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Applied Thermal Engineering 67 (2014) 1e8

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Exergy analysis of parabolic trough solar receiver

Ricardo Vasquez Padilla a,*, Armando Fontalvo a, Gokmen Demirkaya b, Arnold Martinez a,Arturo Gonzalez Quiroga a

aDepartment of Mechanical Engineering, Universidad del Norte, Barranquilla, ColombiabClean Energy Research Center, University of South Florida, 4202 E. Fowler Av., ENB 118, Tampa, FL 33620, USA

h i g h l i g h t s

* Corresponding author. CSIRO Energy Technology,2300, Australia. Tel.: þ61 2 4960 6293.

E-mail addresses: Ricardo.Vasquezpadilla@csiro.auninorte.edu.co (A. Fontalvo), gdemirka@mail.usf.eduninorte.edu.co (A. Martinez), arturoq@uninorte.edu.

http://dx.doi.org/10.1016/j.applthermaleng.2014.03.051359-4311/� 2014 Elsevier Ltd. All rights reserved.

g r a p h i c a l a b s t r a c t

� A comprehensive exergy balance of aparabolic trough is performed.

� The thermal and exergy efficiencyshowed an opposite trend.

� The highest exergy destruction takesplace at the absorber.

� The highest exergy losses are due tooptical errors.

a r t i c l e i n f o

Article history:Received 15 November 2013Accepted 22 March 2014Available online xxx

Keywords:Solar receiverParabolic troughExergy analysis

a b s t r a c t

This paper presents an exergy analysis to study the effects of operational and environmental parameterson the performance of Parabolic Trough Collectors. The exergy analysis is based on a previous heattransfer model published by the authors. The main parameters considered for the analysis are: inlettemperature and mass flow rate of heat transfer fluid, wind speed, pressure or vacuum in annulus andsolar irradiance. The results showed that inlet temperature of heat transfer fluid, solar irradiance, andvacuum in annulus have a significant effect on the thermal and exergetic performance, but the effect ofwind speed and mass flow rate of heat transfer fluid is negligible. It was obtained that inlet temperatureof heat transfer fluid cannot be optimized to achieve simultaneously maximum thermal and exergeticefficiency because they exhibit opposite trends. Finally, it was found that the highest exergy destructionis due to the heat transfer between the sun and the absorber while for exergy losses is due to opticalerror.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Solar Parabolic Trough Collectors (PTCs) are currently used forelectricity generation and applications with temperatures up to400 �C [1]. PTCs concentrate solar radiation onto a focal line to

PO Box 330, Newcastle, NSW

u (R.V. Padilla), aefontalvo@u (G. Demirkaya), arnoldg@co (A.G. Quiroga).

3

transform it into useful energy by increasing the temperature of aHeat Transfer Fluid (HTF). The performance of PTCs depends onthe combination of several operation parameters under differentmeteorological conditions. In this context, this paper presents anexergy analysis to determine the performance of PTCs in terms ofwork potential and location, type, and magnitude of exergylosses.

This research is based on a detailed and validated heat transfermodel [2] that takes into account all heat transfer mechanismamong collector components and includes the thermal interactionwith the environment. Results of the heat transfer model are in

Nomenclature

Aa cross sectional area of absorber [m2]Ib solar irradiance [W/m2]Cp specific heat capacity [kJ/kg K]e specific exergy [kJ/kg]h specific enthalpy [kJ/kg]s specific entropy [kJ/kg K]v specific volume [m3/kg]E exergy [kJ]_Ed exergy destroyed rate [kW]_Eloss Exergy loss rate [kW]_Eqj exergy of heat transfer rate [kW]g gravity [m/s2]_m mass flow rate [kg/s]P annulus gas pressure [Torr], heat transfer fluid

pressure [bar]_Q heat transfer rate [kW]T temperature [�C, K]t time [s]V heat transfer fluid velocity [m/s]_Wcv work rate [kW]z height, axial length [m]

Greek symbolsd Sun’s cone angleho peak optical efficiencyj maximum useful work available from radiationr heat transfer fluid density [kg/m3]HCE heat collection element

Subscriptsa absorbercv control volumef heat transfer fluide exiti inlet, surface ij surface j, Element jgain gainedo surroundingsopt opticalq heat transfersr solar radiation

Superscriptsaverage

R.V. Padilla et al. / Applied Thermal Engineering 67 (2014) 1e82

excellent agreement with experimental data obtained at SandiaNational Laboratory [3], and also showed improvements whencompared with prior models [4,5].

