Energy Conversion and Management 75 (2013) 191–201

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Energy Conversion and Management

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Estimation of the temperature, heat gain and heat loss by solar parabolictrough collector under Algerian climate using different thermal oils

0196-8904/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.enconman.2013.06.011

⇑ Corresponding author.E-mail address: ouagued_malika@yahoo.fr (M. Ouagued).

Malika Ouagued a,⇑, Abdallah Khellaf b, Larbi Loukarfi c

a Laboratory for Theoretical Physics and Material Physics LPTPM, Department of Process Engineering, Faculty of Technology, University Hassiba Benbouali of Chlef, PO Box151,Chlef 02000, Algeriab Centre de Développement des Energies Renouvelables, CDER, PO Box 62, Avenue de l’Observatoire de Bouzaréah, Algeriac Department of Mechanical Engineering, Faculty of Technology, University Hassiba Benbouali of Chlef, PO Box151, Chlef 02000, Algeria

a r t i c l e i n f o a b s t r a c t

Article history:Received 24 December 2012Accepted 13 June 2013

Keywords:Direct normal solar irradianceTilted apertureTracking apertureSolar parabolic trough collectorHeat balanceThermal oil performanceAlgerian climatic conditions

Algeria is blessed with a very important renewable, and more particularly solar, energy potential. Thispotential opens for Algeria reel opportunities to cope with the increasing energy demand and the grow-ing environmental problems link to the use of fossil fuel. In order to develop and to promote concreteactions in the areas of renewable energy and energy efficiency, Algeria has introduced a national daringprogram for the period 2011–2030. In this program, solar energy, and more particularly solar thermalenergy plays an important role. In this paper, the potential of direct solar irradiance in Algeria and theperformance of solar parabolic trough collector (PTC) are estimated under the climate conditions ofthe country. These two factors are treated as they play an important role in the design of solar thermalplant. In order to determine the most promising solar sites in Algeria, monthly mean daily direct solarradiation have been estimated and compared for different locations corresponding to different climaticregion. Different tilted and tracking collectors are considered so as to determine the most efficient systemfor the PTC. In order to evaluate the performance of a tracking solar parabolic trough collector, a heattransfer model is developed. The receiver, heat collector element (HCE), is divided into several segmentsand heat balance is applied in each segment over a section of the solar receiver. Different oils are consid-ered to determine the thermal performances of the heat transfer fluid (HTF). Then, the HTF temperatureand heat gain evolutions are compared under the topographical and climatic conditions.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years, the risk of global warming associated with theemission of green house gases during the combustion of fossil fuelsis driving research in the efficient use of energy and renewable en-ergy sources [1]. The solar energy incident on the Earth surface isabout 10.000 times the world energy demand. The use of thesouthern Mediterranean countries areas for solar energy harvest-ing would by far suffice to supply the energy needs of those coun-tries and of all the northern European industrialized countries. In astudy carried by Greenpeace [2], it has been found that the use ofconcentrating solar power (CSP) can prevent the emission of154 million tons of CO2 by 2020. Just one 50 MWel parabolic troughpower plant can cut the annual heavy oil consumption by 30 mil-lion litters and thus eliminate 90.000 tons of CO2 emissions [2].

The issues of energy, climate change and sustainable develop-ment occupy a large place in the Algerian development programs.In 2011, Algeria has launched the renewable energies (REs) and en-

ergy efficiency program. With a total budget of 120 billion US $[3,4], this program is based on a strategy focused on developingand expanding the use of the inexhaustible resources, such as solarenergy, in order to diversify Algeria energy sources and to prepareit for tomorrow. Electricity of solar origin should represent morethan 37% of the national electricity production by 2030 [3,4]. Thegeographic location of Algeria represents the best climatic condi-tions such as the abundant sunshine throughout the year, lowhumidity and precipitation, and plenty of unused flat land closeto road networks and transmission grids. The sunshine durationexceeds 2500 h/year over most of the territory and it could be ashigh as 3900 h/year in the high plains and in the Sahara. Algeriahas several advantages for the extensive use of the solar energyas enormous potential for power generation compared to globalenergy demands [4].

