIqITqACI

þ

qCCCII

qACIIqIT

qACII

þ

qCCSC

qASCqITqASC

þ

qCCSH

qASHqITqASH

!sE

qCCE

qAE. (46)

For the superheating heat exchanger:

qISH

qASH

� �Opt

¼ �1

tOP

aCCe

INsSH þqCC

CIqACIqITqACI

þ

qCCCII

qACIIqIT

qACII

þ

qCCSC

qASCqITqASC

þ

qCCE

qAEqITqAE

!sSH

qCCSH

qASH. (47)

Finally, the capital recovery factor can be calculated from [23]

aC ¼iR 1þ iRð Þ

N

1þ iRð ÞN� 1

, (48)

where N is the period of repayment and iR is the interest rate.

7. Results and discussion

Thermoeconomic optimization procedure was applied to subcooled and superheated vapor compressionrefrigeration system.

For the optimization, overall heat transfer coefficients of each heat exchanger for three refrigerants werecalculated given in Table 5 [11,24–26].

The condenser and evaporator prices are obtained from 2004 Unit Costs of Turkish Ministry of PublicWorks and exchanger costs were formulated as functions of exchanger areas.

CCCIð$Þ ¼ CC

CIIð$Þ ¼ CCSCð$Þ ¼ 516:621AC þ 268:45, (49)

CCEð$Þ ¼ CC

AKð$Þ ¼ 309:143AE þ 231:915. (50)

These equations and assumptions were put in the general optimization equation, and thermoeconomicoptimization procedure performed for the refrigeration system. Optimization procedure was carried out fordifferent system parameters with MATLAB computer program. For three different refrigerants, optimumsubcooling and superheating temperatures were determined with the optimum heat exchanger areas. In theanalysis, firstly, condenser temperature was kept constant and other parameters were varied, secondly,evaporator temperature was kept constant.

As seen from the tables, for example, in Table 6 analysis made for R22, when condenser and evaporatortemperatures were taken 35 and 11 1C, respectively, optimum condenser area was found to be 0.235m2,

Table 5

Mean Average overall heat transfer coefficients (kW/m2K)

KCI KCII KSC KE KSH

R22 0.1123 0.9121 0.2236 0.6749 0.2486

R134a 0.1425 0.9642 0.2321 0.6749 0.3146

R407c 0.1668 0.9938 0.2507 0.6749 0.3787

ARTICLE IN PRESS

Fig. 5. Optimum thermoeconomic area.

Table 6

Thermoeconomic optimization results for various condenser temperatures (R22)

TC ¼ 35 1C TC ¼ 45 1C TC ¼ 55 1C

TE (1C) 7 9 11 7 9 11 7 9 11

DTSC (1C) 5.4 5.2 4.2 4.8 5 5.6 6.65 5.4 5.8

DTSH (1C) 9.64 7.651 5.633 9.651 7.639 5.594 9.648 7.628 5.561

AC (m2) 0.245 0.239 0.235 0.169 0.164 0.159 0.142 0.14 0.136

ASC (m2) 0.038 0.036 0.027 0.018 0.019 0.021 0.021 0.017 0.018

AE (m2) 0.263 0.321 0.411 0.263 0.321 0.411 0.263 0.321 0.411

ASH (m2) 0.056 0.066 0.048 0.074 0.0578 0.041 0.073 0.057 0.041


subcooling heat exchanger area was found to be 0.027m2, evaporator area was found to be 0.411m2 andsuperheating heat exchanger area was found to be 0.048m2. Optimum subcooling and superheatingtemperatures were found to be 4.2 and 5.63 1C, respectively.

In thermoeconomic optimization part of the work, optimization equations of each heat exchanger oftheoretical refrigeration system were derived subject to Kotas’ [23] optimization procedure. Analyses werecarried out for different condenser, evaporator, subcooling and superheating temperatures iteratively.Optimum heat exchanger areas with corresponding subcooling–superheating temperatures were determinedand given in tables. As an example, for R22, condenser and evaporator temperatures of the system were takenat 45 and 11 1C, respectively, and analysis was carried out iteratively. As a result, optimum subcooling andsuperheating temperatures were found to be 4.2 and 5.6335 1C, respectively. This means, a refrigeration systemwith the determined optimum values, will have optimum investment and operation costs (Table 12). At thesame time, optimum COP and irreversibility were found to be 4.7503 and 0.38796 kW, respectively.