Most of the previous research on exergy analysis of PTCs hasbeen focused on heat and power production systems. In thesesystems, the exergy analysis is used either to find optimal operationconditions or to evaluate the performance of the system [6e13].Some applications involve the optimization of the coupling condi-tions between the heat transfer fluid and the power cycle [6e8].Other applications have used the exergy analysis to minimize theuse of fossil fuels in polygeneration units [9e13]. Exergy analysishas also been used in desalination processes that rely on thermalsolar power obtained from PTCs [14,15]. It is important to highlightthat in this last application, PTCs are only a component of the sys-tem under analysis, and what it is optimized is the coupling be-tween PTCs in the solar field with the thermal desalination system.

Somestudies onexergyanalysis of PTCshavebeen focusedon theperformance evaluation of the collectors tomaximize the use of theincoming solar energy. Previous studies have reported the depen-dence of exergy efficiency on the length of the collector and HTFtemperature [16]; the influence of mass flow of HTF, solar intensityand concentration ratio on energy and exergy efficiencies [17]; andthe effect of the collector length, absorber tube diameter, workingtemperature andpressureon the energyandexergyefficiencies [18].

In this paper, a comprehensive exergetic balance of a PTC basedon a control volume analysis is performed. This analysis is based ona previous heat transfer model developed by the authors [2]. Thisanalysis shows the effect of inlet temperature and mass flow rate ofthe heat transfer fluid, solar irradiance, annulus condition (vacuumor air) andwind speed on the thermal and exergetic performance ofthe PTC. The exergetic balance is very useful to identify the irre-versibility sources which can be used to redesign and improve thethermal performance of PTCs.

2. Solar receiver model

The solar receiver consists of a heat collection elementcomposed of a stainless steel tube with a selective absorber surface,which has high values of absorptance and low values of emittance

for the temperature range of operation. Most of the incoming solarradiation has wavelengths below 3 mmwhich reduces the radiationlosses because of the emittance of the absorber [19]. The stainlesstube is covered by an evacuated glass tube (glass envelope) whichprevents oxidation and minimizes the heat losses to the environ-ment. Glass to metal seals and metal bellows are employed toachieve the vacuum inside the envelope and compensate thethermal expansion difference [20]. Bellows also allow extendingthe absorber to extend beyond the glass envelope so that the HCEcan form a continuous receiver (see Fig. 1).

The heat transfer model is an energy balance between the heattransfer fluid and its surroundings. Fig. 2 shows the heat transferresistance model in a cross section of the HCE. Readers areencouraged to consult the details and assumptions of the heattransfer model developed by the authors in Ref. [2]. The heattransfer model was compared with experimental data obtainedfrom Sandia National Laboratory (SNL) [3] and compared withother solar receiver models [4,5]. Experimental results used in themodel validation were taken from LS-2 module placed at theAZTRAK rotating platform located at the SNL.

3. Exergy analysis model

An exergy balance was applied to the control volume shown inFig. 1. It should be noted that the same assumptions of the heattransfer model are used. The partial differential equation of theexergy balance is as follows [21]:

dEcvdt

¼Xj

_Eqj � _Wcv þXi

_mi efi �Xe

_me efe � _Ed � _Eloss (1)

with:

_Eqj ¼ 1� To

Tj

!_Qj (2)

ef ¼ h� ho � To ðs� soÞ þ V2

2þ g z (3)

Expansion bellows Glass EnvelopeAbsorber tube with

selective coatingVacuum between envelope and absorber

Fig. 1. Parts of a heat collection element (HCE) and control volume used for the heat transfer analysis. Adapted from [27].