In order to deliver high temperatures with good efficiency, ahigh performance solar collector is required. Systems with lightstructures and low cost technology for process heat applicationup to 773 K could be obtained with solar parabolic trough collector(solar PTC) [5,6]. Solar PTC is a proven technology that has reachedindustrial maturity and that is viable for commercial scale solar

Nomenclature

Ac collector aperture (m2)Aa receiver tube cross-section area (m2)Af fluid flow cross-section area (m2)Av glass envelope tube cross-section area (m2)Ca absorber specific heat (J/kg K)Cair air specific heat at Tamb (J/kg K).Cf HTF specific heat in segment ‘‘i’’ (J/kg K)Cv glass envelope specific heat (J/kg K)Dae outside diameter of absorber pipe (m)Dai inside diameter of absorber pipe (m)Dve outside diameter of glass envelope (m)Dvi inside diameter of glass envelope (m)f friction factor for the inner surface of the absorber pipeFf HTF flow rate (m3/s)ha convection heat transfer coefficient of annulus gas at

Tmoy1 (W/m2 K)hf convection heat transfer coefficient of the HTF (W/m2 K)hv convection heat transfer coefficient of ambient air (W/

m2 K)Iba direct normal irradiance per unit of collector area (W/

m2)kair thermal conductivity of the ambient air at temperature

Tmoy2 (W/m K)kf thermal conductivity of the HTF at temperature Ti

f (W/m K)

kstd thermal conductivity (W/m K)L receiver length (m)mi

a absorber mass in segment ‘‘i’’ (kg)mi

f HTF mass at inlet of receiver segment ‘‘i’’ (kg)mi

v glass envelope mass in segment ‘‘i’’ (kg)Nuair Nuselt number at Tmoy2

Nuf Nuselt number at Tif

Pr0air air Prandtl number at Tamb

Pr00air air Prandtl number at Tiv

Prf Prandtl number at Tif

Q iaconv convection heat transfer rate for receiver segment ‘‘i’’

between the surface of the absorber to the surface ofthe envelope (W)

Qiarad radiation heat transfer rate for receiver segment ‘‘i’’ be-

tween the surface of the absorber to the surface of theglass envelope (W)

Qasol direct incident solar irradiance absorption rate into thereceiver segment ‘‘i’’ (W)

Qifconv convection heat transfer rate between the heat transfer

fluid and wall of the absorber pipe in the segment ‘i’ (W)Qi

vconv convection heat transfer rate between the surface of theenvelope to the atmosphere for receiver segment ‘‘i’’(W)

Qivrad radiation heat transfer rate between the outer surface of

the envelope to the sky receiver segment ‘‘i’’ (W)Qvsol direct incident solar irradiance absorption rate into the

envelope of receiver segment ‘‘i’’ (W)Qsol direct incident solar irradiance per unit length of recei-

ver (W/m)Qz heat rate coming to the segment ‘i’ (W)Qz+Dz heat rate leaving from the segment ‘i’ (W)Ref Reynolds number at Ti

ft time (s)Ti

a absorber pipe temperature in segment ‘i’ (K)Tamb ambient temperature (K)Ti

f HTF temperature inlet of receiver segment ‘‘i’’ (K)Ti�1

f HTF temperature in the segment ‘‘i � 1’’ (K)Tmoy1 average temperature, ðTmoy1 ¼ ðTa þ TvÞ=2Þ (K)Tmoy2 average temperature, Tmoy2 ¼ Ti

v þ Tamb

� �=2

� �(K)

Tsky estimated effective sky temperature (K)Ti

v glass envelope temperature in segment ‘‘i’’ (K)w collector width (m)

Greek lettersaa absorptance of the absorber selective coatingav glass envelope absorptanceqa density of the absorber selective coating (kg/m3)qair air density at Tamb (kg/m3)qf HTF density at average temperature of receiver segment

‘‘i’’ (kg/m3)qv density of glass envelope (kg/m3)ga effective optical efficiency of the absorbergcol collector efficiencygv effective optical efficiency of the glass envelopesv glass envelope transmittanceDz receiver segment length (m)k mean-free-path between collisions of a molecule (cm)d molecular diameter of annulus gas (cm)c ratio of specific heats for the annulus gasr Stefan–Boltzmann constant (5.6697 W/m2 K4)

192 M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201

power generation in the sunbelt countries of the world [7–9]. Thecommercialization of this technology took a major step forward inthe mid 1980s and early 1990s with the development of the SEGSplants in California by Luz International Ltd. More than 1.2 billionUS $ in private capital was raised in debt and equity financingfor the nine SEGS plants. Whereas a conventional power plant de-pends on fuel that is purchased as a continuous string of paymentsduring the lifetime of the plant, a solar power plant needs to fi-nance its ‘‘fuel costs’’ through capital investment at the beginningof the project. In a typical parabolic trough SEGS-type plant, the so-lar field represents 50% of the total investment costs. However,once a solar plant is built the ‘‘solar fuel’’ is free, resulting in lessuncertainty in the cost of power over the life of the project. Besidesreducing the dependence on the hydrocarbon limited resources,solar PTC offers the opportunity to increase the country energymix and to contribute to the local development through job crea-tion during construction. A parabolic trough power plant also less-ens dependence on fossil fuels, which provides a hedge againstfossil fuel price fluctuations [2,9].