As seen in Table 12, optimum heat exchanger area was found to be 0.634726m2 at the end of thethermoeconomic analysis carried out for R22 with condenser temperature of 45 1C and evaporatortemperature of 11 1C. Fig. 5 shows the result of the iteration made for determining optimum values in casestudy. The intersection of two lines is optimum point and corresponding area is the optimum area subject toconstrains.

Thermoeconomic optimization results were compared with manufacturers’ values and it was seen thatresults were parallel with them. Refrigerator, deep freezer and climate system manufacturer producerSaginomiya, a Japan firm, prepares its expansion valves with superheating temperature of 1–7 1C adjustableand advises as to take 5–6 1C of superheating temperature [27]. An another firm, Danfoss, recommends that itis appropriate to take superheating temperature as 4–5 1C in its technical notes [28]. Hansen Technologiesfirm, produces expansion valves in which superheating temperature can be adjusted between 1 and 11 1C andfixes factory settings as 6 1C [29].


A refrigerant manufacturer Dupont firm takes subcooling temperature as 5.6 1C for R407c [13]. A climatesystems and heat pumps manufacturer Carrier firm takes subcooling temperature as 5 1C in its condensingunits [30]. A compressor manufacturer Bitzer firm, takes 5–8K of subcooling temperature and 10K ofsuperheating temperature in its compressors working with R22, R134a and R407c [31]. It can be seen thatoptimization results are parallel with manufacturers’ values.

Figs. 6–8 show the variation of heat exchanger costs and irreversibility rates with condenser temperature forR22, R134a and R407c, respectively. As can be seen from the figures, the heat exchanger cost decrease and theirreversibility rate increases by the increase of the condenser temperature. This is because, by increasing the

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

35 40 45 50 55 60320

330

340

350

360

370

380

390

400

Irreversibility

Heat exchanger cost

I, k

W

Hea

t exc

hang

er c

ost,

$

TC, °C

Fig. 6. The variation of heat exchanger costs and irreversibility rates with condenser temperature for R22.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

35 40 45 50 55 60340

350

360

370

380

390

400

410

Irreversibility

Heat exchanger cost

I, k

W

Hea

t exc

hang

er c

ost,

$

TC, °C

1

Fig. 7. The variation of heat exchanger costs and irreversibility rates with condenser temperature for R134a.

0

0.2

0.4

0.6

0.8

1

35 40 45 50 55 60

410

420

340

350

360

370

380

390

400

Irreversibility

Heat exchanger cost

I, k

W

Hea

t exc

hang

er c

ost,

$

TC, °C

1.2

Fig. 8. The variation of heat exchanger costs and irreversibility rates with condenser temperature for R407c.


condenser temperature, total heat exchanger area decreases and as a result, the heat exchanger cost decreases(Tables 6, 8 and 10). But at the same time the irreversibility rate increases.

Figs. 9–11 show the variation of heat exchanger costs and irreversibility rates with evaporator temperaturefor R22, R134a and R407c refrigerants, respectively. As can be seen from Tables 7, 9 and 11, total heatexchanger area increases by increase of the evaporator temperature. Therefore, it can be seen from figures thatthe heat exchanger area curve shows a little increase till –5 1C, and then the increase of the curve is moreinclined. The irreversibility rate decreases with the increase of the evaporator temperature (see Tables 7–12).

-15 -10 -5 0 5 100

100

200

300

400

500

600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Irreversibility

Heat exchanger cost

I, k

W

Hea

t exc

hang

er c

ost,

$

TE, °C

Fig. 10. The variation of heat exchanger costs and irreversibility rates with evaporator temperature for R134a.

-15 -10 -5 0 5 100

100

200

300

400

500

600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Irreversibility

Heat exchanger cost

I, k

W

Hea

t exc

hang

er c

ost,

$

TE, °C

Fig. 9. The variation of heat exchanger costs and irreversibility rates with evaporator temperature for R22.

-15 -10 -5 0 5 100

100

200

300

400

500

600

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Irreversibility

Heat exchanger cost

I, k

W

Hea

t exc

hang

er c

ost,

$

TE, °C

Fig. 11. The variation of heat exchanger costs and irreversibility rates with evaporator temperature for R407c.