R.V. Padilla et al. / Applied Thermal Engineering 67 (2014) 1e8 3

3.1. Exergy input

The exergy input includes the exergy inflow rate coming fromthe heat transfer fluid and the exergy of the solar radiation. Thetotal exergy input is:

_Ei ¼ _m

264 Z

Ti

To

CpðTÞdT þ nðPi � PoÞ � To

ZTiTo

CpðTÞT

dT þ V2i2

375

þ IbAa j

(4)

For an ideal process, the relative potential of the maximumuseful work available from radiation, j, is calculated with Petela’sformula [22]:

(a)

(b)

Fig. 2. Heat transfer and thermal resistance model in a cross section at the heat coll

j ¼ 1� 43ToTs

þ 13

�ToTs

�4

(5)

where Ts is the equivalent temperature of the sun as a black body(w5800 K). Parrot [23] introduced the effect of the sun’s cone angle(d w 0.005 rad) on the limiting efficiency for utilization of solarenergy, the expression obtained was:

j ¼ 1� 43ToTsð1� cosdÞ1=4 þ 1

3

�ToTs

�4

(6)

ection element (HCE). (a) Heat transfer, (b) thermal circuit. Adapted from [3,4].

R.V. Padilla et al. / Applied Thermal Engineering 67 (2014) 1e84

3.2. Exergy output

The exergy output only includes the exergy outflow rate comingfrom the heat transfer fluid exiting the solar receiver. The totalexergy output is as follows:

_Ee ¼ _m

264 Z

Te

To

CpðTÞdT þ nðPe � PoÞ � To

ZTeTo

CpðTÞT

dT þ V2e2

375 (7)

The exergy gained by the heat transfer due to the incident ra-diation on the solar collector is given by:

_Egain ¼ _m

264 Z

Te

Ti

CpðTÞdT � To

ZTeTi

CpðTÞT

dT � nDP

375 (8)

where the first two terms represent the exergy gain as result of anincrease in the heat transfer fluid temperature due to the solarinsolation and flow friction and the last term represents thedecrease of mechanical energy due to flow friction. The exergy ef-ficiency is defined as the ratio of gain exergy to solar radiationexergy:

hex ¼_Egain_Esr

(9)

then:

hex ¼

_m

264Z Te

TiCpðTÞdT � To

Z Te

Ti

CpðTÞT

dT � nDP

375

IbAaj(10)

The last equation does not present the terms of loss anddestroyed exergy which are useful to identify the causes andlocation of thermal losses. The exergy losses include heat transferlosses to the surroundings while the exergy destruction is causedby internal irreversibilities [24]. For steady state conditions(dEcv=dt ¼ 0), Eq. (10) can be rewritten as:

hex ¼ 1�_Ed þ _ElossIbAaj

(11)

3.3. Exergy losses

In this paper exergy losses are due to optical error and heattransfer losses from the solar receiver to the ambient [25].

_Eloss ¼ _Eloss;opt þ _Eloss;q; (12)

The exergy leakage due to optical errors is as follows:

_Eloss;opt ¼ ð1� hoÞIbAaj (13)

ho is defined as the optical efficiency of the solar collector. Theexergy loss due to heat transfer from absorber to the ambient isgiven by [25]:

_Eloss;q ¼Xi

ZTa;iTo

_Qi;lossToT2

dT (14)

where _Qi;loss are the thermal losses. Simplifying:

_Eloss;q ¼X

_Qj;loss 1� To (15)

j

Ta;j

!

3.4. Exergy destruction

In the solar receiver, exergy destruction is caused by twomechanism: friction of the viscous fluid (HTF) and heat transferfromhigh to low temperatures [25]. The friction of the heat transferfluid generates a pressure drop through the solar receiver. Theentropy generation (exergy destruction) during this process is asfollows [21]:

_Ed;DP ¼ To _mf

Xj

DPjrj

ln�Te;j�Ti;j�

Te;j � Ti;j(16)

Exergy destruction due to heat transfer process is present on theabsorber surface. The first process is the heat transfer from the sunto the absorber surface, in this case the entropy generation is givenby [26]:

_Ed;q1 ¼ hoIbAaj�Xj

hoI0bDzAa

1� To

Ta;j

!(17)

The second heat transfer process is between the absorber andthe HTF. The exergy destruction by heat conduction from theabsorber to the fluid is [25]:

_Ed;q2 ¼ To _mf

264Z

Te

Ti

CpðTÞdTT �Xj

1Ta;j

ZTe;jTi;j

CpðTÞdT

375 (18)

Then, the total exergy destruction is:

_Ed ¼ _Ed;DP þ _Ed;q1 þ _Ed;q2 (19)

Replacing all terms Eq. (13)e(18), the exergy efficiency can berewritten by introducing dimensionless exergy term ( _E

0 ¼ _E= _Esr):

hex ¼ 1��_E0d;DP þ _E

0d;q1 þ _E

0d;q2 þ _E

0loss;opt þ _E

0loss;q

�(20)

with:

_E0loss;opt ¼ ð1� hoÞ (21)

_E0loss;q ¼

Pj

_Qj;loss

�1� To

Ta;j

�IbAaj

(22)

_E0d;DP ¼ To _mf

Pj

DPjrj

lnðTe;j=Ti;jÞTe;j�Ti;j

IbAaj(23)

E0d;q1 ¼ ho

241þ 1

j

0@Dz

Lc

Xj

ToTa;j

� 1

1A35 (24)

_E0d;q2 ¼ To _mf

Z Te

TiCpðTÞdTT �

Xj

1Ta;j

Z Te;j

Ti;jCpðTÞdT

IbAaj(25)

Table 2Summary of the parameters assumed for the analysis.

Parameters Values Units

HTF mass flow rate 4, 7, 10 kg/sSolar irradiance 250, 500, 750, 1000 W/m2

Wind speed 0, 5 m/sVacuum in annulus P < 1 Torr (vacuum)

P � 1 Torr (pressure in annulus)

R.V. Padilla et al. / Applied Thermal Engineering 67 (2014) 1e8 5

4. Results and discussion

A parametric study was performed by using a LS-3 parabolictrough solar collector in order to study the effect of some operatingand environmental parameters on the collector efficiency andcollector exergy efficiency. The geometrical parameters of the LS-3collector are listed in Table 1. The variations of exergy leakages andexergy destruction with these parameters were also studied.Table 2 shows the operating conditions used for the parametricanalysis.

Figs. 3e8 shows the effect of HTF inlet temperature (Ti), massflow rate ð _mÞ and solar irradiance (Ib) on Collector Efficiency (hc)and Collector Exergy Efficiency (hex). Collector Exergy Efficiency isstrongly dependent on HTF inlet temperature. This result may beexplained by the influence of exergy leakage due to thermal losses,and exergy destruction due to heat transfer from the sun to theabsorber, which are strongly dependent of HTF temperature. Ac-cording to Figs. 3e6, an increase in the HTF inlet temperature leadsto a significant increase in Collector Exergy Efficiency, but it causesa reduction in Collector Efficiency. When HTF inlet temperatureincreases, Collector Efficiency shows an average reduction of 15.5%and 7.6% for irradiance levels of 250 and 500 W/m2 respectivelyaccording to Figs. 3 and 4, whereas the average reduction of Col-lector Efficiency for irradiances of 750 and 1000W/m2 are 4.7% and3.25% respectively, as it is shown in Figs. 5 and 6.

On the other hand, Figs. 3 and 4 showed an average increase of6.9% and 7.9% in Collector Exergy Efficiency for solar irradiancelevels of 250 and 500 W/m2, respectively. For high solar irradiance,according to Figs. 5 and 6, the average increase was 7.3% and 7.7%for solar irradiance of 750 and 1000 W/m2, respectively. Themaximum Collector Exergy Efficiency, under vacuum condition,was between 30.3% and 36.6%, for irradiance levels of 250 W/m2

and 1000 W/m2, respectively. Results described above allows toconclude that in days with low irradiance levels (250�500 W/m2)the increase of HTF inlet temperature to achieve maximum Col-lector Exergy Efficiency would significantly penalize the CollectorEfficiency, but in days with high irradiance levels (750e1000 W/m2) the maximum or near maximum Collector Exergy Efficiencycan be achieved with a less severe impact on Collector Efficiency.However, it is clear that a simultaneous maximization of bothefficiencies is not possible by just adjusting the HTF inlet temper-ature. This opposite trend of Collector Efficiency and CollectorExergy Efficiency is explained by the behavior of the exergydestruction due to heat transfer between the absorber and the HTF,and the thermal losses due to heat transfer from absorber to theenvironment. An increase in HTF inlet temperature would increasethe thermal losses and a decrease in exergy destruction due to heattransfer between the absorber and the HTF, as it can be seen inFigs. 9 and 10, causing a decrease in Collector Efficiency and anincrease in Collector exergy efficiency.