PTC heat transfer analyzes have received increasing attentionsince 1980. Clark [10] has presented an identification of the princi-pal design factors that influence the technical performance of aparabolic trough concentrator. These factors include reflectivityof the mirror system, the mirror-receiver tube intercept factor,the incident angle modifier and the absorptivity–transmissivityproduct of the receiver tube and cover tube. The temperature pro-file in the absorber tube of a direct steam generating PTC has beenestimated by Heidemann et al. [11]. To this end, a computer pro-gram has been developed to calculate the two-dimensional tran-sient temperature field using a modular nodal point library.Using different type of receiver selective coating and different re-ceiver configuration, Dudley et al. [12] have tested LS-2 PTC todetermine the collector efficiency and the thermal losses. LS-2 isthe second-generation PTC installed in SEGS solar plant. Thomasand Thomas [13] have presented a design data for the computationof thermal losses in the receiver of a PTC for specific absorber tubediameters, various ambient temperatures, wind velocity andabsorber temperatures. A numerical model has been used by

M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201 193

Kalogirou et al. [14] to quantify the steam produced PTC system.Performance tests of the model have indicated that the modelingprogram was accurate to within 1.2% which has been consideredvery adequate. Odeh et al. [15] have carried out a numerical studyto evaluate the performance of PTC direct steam generation solarcollector. The model has been based on absorber wall temperaturerather than fluid bulk temperature. Forristall [16] has described thedevelopment, the validation, and the use of a heat transfer modelimplemented in Engineering Equation Solver (EES). Numerical sim-ulations of thermal and fluid-dynamic behavior of a single-passand double-pass solar parabolic trough collector have been carriedout by García-Valladares and Velázquez [17]. Their results haveshown that the double-pass can enhance the thermal efficiencycompared with the single-pass. Kumar and Reddy [18] have ana-lyzed a 3-D numerical simulation of the porous disc line receiverfor PTC. The analysis has been carried out based on renormaliza-tion-group (RNG) turbulent model by using Therminol-VP1 asworking fluid. Cheng et al. [19] have presented a 3-D numericalsimulation of heat transfer characteristics in the receiver tube bycombining the Monte Carlo Ray Trace Method (MCRT) and the FLU-ENT software. Gong et al. [20] have established a 1-D theoreticalmodel using Matlab software to compute the receiver’s major heatloss through glass envelope in Sanle-3 HCE (China’s first high tem-perature vacuum receiver). A coupled simulation method based onMCRT and Finite Volume Method (FVM) has been presented by Heet al. [21] to solve the complex coupled heat transfer problem ofradiation, heat conduction and convection in PTC system. The heattransfer and fluid flow performance in the LS-2 collector tube hasbeen investigated to validate the coupled simulation model. Vas-quez Padella et al. [22] have studied a 1-D numerical heat transferanalysis of a PTC. The receiver and envelope have been divided intoseveral segments and mass and energy balance have been appliedin each segment. The results obtained have shown good agreementwith experimental data. Cheng et al. [23] have used the samemethod as He et al. [21] to analyze the total photo-thermal conver-sion process of an experimental LS-2 PTC system. The numericalresults have been compared to the experimental data and goodagreement has been obtained. Solar repowering of the Soma-Athermal power plant in Turkey has been investigated using simula-tions by ZekiYılmazoglu et al. [1]. According to their results, solarrepowering of Soma-A thermal power plant with parabolic troughtype collectors can result in 14% power increment at full load oper-ation of the boiler and 14% CO2 decrement at part load operation ofthe boiler. Kalogirou [24] has presented a detailed thermal modelof a PTC using the EES and validated with known performance ofexisting collectors. Wang et al. [25] have investigated the effectof inserting metal foams in receiver tube of parabolic trough collec-tor on heat transfer. Dongqiang et al. [26] have examined overallheat loss, end loss and thermal emittance of the coating of a newlydesigned receiver of PTC in order to evaluate its thermal character-ization. A heat loss comparison between Solel UVAC3, Schott 2008PTR-70, and Himin PTR-2011 showed that the new receiver hadvery good thermal performance and distinctly decreased heat lossin the parabolic trough solar field.