ARTICLE IN PRESS

Table 7

Thermoeconomic optimization results for various evaporator temperatures (R22)

TE ¼ 8 1C TE ¼ 10 1C TE ¼ 12:5 1C

TC (1C) 35 45 55 35 45 55 35 45 55

DTSC (1C) 4 6.5 4.4 5.7 5 5 5.3 4.5 5

DTSH (1C) 8.653 8.647 8.641 6.647 6.624 6.605 4.084 3.98 3.91

AC (m2) 0.244 0.164 0.143 0.235 0.162 0.139 0.228 0.157 0.134

ASC (m2) 0.026 0.025 0.013 0.040 0.019 0.015 0.036 0.017 0.015

AE (m2) 0.289 0.289 0.289 0.360 0.360 0.360 0.523 0.523 0.523

ASH (m2) 0.075 0.065 0.066 0.057 0.049 0.049 0.034 0.029 0.028


Figs. 12–14 show the variation of heat exchanger costs and irreversibility rates with subcooling temperature
Table 8
Thermoeconomic optimization results for various condenser temperatures (R134a)

TC ¼ 35 1C TC ¼ 45 1C TC ¼ 55 1C

TE (1C) 8 10 12 8 10 12 8 10 12

DTSC (1C) 5.2 5 6.2 5 5 5.5 3.7 5 5.5

DTSH (1C) 8.654 6.652 4.641 8.653 6.646 4.608 8.651 6.640 4.583

AC (m2) 0.189 0.187 0.180 0.123 0.121 0.118 0.105 0.101 0.099

ASC (m2) 0.098 0.093 0.120 0.046 0.046 0.050 0.018 0.025 0.027

AE (m2) 0.289 0.360 0.479 0.289 0.360 0.479 0.289 0.360 0.479

ASH (m2) 0.088 0.053 0.023 0.079 0.047 0.020 0.085 0.050 0.021

for R22, R134a and R407c refrigerants, respectively. The heat exchanger cost increases and the irreversibility
Table 9
Thermoeconomic optimization results for various evaporator temperatures (R134a)

TE ¼ 11 1C TE ¼ 13 1C TE ¼ 14 1C

TC (1C) 35 45 55 35 45 55 35 45 55

DTSC (1C) 4.9 4 3.5 5 5.3 4.5 5 5 3.5

DTSH (1C) 5.649 5.634 5.622 3.610 3.542 3.495 2.526 2.387 2.297

AC (m2) 0.186 0.123 0.103 0.183 0.117 0.100 0.181 0.117 0.100

ASC (m2) 0.090 0.036 0.017 0.092 0.048 0.022 0.091 0.045 0.017

AE (m2) 0.411 0.411 0.411 0.575 0.575 0.575 0.722 0.722 0.722

ASH (m2) 0.037 0.033 0.035 0.011 0.009 0.010 0.001 0.001 0.001

Table 10

Thermoeconomic optimization results for various condenser temperatures (R407c)

TC ¼ 35 1C TC ¼ 45 1C TC ¼ 55 1C

TE (1C) 8 10 12 8 10 12 8 10 12

DTs (1C) 5.2 5 5 5.5 5 3.5 5 4.9 5.5

DTk (1C) 8.654 6.653 4.647 8.654 6.651 4.630 8.653 6.649 4.619

AK (m2) 0.211 0.206 0.200 0.142 0.139 0.136 0.121 0.118 0.113

AAS (m2) 0.051 0.048 0.047 0.025 0.022 0.015 0.012 0.012 0.013

AE (m2) 0.289 0.360 0.479 0.289 0.360 0.479 0.289 0.360 0.479

AAK (m2) 0.080 0.060 0.040 0.074 0.055 0.037 0.079 0.059 0.039

ARTICLE IN PRESS

Table 12

Determined optimum COP and irreversibility values of refrigeration system for the case study working with R22 with condenser

temperature of 45 1C

TC (1C) 45

TE (1C) 11

DTSC (1C) 4.2

DTSH (1C) 5.6335

AC (m2) 0.159483

ASC (m2) 0.021768

AE (m2) 0.41169

ASH (m2) 0.041785

COP 4.7503

IT (kW) 0.38796

Table 11

Thermoeconomic optimization results for various evaporator temperatures (R407c)

TE ¼ 9 1C TE ¼ 11 1C TE ¼ 13 1C

TC (1C) 35 45 55 35 45 55 35 45 55

DTSC (1C) 6.1 4 3.1 5 5.6 5 5.7 5.6 5.4

DTSH (1C) 7.654 7.653 7.652 5.652 5.646 5.641 3.631 3.591 3.565

AC (m2) 0.206 0.142 0.122 0.204 0.135 0.116 0.195 0.130 0.111ASC (m2) 0.063 0.017 0.007 0.047 0.025 0.012 0.056 0.024 0.013