The optimum operating conditions for PTCs can be assessed bymeans of collector efficiency analysis and collector exergy effi-ciency analysis. The common aim is to optimize the thermal

Table 1Geometrical and optical data for the LS-3 parabolic trough col-lector. Adapted from [20].

Parameter Value

Aperture width (m) 5.76Focal length (m) 1.71Length per element (m) 12Length per collector (m) 99Receiver diameter (m) 0.07Geometric concentration 82:1Peak optical efficiency (%) 80

efficiency of any collector, which is defined as the ratio of ‘usefulenergy output’ to that of ‘incident solar energy’ during the sametime period. In this work, the performance of PTCs is examinedfrom the standpoint of exergy, which is a useful method to com-plement, not to replace the energy analysis. Exergy analysis quan-tifies the collection and useful consumption of exergy andpinpoints the unrecoverable losses, leading the way to improve thesystem. Results show that collector efficiency and collector exergyefficiency are increasing functions of mass flow rate for a givenvalue of solar intensity. On the other hand, for low values of solarintensity (I < 500 W/m2) and a given mass flow rate, collectorexergy efficiency exhibits a maximum as inlet temperatureincreases. Collector efficiency is a decreasing function of inlettemperature over the whole solar intensity range studied (100 W/m2 < I < 1000 W/m2). However the influence of inlet temperatureon collector efficiency significantly diminishes at high solarintensities.

The effect of wind speed and vacuum in annulus on both Col-lector Efficiency and Collector Exergy Efficiency is shown in Figs. 7e10. According to Figs. 7 and 8, results indicate that vacuum inannulus reduces the effect of wind speed because both efficienciesshowed no significant variation with wind speed. However, inabsence of vacuum, the increase of wind speed leads to averagereductions of 5% and 4% for Collector Efficiency and CollectorExergy Efficiency, respectively. According to Figs. 9 and 10, whenpressure in annulus is below 1 Torr, convective heat transfer insidethe annulus is not significant, consequently its contribution to theexergy loss due to heat transfer from absorber to the surroundingsis also reduced. On the other hand, if pressure in annulus is above1 Torr, convective heat transfer inside the annulus is increasedthereby increasing its contribution to the exergy loss due to heat

Fig. 3. Collector efficiency and collector exergy efficiency vs HTF inlet temperature fordifferent values of mass flow. I ¼ 250 W/m2.

Fig. 4. Collector efficiency and collector exergy efficiency vs HTF inlet temperature fordifferent values of mass flow. I ¼ 500 W/m2.

Fig. 6. Collector efficiency and collector exergy efficiency vs HTF inlet temperature fordifferent values of mass flow. I ¼ 1000 W/m2.

R.V. Padilla et al. / Applied Thermal Engineering 67 (2014) 1e86

transfer from absorber to the surroundings, which is the exergywaste that can be affected by the wind speed.

For mass flow rate, Figs. 3e6 shows that both Collector Effi-ciency and Collector Exergy Efficiency have small variations withmass flow rate and the optimum value for both efficiencies waspractically the same for the three mass flow rates considered.Figs. 11 and 12 show that exergy losses and exergy destruction arealmost independent from mass flow rate because exergy destruc-tion due to the friction of the HTF and heat transfer between theabsorber and the HTF are the ones that have a noticeable variationwithmass flow rate, but their contribution to the total exergy lossesand destruction is less than 0.5%.

Figs. 9 and 10 illustrate the effect of HTF inlet temperature onthe exergy destruction due to heat transfer between the sun andthe absorber. This exergy destruction accounts for 35%e40% of thetotal exergy wasted. When HTF inlet temperature increases, the

Fig. 5. Collector efficiency and collector exergy efficiency vs HTF inlet temperature fordifferent values of mass flow. I ¼ 750 W/m2.

exergy destruction diminishes because the temperature differenceis lower. However, the exergy losses to the surroundings increase asthe HTF inlet temperature raises as a consequence of the temper-ature difference. The combine effect of exergy destruction due toheat transfer between the sun and the absorber and exergy lossesto the surroundings is accountable for an optimum exergy effi-ciency point. After this point is reached, exergy losses to sur-roundings accounts for 5%e10% of the total exergy wasted andincrease more rapidly than the decrease of exergy destruction dueto heat transfer.