In this paper, we present a heat transfer model of tracking SolarParabolic Trough Collector. The present work is divided into twoparts. The first one consists in the estimation of the direct normalsolar irradiance (DNI) in selected Algerian sites. Different tilted andtracking collector apertures are considered in order to select themost efficient system for the parabolic trough collector. To com-pare the solar potential in different Algerian locations, the monthlydirect solar radiation has been estimated. In the second part, anumerical model to predict thermal performance of parabolictrough collector under Algerian conditions has been proposed. Inthis model, the climatic and topographical conditions specific tothe area have been taken into account by exploiting the direct solar

radiation. To develop this model, the receiver has been divided intoseveral segments and the energy balance has been applied in eachsegment over a section of the solar receiver. The system of differ-ential equations that govern the heat balances in each segmenthas been solved using the modified Euler method. Three compara-tive studies are drawn up in this part. The first one analyzes thetemperature change, HTF heat gain and heat losses in the absorberand glass envelope for typical winter and summer days. The secondcomparison consists to employ different thermal oils as heat trans-fer fluid in the receiver and to compare their temperature profileand their thermal energy cost. The last one presents a comparisonof HTFs monthly heat gain for different Algerian location in orderto study the influence of the climatic conditions and solar radiationon the performances of the PTC.

2. Estimation of the hourly and daily direct normal solarirradiance in Algeria

Due to the nature of the parabolic trough collector, only the di-rect normal irradiance (DNI) can be used. This limits the PTC sitesto areas with low levels of atmospheric moisture and aerosols, lit-tle or no cloud cover, and high levels of DNI around the year [27].The estimation of the direct normal irradiance (DNI) and the sunnyperiod available allows the identification of the most suitable sitesavailable for deploying the solar parabolic trough collector plants.The analysis of a solar energy system design is typically establishedby predicting its performance over a ‘‘typical’’ ‘‘clear’’ day. Manyclear-day mathematical solar irradiance models may be used topredict the expected maximum hourly DNI [28–30]. Hottel haspresented a model, with good accuracy and simple use, to estimatethe clear-day transmittance of direct solar radiation through clearsky. Hottel’s clear-day model of direct normal solar irradiance isbased on atmospheric transmittance calculations for four differentclimate zones in the globe using Standard Atmosphere [29–36].Using this model for different tracking systems and orientations,we have compared the DNI for summer and winter typical day inthe following cases [36–41]:

- Fixed collector aperture: tilted aperture facing south, horizontalapertures and vertical apertures.

- Single-axis tracking apertures: Horizontal tracking axis ori-ented to North–South, Horizontal tracking axis oriented toEast–West and tilted tracking axis toward the south at the locallatitude angle.

- Two-axis tracking apertures: Polar tracking axis and Azimuth/Elevation tracking axis.

To determinate the hourly direct normal solar irradiance andthe daily direct solar radiation incident on the concentrating mir-ror, a computer program in FORTRAN based on the Hottel model,has been developed. The input data required are the day, the loca-tion, the position and the orientation of the concentrating mirrorand whether the collector is fixed or tracking the sun about oneor two axes. Since it does not change rapidly, the declination anglemay be calculated only once a day. Hourly calculations are thencarried out for the hour angle and the sun’s altitude and azimuth.Figs. 1 and 2 show results for the location of Ghardaia (latitude+32.48� – longitude +3.66� – altitude 500 m). Fig. 1 represents atypical summer clear day and Fig. 2 represents a typical winterclear day.

Figs. 1 and 2 show that the maximum amount of the direct solarirradiance is collected when a collector aperture points directly to-wards the sun. This occurs in the case of two-axis tracking aperture(equatorial and azimuth-altitude two axis). Fig. 1 shows that in thesummer, if the single axis of tracking is oriented to the North/South

0

200

400

600

800

1000

5 10 15 20

fixed to southfixed horizontalfixed verticalhorizontal axis N-Shorizontal axis E-Wtilted axis to south per latitudeequatorial two axisazimut-altitude two axis

Dire

ct s

olar

irra

dian

ce p

er u

nit o

f co

llect

or a

rea,

(W/m

2)

Time (Hours)

Fig. 1. Clear-day direct solar irradiance for different fixed and tracking systemconfigurations for Ghardaia on June 21.

0

200

400

600

800

1000

5 10 15 20

fixed to southfixed horizontalfixed verticalhorizontal axis N-Shorizontal axis E-Wtilted to south per latitudeequatorial two axisazimut-altitude two axis

Dire

ct s

olar

irra

dian

ce p

er u

nit o

f co

llect

or a

rea,

(W/m

2)

Time (Hours)

Fig. 2. Clear-day direct solar irradiance for different fixed and tracking systemconfigurations for Ghardaia on December 21.

0

5

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9 10 11 12

Two axis trackinghorizontal axis N-SHorizontal one axis E-WTilted one axis to the South per Latitude

Mon

thly

mea

n da

ily d

irect

sol

ar

radi

atio

n (M

J/m

2/D

ay)

Month

Fig. 3. Monthly mean daily direct solar radiation for one and two axis trackingsystem in Ghardaia.