AE (m2) 0.321 0.321 0.321 0.411 0.411 0.411 0.575 0.575 0.575

ASH (m2) 0.071 0.065 0.070 0.050 0.046 0.049 0.031 0.028 0.029

1 3 5 7 9 11 13 15395

400

405

410

415

420

I, k

W

Hea

t exc

hang

er c

ost,

$

0.302

0.3

0.298

0.296

0.294

0.292

0.29

0.288

0.286

Irreversibility

Heat exchanger cost

∆TSC, °C

Fig. 12. The variation of heat exchanger costs and irreversibility rates with subcooling temperature for R22.


rate decreases by increasing the subcooling temperature.Figs. 15–17 show the variation of heat exchanger costs and irreversibility rates with superheating

temperature, respectively, for R22, R134a and R407c refrigerants. It is shown that the heat exchanger costincreases and the irreversibility rate decreases by increasing the superheating temperature for R22, R134a andR07c refrigerants in figures.

ARTICLE IN PRESS

408

410

412

414

416

418

420

422

I, k

W

Hea

t exc

hang

er c

ost,

$

0.336

0.335

0.334

0.333

0.332

0.331

0.33

0.329

0.328

0.3271 3 5 7 9 11 13 15

Irreversibility

Heat exchanger cost

∆TSC, °C

Fig. 13. The variation of heat exchanger costs and irreversibility rates with subcooling temperature for R134a.

0.342

0.344

0.346

0.348

0.35

0.352

0.354

0.356

0.358

0.36

405

410

415

420

425

430

1 3 5 7 9 11 13 15

I, k

W

Hea

t exc

hang

er c

ost,

$

Irreversibility

Heat exchanger cost

∆TSC, °C

Fig. 14. The variation of heat exchanger costs and irreversibility rates with subcooling temperature for R407c.

403

404

405

406

407

408

409

410

411

412

413

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

I, k

W

Hea

t exc

hang

er c

ost,

$

Irreversibility

Heat exchanger cost

1 3 5 7 9 11∆TSH, °C

Fig. 15. The variation of heat exchanger costs and irreversibility rates with superheating temperature for R22.


8. Conclusions

Vapor compression refrigeration systems are used widely in refrigeration applications. In refrigerationsystems, system performance increases with subcooling and superheating operations. However, applyingsubcooling and superheating operations different from desired values, system performance affectsunfavorably. In this work, thermodynamic and thermoeconomic analysis of a subcooled–superheatedrefrigeration system was carried out. The results of the analysis were given in tables and figures. Kotas’ [23]

ARTICLE IN PRESS

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.36

0.365

0.37

0.375

0.38

0.385

0.39

0.395

0.4

0.405

I, k

W

Hea

t exc

hang

er c

ost,

$

Irreversibility

Heat exchanger cost

1 3 5 7 9 11∆TSH, °C

Fig. 17. The variation of heat exchanger costs and irreversibility rates with superheating temperature for R407c.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

406

408

410

412

414

416

418

420

422

424

I, k

W

Hea

t exc

hang

er c

ost,

$

Irreversibility

Heat exchanger cost

1 3 5 7 9 11∆TSH, °C

Fig. 16. The variation of heat exchanger costs and irreversibility rates with superheating temperature for R134a.


optimization procedure was used as thermoeconomic optimization method. For a system with capacity of2 kW, optimum heat exchanger areas with corresponding subcooling–superheating temperatures weredetermined. With the increase of the energy prices and investment costs, thermoeconomic analysis facilitatesdetermination of a thermal system’s optimum design parameters for given conditions.

In addition, in this study, thermodynamic property equations are achieved for R22, R134a and R407c withANN method. With the derived equations, saturation pressure, saturated liquid enthalpy, saturated vaporenthalpy, saturated vapor entropy, superheated vapor enthalpy and superheated vapor temperature values canbe calculated easily. Thermodynamic properties of the refrigerants were then compared with the calculatedvalues and the results showed that the deviation ratio was within the acceptable limits.

As a result, it is important to determine optimum operating temperatures and parameters in a refrigerationsystem design. This study will provide facilities in determining optimum working criteria of vapor compressionrefrigeration systems for further applications. Furthermore, it is necessary to investigate effects of subcoolingand superheating applications in systems that use new refrigerants which are not harmful for ozone layer andenvironmentally friendly. Analysis in this work can provide advantage for new thermoeconomic optimizationapplications of systems that use new refrigerants.