5. Conclusions

An exergy analysis of parabolic trough solar receiver was carriedout based on a heat transfer model proposed by the authors. Theperformance of the solar receiver was simulated for a fixed values

Fig. 7. Collector efficiency and collector exergy efficiency vs HTF inlet temperaturewith and without vacuum, for natural and forced convection. I ¼ 250 W/m2.

Fig. 8. Collector efficiency and collector exergy efficiency vs HTF inlet temperaturewith and without vacuum, for natural and forced convection. I ¼ 750 W/m2.

Fig. 10. Dimensionless exergy losses vs Inlet temperature. Conditions: _m ¼ 7 kg=s;Vair ¼ 5 m=s (forced convection); without vacuum.

R.V. Padilla et al. / Applied Thermal Engineering 67 (2014) 1e8 7

of solar irradiance, HTF mass flow rate, HTF inlet temperature, withand without vacuum in annulus, and with presence and absence ofwind. Based on the results obtained, the following conclusions areproposed:

� Current results are useful to improve the design of PTCs andcompare performances between PTCs options. However oper-ating conditions are also determined by others factors beyondexergy analysis of the collector like collector area, which impactscapital costs as the fuel (sunlight is free), and pumping power atincreasing mass flow rates.

� HTF inlet temperature has a significant effect on Collector Effi-ciency and Collector Exergy Efficiency. HTF inlet temperatureaffects the exergy leakage due to thermal losses, and exergydestruction due to heat transfer from the sun to the absorber.

Fig. 9. Dimensionless exergy losses vs inlet temperature. Conditions: _m ¼ 7 kg=s;Vair ¼ 0 m/s (natural convection); without vacuum.

� Solar Irradiance has a significant effect on the performance ofthe parabolic trough solar receiver. High solar irradiances allowsto work at higher HTF inlet temperatures, which leads to highvalues of Collector Exergy Efficiency with a negligible reductionof the Collector Efficiency.

� The optimal performance of PTC is independent from the massflow rate, since exergy destruction due to friction of the heattransfer fluid and heat transfer between the absorber and theHTF depends on mass flow rate, but their contribution to thetotal exergy wasted is less than 0.5%.

� The performance of the solar receiver is strongly dependent onvacuum in annulus. Vacuum in annulus mitigates the effect ofwind speed, but its absence increases the thermal losses to thesurroundings, which leads to a reduction of both Collector Ef-ficiency and Collector Exergy Efficiency.

Fig. 11. Dimensionless exergy losses vs mass flow rate. Conditions: I ¼ 750 W/m2;Vair ¼ 0 m/s (natural convection); without vacuum in annulus.

Fig. 12. Dimensionless exergy losses vs mass flow rate. Conditions: I ¼ 750 W/m2;Vair ¼ 5 m/s (forced convection); without vacuum in annulus.

R.V. Padilla et al. / Applied Thermal Engineering 67 (2014) 1e88

References

[1] A. Fernández-García, E. Zarza, L. Valenzuela, M. Pérez, Parabolic-trough solarcollectors and their applications, Renewable Sustainable Energy Rev. 14 (7)(2010) 1695e1721.

[2] R.V. Padilla, G. Demirkaya, D.Y. Goswami, E. Stefanakos, M.M. Rahman, Heattransfer analysis of parabolic trough solar receiver, Appl. Energy 88 (12)(2011) 5097e5110.

[3] V. Dudley, G. Kolb, M. Sloan, D. Kearney, SEGS LS2 Solar Collector-Test Results,Report of Sandia National Laboratories, SAN94e1884, 1994.

[4] R. Forristall, Heat Transfer Analysis and Modeling of a Parabolic Trough SolarReceiver Implemented in Engineering Equation Solver, National RenewableEnergy Laboratory (NREL), Colorado, 2003.

[5] O. García-Valladares, N. Velázquez, Numerical simulation of parabolic troughsolar collector: improvement using counter flow concentric circular heat ex-changers, Int. J. Heat Mass Transfer 52 (3e4) (2009) 597e609.