194 M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201

(N/S) direction, the reduction in DNI from the two-axis trackingcase is minimal. In the winter, as shown in Fig. 2, the reverse istrue. The performance of the E/W oriented single axis tracked aper-ture approaches that of the two-axis tracked aperture even in themorning and afternoon. For fixed aperture collector cases, the fixedhorizontal aperture receives more direct normal irradiance overtypical summer day than does latitude-tilted and south-facingapertures. In the winter, however, the horizontal fixed surface re-ceives only 49% of the daily energy that a latitude-tilted surfacedoes.

To select the most suitable solar tracking system over the yearfor the collector, we compared the monthly mean daily direct solarradiation with one and two axes tracking apertures in Ghardaia.The results are reported in Fig. 3.

The results in Fig. 3 show clearly that the collector equippedwith two-axis tracking system is most efficient than collectorequipped with one axis tracking system for the whole year. Itcan be seen also that the direct solar radiation provided by hori-zontal tracking axis North–South aperture is important in summer.In winter, the inverse is true; the direct solar radiation provided byhorizontal tracking axis East–West is more important, while thetilted tracking axis aperture to the south per local latitude is theleast efficient for all the year.

In order to compare the importance of direct solar radiation indifferent sites, we report in Fig. 5 the monthly mean daily direct so-lar radiation for a two-axis tracking system at six typical locationsin Algeria namely, Algiers, Annaba, Oran, Béchar, Ghardaia andTamanrasset. As shown in Fig. 4, these locations correspond to dif-ferent climatic regions.

Fig. 5 shows that the most important direct solar radiation po-tential is found in the Sahara for Ghardaia, Béchar and the best inTamanrasset. The monthly mean direct solar radiation varies forOran, Algiers and Annaba between 16 MJ/m2/day and 32 MJ/m2/day, for Bechar between 23 MJ/m2/day and 37 MJ/m2/day, Ghar-daia between 20 MJ/m2/day and 35 MJ/m2/day and Tamanrassetbetween 28 MJ/m2/day and 38 MJ/m2/day. The peak of direct solarradiation occurs in July in the cases of Algiers with 32.25 MJ/m2/day and June for Annaba, Oran, Bechar, Ghardaia and Tamanrassetwith 31.85 MJ/m2/day, 32.83 MJ/m2/day, 36.37 MJ/m2/day,34.61 MJ/m2/day and 38.24 MJ/m2/day, respectively. Knowledgeof solar radiation potential enables us to derive information aboutthe performance of solar energy systems for the cities studied andpossibly elsewhere with similar climatic conditions.

3. Energy balance model of the parabolic trough collector

PTCs are made by bending a sheet of reflective surface into aparabolic shape. Typically thermal fluid circulating through a metalblack tube absorber is placed along the focal line of the receiver.The absorber is covered with a glass envelope, with vacuum orair in the space between the receiver and cover, to decrease con-vective heat losses. The glass envelope protects the absorber fromdegradation and reduces heat losses. It is made typically from Pyr-ex, which maintains good strength and transmittance under hightemperatures [16,21,25]. The distance between the absorber tubeand glass envelope is sufficient to prevent large deflections fromthe hot absorber tube that might cause breakages in the cover[19]. The surface of absorber is typically in stainless steel covered

Fig. 4. Algerian map with the six locations selected [42].

05

10152025303540

31 2 4 5 6 7 8 9 10 11 12Month

OranAlgiers

AnnabaGhardaia

BecharTamanrasset

Mon

thly

mea

n da

ily d

irect

sola

r rad

iatio

n (M

J/m

2/da

y)

Fig. 5. Monthly mean daily direct solar radiation for a two-axis tracking system fordifferent locations in Algeria.

Fig. 6. Two axis azimuth–altitude sun tracking system [38].

Fig. 7. Heat transfer plant for a solar PTC.

M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201 195

with a selective coating that has a high solar absorptance of 95% forsolar radiation, and low thermal emittance (10%, 673 K) for ther-mal radiation loss [26,32,33,44].

The following assumptions have been made in the mathemati-cal model:

(1) One dimensional flow.(2) Vacuum is considered in the annular space; there is no

conduction and no convection from the high temperatureabsorber tube to the low temperature glass envelope.

(3) Constant diameters and concentrator surfaces.(4) Negligible conduction losses at the ends of each trough.(5) The solar PTC has two-axis tracking system that perfectly

follows the sun during the day.

With two-axis tracking, the collector aperture will always benormal to the sun. For aiming an aperture toward the sun at alltimes, rotation about two axes is always required. The type oftracking mechanism commonly in use for this purpose are the azi-muth-altitude tracking systems. The design of the azimuth–alti-tude tracking system includes one axis rotating about the zenithaxis (perpendicular axis) with a tracking angle equivalent to theazimuth angle. While the other axis is parallel to the surface ofthe earth and is rotating with a tracking angle equal to the altitudeangle (see Fig. 6) [38–43].