References

[1] Dossat RJ. Principles of refrigeration. New Jersey: Prentice Hall; 1997.

[2] Dingec- H, Ileri A. Thermoeconomic optimization of simple refrigerators. Int J Energy Res 1999;23:949–62.

[3] Wall G. Optimization of refrigeration machinery. Int J Refrig 1991;14(6):336–40.

[4] D’Accdia MD, Rossi F. Thermoeconomic optimization of a refrigeration plant. Int J Refrig 1998;18(1):42–54.


[5] Usta N, Ileri A. Computurized economic optimization of refrigeration system design. Energy Conversion Manage 1999;40:1089–109.

[6] S-encan A, Kalogirou SA. A new approach using artificial neural networks for determination of the thermodynamic properties of fluid

couples. Energy Conversion Manage 2005;46(15–16):2405–18.

[7] Kalogirou SA. Applications of artificial neural networks in energy systems A review. Energy Conversion Manage 1999;40:1073–87.

[8] Kalogirou SA. Artificial neural networks in renewable energy systems applications: a review. Renew Sustain Energy Rev

2000;5:373–401.

[9] Kalogirou SA. Optimization of solar systems using neural-networks and genetic algorithms. Appl Energy 2004;77(4):383–405.

[10] Chouai A, Laugier S, Richon D. Modeling of thermodynamic properties using neural networks: application to refrigerants. Fluid

Phase Equilibria 2002;199(1-2):53–62.

[11] Kizilkan O. Examination of superheating and subcooling effects in refrigeration systems with compressor in terms of

thermoeconomics for different refrigerants. Master thesis, Isparta, Turkey. S.D.U., The Graduate School of Natural and Applied

Sciences, 2004.

[12] Fu LM. Neural networks in computer intelligence. New York: McGraw-Hill International Editions; 1994.

[13] duPont de Nemours and Company Inc. Thermodynamic properties of refrigerants, 2003. See also: http://www.dupont.com/suva.

[14] Lin CT, Lee CSG. Neural fuzzy systems. New Jersey: Printice-Hall; 1996.

[15] Yumrutas- R, Kunduz M, Kanoglu M. Exergy analysis of vapor compression refrigeration systems. Exergy, Int J 2002;2(4):266–74.

[16] Chen Q, Prasad RC. Simulation of a vapour-compression refrigeration cycle using HFC 134a and CFC12. Int Comm Heat Mass

Transfer 1999;26(4):513–21.

[17] Ashrae Fundamentals. Atlanta: American Society of Heating Refrigerating and Air Conditioning Engineers Inc.; 1993.

[18] Usta N. Computer analysis and economic optimization of refrigeration systems. Master thesis, M.E.T.U., The Graduate School of

Natural and Applied Sciences, Ankara, Turkey, 1993.

[19] Fratzscher W. Exergy and possible applications. Rev Gen Therm 1997;36:690–6.

[20] Dinc-er I. Thermodynamics, exergy and environmental impact. Energy Sour 2000;22:723–32.

[21] Bejan A. Advanced engineering thermodynamics. New York: Wiley; 1997.

[22] C- engel AY, Boles AM. Thermodynamics: an engineering approach. New York: McGraw-Hill; 1994.

[23] Kotas TJ. The exergy method of thermal plant analysis. London: Butter-Worths; 1985.

[24] Rohsenow WM, Hartnett JP. Handbook of heat transfer. New York: McGraw-Hill Book Company; 1973.

[25] Kern DQ. Process heat transfer. Singapore: McGraw-Hill International Book Company; 1984.

[26] Incropera PF, DeWitt DP. Fundamentals of heat and mass transfer. New York: Wiley; 1990.

[27] Saginomiya Seisakusho Inc. Expansion, solenoid & other valves products catalog, 2003. See also: http://www.saginomiya.co.jp

[28] Danfoss A/S. Product catalogs, 2003. See also: http://www.danfoss.com

[29] Hansen Technologies. Product information detail, 2003. http://www.hantech.com

[30] Carrier. Carrier Corporation. Expansion valves products, 2003. See also: http://www.carrier.com

[31] Bitzer Kuhlmaschinenbau GMBH. Technical documentation of Bitzer products, 2003. See also: http://www.bitzer.de

http://www.dupont.com/suva

http://www.saginomiya.co.jp

http://www.danfoss.com

http://www.hantech.com

http://www.carrier.com

http://www.bitzer.de