[6] M. Kane, D. Favrat, K. Ziegler, Y. Allani, Thermoeconomic analysis of advancedsolar-fossil combined power plants, Int. J. Thermodyn. 3 (4) (2010) 191e198.

[7] Y. You, E.J. Hu, A medium-temperature solar thermal power system and itsefficiency optimisation, Appl. Therm. Eng. 22 (4) (2002) 357e364.

[8] N. Singh, S. Kaushik, R. Misra, Exergetic analysis of a solar thermal powersystem, Renewable Energy 19 (1) (2000) 135e143.

[9] G. Song, H. Hongjuan, Y. Yongping, Optimize on the temperature of solarcollectors in solar aided coal-fired electric generation, in: Sustainable PowerGeneration and Supply, 2009. SUPERGEN’09. International Conference on,IEEE, 2009, pp. 1e4.

[10] H. Zhai, Y. Dai, J. Wu, R. Wang, Energy and exergy analyses on a novel hybridsolar heating, cooling and power generation system for remote areas, Appl.Energy 86 (9) (2009) 1395e1404.

[11] A. Baghernejad, M. Yaghoubi, Exergy analysis of an integrated solar combinedcycle system, Renewable Energy 35 (10) (2010) 2157e2164.

[12] V.S. Reddy, S. Kaushik, S. Tyagi, Exergetic analysis and performance evaluationof parabolic trough concentrating solar thermal power plant (ptcstpp), Energy39 (1) (2012) 258e273.

[13] F.A. Al-Sulaiman, I. Dincer, F. Hamdullahpur, Exergy modeling of a new solardriven trigeneration system, Sol. Energy 85 (9) (2011) 2228e2243.

[14] A. Nafey, M. Sharaf, Combined solar organic rankine cycle with reverseosmosis desalination process: energy, exergy, and cost evaluations, Renew-able Energy 35 (11) (2010) 2571e2580.

[15] M. Sharafa, A. Nafeya, L. García-Rodríguez, Exergy and thermo-economic an-alyses of a combined solar organic cycle with multi effect distillation (MED)desalination process, Desalination 272 (1e3) (2011) 135e147.

[16] S.N. Trushevskii, R.T. Rabbimov, R.R. Avezov, Exergic efficiency of solar ther-mal units with linear concentrators, Appl. Sol. Energy 41 (1) (2005) 24e28.

[17] S. Tyagi, S. Wang, M. Singhal, S. Kaushik, S. Park, Exergy analysis and para-metric study of concentrating type solar collectors, Int. J. Therm. Sci. 46 (12)(2007) 1304e1310.

[18] M. Montes, A. Abánades, A. nades, J. Martinez-Val, Thermofluidynamic modeland comparative analysis of parabolic trough collectors using oil, water/steam, or molten salt as heat transfer fluids, J. Sol. Energy Eng. 132 (2) (2010).

[19] D.Y. Goswami, F. Kreith, J.F. Kreider, F. Kreith, Principles of Solar Engineering,second ed., Taylor & Francis, Philadelphia, PA, 2000.

[20] H. Price, E. Lüpfert, D. Kearney, E. Zarza, G. Cohen, R. Gee, R. Mahoney, Ad-vances in parabolic trough solar power technology, J. Sol. Energy Eng. Trans.ASME 124 (2) (2002) 109e125.

[21] M.J. Moran, H.N. Shapiro, Fundamentals of Engineering Thermodynamics,Student Problem Set Supplement, fifth ed., Wiley, 2004.

[22] R. Petela, Exergy of undiluted thermal radiation, Sol. Energy 74 (6) (2003)469e488.

[23] J. Parrott, Theoretical upper limit to the conversion efficiency of solar energy,Sol. Energy 21 (3) (1978) 227e229.

[24] I. Dincer, M.A. Rosen, EXERGY: Energy, Environment and Sustainable Devel-opment, Elsevier Science, 2007.

[25] A. Suzuki, General theory of exergy-balance analysis and application to solarcollectors, Energy 13 (2) (1988) 153e160.

[26] A. Bejan, G. Tsatsaronis, M. Moran, Thermal Design and Optimization, Wiley-Interscience, 1996.

[27] F. Kreith, D.Y. Goswami, Handbook of Energy Efficiency and Renewable En-ergy, first ed., CRC, 2007.