The heat transfer model is based on an energy balance betweenthe fluid and the surroundings. As shown in Fig. 7, the solar energyis reflected by the mirrors to the collector absorber where it is con-verted into thermal heat. A large fraction of this thermal energy istransferred to the HTF by forced convection. The remaining energyis transferred back to the glass envelope by radiation and natural

196 M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201

convection. This fraction passes through the glass envelope by con-duction and along with the energy absorbed by the glass envelopeis lost to the environment by convection and to the sky by radia-tion [16,22]. In order to obtain the ordinary differential equationsthat govern the heat transfer phenomena, the receiver and enve-lope were divided into several segments and the energy balanceprinciple has been applied in each segment over a section of the so-lar receiver. The equations obtained for each component areshowed below. It includes all equations and correlations necessaryto predict the terms in the energy balances, which depend on thecollector type, HCE condition, nature of HTF, optical properties,and ambient conditions [17,22,32,45].

3.1. Energy balance on the HTF

We start with the HTF heat balance. This could be expressed bya temperature differential equation [17,32,43,45]. For a segment‘‘i’’ of length Dz along the z position, the HTF partial equation isgiven:

mif � Cf �

dTif

dt¼ Q z � Q ðzþDzÞ þ Q i

fconv ; ði ¼ 1;NÞ ð1Þ

From the above equation, the heat balance per unit of segmentlength is:

qf � Af � Cf �dTi

f

dt¼ Ff � qf � Cf � Ti�1

f � Tif

� �=DZ þ hf � p � Dai

� Tia � Ti

f

� �ð2Þ

with

Af ¼ p � Dai

4ð3Þ

The HTF convection heat transfer coefficient hf is given by:

hf ¼ Nuf �kf

Daið4Þ

The Nusselt number depends on the type of flow through theHCE. At typical operating conditions, the flow is well within theturbulent region and the following number correlation developedby Gnielinski [46,47] is used.

Nuf ¼ðf=8Þ � ðRef � 1000Þ � Prf

1þ 12:7 �ffiffiffiffiffiffiffiffif=8

p� Pr2=3

f � 1� � ð5Þ

with

f ¼ ð0:79 � log10ðRef Þ � 1:64Þ�2 ð6Þ

3.2. Energy balance on the receiver

By the analogy with the equation of the HTF, the equation of thetube receiver on the segment ‘‘i’’ is given [17,32,48]:

mia � Ca �

dTia

dt¼ Q asol � Qi

fconv � Q iaconv � Qi

arad; ði ¼ 1;NÞ ð7Þ

The heat balance per unit of segment length is then:

qa �Aa �Ca �dTi

a

dt¼ Q sol �ga �aa�hf �p �Dai � Ti

a�Tif

� �h

�ha �p �Dae � Tia�Ti

v

� ��

r �p �Dae � Ti4

a �Ti4

v

� �1eaþð1�ev Þ�Dae

ev �Dvi

35 ð8Þ

with

Aa ¼p4� D2

ae � D2ai

� �ð9Þ

The direct normal incident solar irradiation per unit length ofreceiver is:

Qsol ¼ Iba �Ac

Lð10Þ

with

Ac ¼ w � L ð11Þ

The effective optical efficiency at the absorber is:

ga ¼ gv � sv ð12Þ

To determine the convection heat transfer coefficient betweenthe absorber and the glass envelope, we suppose the HCE annulusis under vaccum (Pa 6 100 mmHg). The convection heat transferbetween the absorber and the glass envelope occurs by free-molec-ular convection [46]. Then, we have:

ha ¼kstd

Dae2�LnðDvi=DaeÞ þ b � k � Dae

Dviþ 1

� �� � ð13Þ

with

k ¼ 2:331 � 10�20 � Tmoy1

Pa � d2 ð14Þ

b ¼ ð2� aÞ � ð9 � c� 5Þ2a � ðcþ 1Þ ð15Þ

where b is the interaction coefficient and a is the accommoda-tion coefficient.

3.3. Energy balance on the glass envelope

By analogy with the equation of the receiver and the HTF, theequation of the glass envelope on every segment ‘‘i’’ is given by[17,32,45,46]:

miv � Cv �

dTiv

dt¼ Q i

vsol þ Q iarad þ Q i

aconv � Qivrad � Q i

vconv

h iði

¼ 1;NÞ ð16Þ

The heat balance per unit of length is then:

qv � Av � Cv �dTi

vdt¼ Q sol � gv � av þ ha � p � Dae � Ti

a � Tiv

� �h

þr � p � Dae � Ti4

a � Ti4

v

� �1eaþ ð1�ev Þ�Dae

ev �Dvi

� hv � p � Dve � Tiv � Tamb

� �

�r � p � Dve � ev � Ti4

v � T4sky

� �ið17Þ

with

Av ¼p4� D2

ve � D2vi

� �ð18Þ

Tsky ¼ 0:0552 � T1:5amb ð19Þ

The convection heat transfer coefficients form the glass enve-lope to the atmosphere is given by:

hv ¼ Nuair �kair

Dveð20Þ

The Nusselt number depends on whether the convection heattransfer is natural or forced. If there is wind, the convection heattransfer will be forced convection. The correlation developed byZhukauskas will be used to estimate the Nuselt number [46].

M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201 197

Nuair ¼ C � Remair � Prn

air �Pr0air

Pr00air

� �1=4

ð21Þ

The correlation parameters are given in Table 1.The exponential term is given by:

n ¼ 0:37 pour Pr 6 10n ¼ 0:36 pour Pr > 10

Table 2Solar PTC specification used in the model validation [12,49].

Receiver length 7.80 mCollector width 5 mFocal distance 1.84Receiver internal diameter 0.066 mReceiver external diameter 0.07 mReceiver thermal conductivity 54 W/m KGlass cover internal diameter 0.115 mGlass cover internal diameter 0.109 mConcentration ratio 22.42Receiver absorptance 0.906Receiver emittance 0.14Glass cover transmittance 0.95Inclinaison angle modifier 1Heat transfer fluid flow rate 0.0001 m3/sAnnulus pressure 0.01 mmHgDensity of the absorber selective coating 8.02 � 103 kg/m3

3.4. Heat balance for the system

The total HTF heat gained by convection per unit length of thereceiver Qgain (W/m) is given by [17,22,26]:

Q gain ¼PN

i¼1Q ifconv � DZL

ð22Þ

The heat loss of the system per unit length of receiver, Qloss (W/m), includes heat loss by convection and radiation from the absor-ber to the envelope and heat loss by convection and radiation fromthe envelope to the environment:

Q loss ¼PN

1 Q iaconv þ Q i

arad þ Qivrad þ Q i

vconv

� �� DZ

Lð23Þ

The daily HTF heat gained by convection per unit of receiverlength, Qgainday (W/m/day), is given by:

Q gainday ¼ h �XS0�1

i¼1

Q igain ð24Þ

where h is the integration step is 1 h (3600 s) and S0 is the hours ofdaylight.

The daily thermal energy capacity of the heat transfer fluid HTF,E (kW h/kg/day), is given by:

E ¼XS0�1

i¼1

Cf � Tioutf � Tiin

f

� �ð25Þ

with Tioutf is the HTF temperature at the output of the receiver (K)

and Tiinf is the HTF temperature at the input of the receiver (K).

4. Algorithm

To determine the thermal characterisations of the HCE system,the system of ordinary differential equations obtained above hasbeen solved using the modified Euler method. To this end, a globalalgorithm, developed under FORTRAN language, is used.

– The physical properties including the density, the specific heat,the dynamic viscosity, and the thermal conductivity have beentaken at the HTF saturation pressure for different temperatures.

– The chosen collector is of LS-2 type with two axis tracking sys-tem and with a vacuum in the annulus space between theabsorber and the glass envelope. The LS-2 specifications arereported in Table 2. The operational experience of the LS-2 col-lector about 65% of the collectors installed in nine SEGS built inthe Californian desert has indicated good thermal performance[12,49].

Table 1Parameters of the correlation (21).

Re c M

1–40 0.75 0.440–1000 0.51 0.51000–200,000 0.26 0.6200,000–1,000,000 0.076 0.7

– We consider in this preliminary study a number of 100 collec-tors with 7.8 m in length to demonstrate the PTC performanceunder Algerian conditions.

– Ambient Conditions include direct normal solar irradiance,wind speed, ambient temperature from the selected locationfor clear days from different seasons of the year.

5. Results and discussion

The simulation results propose to evaluate the thermal perfor-mance of PTC for different operating conditions, starting from tem-perature profile, heat gain and heat loss of the system, to thenature of the heat transfer fluid depending on geographic locationof the plant.

5.1. Temperature evolution

In this part of the results, Syltherm 800 HTF temperature profilehave been estimated at the output of the receiver and comparedwith the temperature profiles of the absorber and the glass enve-lope. Two typical days of summer and winter are selected in thedaylight period in clear sky to present this simulation. Resultsare presented in Figs. 8 and 9. In order to study the thermal capac-ity of the PTC, Syltherm 800 heat gain and HCE heat loss per unitlength of receiver are also presented in Figs. 10 and 11.

Figs. 8 and 9 present the variation of the outlet temperatures ofthe Syltherm 800 HTF, of the absorber and the envelope as functionof time for typical days of the year (summer and winter). Accordingto these figures, the temperatures of the absorber and the Syltherm800 HTF increase considerably in June compared to December.These temperatures exceed 800 K at 4 p.m. in June and reachesonly 735 K around 5 p.m. for Syltherm 800. This is due to the differ-ence in the DNI and the sunshine duration. We note from Figs. 1and 2 that the DNI reaches 900 W/m2 in typical day of June witha 14 h sunshine duration, whereas it is less than 800 W/m2 in typ-ical day of December with only 9 h sunshine duration. It can also benoticed that the Syltherm 800 temperature continues to increaseafter sunset since the absorber temperature decrease slowly andremains still higher than the fluid temperature.

Absorber specific heat 500 J/kg KDensity of Pyrex glass envelope 2.23 � 103 kg/m3

Glass envelope specific heat 1090 J/kg KHCE shadowing 0.974Tracking error 0.994Geometry error (mirror alignment) 0.98Reflected surface reflectivity 0.93Clean mirror reflectance 0.935Glass envelope emittance 0.86Glass envelope absorptance 0.02

200

400

600

800

1000

1200

8 10 12 14 16 18 20

TfTaTv

Tem

pera

ture

(K)

Time (Hours)

Fig. 8. Syltherm 800, absorber and glass envelope temperatures in day 21December.

200

400

600

800

1000

1200

5 10 15 20

TfTvTa

Tem

pera

ture

(K)

Time (Hours)

Fig. 9. Syltherm 800, absorber and glass envelope temperatures in day 21 June.

0

200

400

600

800

1000

1200

358,

6

438,

1

507,

9

567,

8

618,

1

659,

9

693,

6

720,

9

735,

8

Heat GainHeat Loss

Hea

t gai

n an

d H

eat l

oss

(W/m

)

Temperature (K)

Fig. 10. Syltherm 800 Heat gain and heat loss in 21 December.

0

200

400

600

800

1000

1200

374,

4

450,

8

520,

9

578,

8

627,

5

669,

8

705,

3

735,

3

758

777,

2

796,

4

815,

6

825,

6

832,

9

Heat GainHeat Loss

Hea

t Gai

n an

d H

eat L

oss

(W/m

)

Temperature (K)

Fig. 11. Syltherm 800 Heat gain and heat loss in 21 June.

200

300

400

500

600

700

800

8 10 12 14 16

Syltherm 800Marlotherm SHMarlotherm XSantotherm 59Santotherm LTSyltherm XLTTherminol D12

Tem

pera

ture

(K)

Time (Hours)

Fig. 12. HTFs temperature in 21 December.

300

400

500

600

700

800

5 10 15 20

Syltherm 800Marlotherm SHMarlotherm XSantotherm 59Santotherm LTSyltherm XLTTherminol D12

Tem

pera

ture

(K)

Time (Hours)

Fig. 13. HTFs temperature in 21 June.

198 M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201

We observe clearly in Figs. 10 and 11 that the increases of theheat gain is proportional to the decline of fluid temperature. Themaximum heat gain is reached in the morning; then it starts todrop during the day. It can be seen also that the heat loss followsperfectly the temperature profile of the absorber. The More the

500

600

700

800

900

1000

1100

300 350 400 450 500 550

Den

sity

(kg/

m3)

syltherm 800marlotherm SHmarlotherm Xsantotherm 59

santotherm LTsyltherm XLTtherminol D12

Temperature (K)

Fig. 14. HTFs density with temperature.

1000

1500

2000

2500

3000

3500

300 350 400 450 500 550

heat

cap

acity

(J/k

g.K

)

syltherm 800Marlotherm SHMarlotherm XSantotherm 59

Santotherm LTsyltherm XLTTherminol D12

Temperature (K)

Fig. 15. HTFs heat capacity with temperature.

0,04

0,06

0,08

0,1

0,12

0,14

300 350 400 450 500 550

Con

duct

ivity

(J/m

.K)

syltherm 800marlotherm SHmarlotherm Xsantotherm 59

santotherm LTsyltherm XLTtherminol D12

Temperature (K)

Fig. 16. HTFs thermal conductivity with temperature.

0

0,01

0,02

0,03

0,04

0,05

300 350 400 450 500 550

Visc

osity

(Pa.

s)

syltherm 800marlotherm SHmarlotherm Xsantotherm 59

santotherm LTsyltherm XLTtherminol D12

Temperature (K)

Fig. 17. HTFs viscosity with temperature.

Table 3Cost comparison of HTF thermal energy capacity.

HTF Thermal energy capacityE (kW h/day)

Thermal energy cost(US $/kW h/day)

M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201 199

temperature difference between the absorber and the ambient isimportant, the more the heat loss towards the outside increases,resulting in reduction in heat gain.

Syltherm 800 1.1064 27.1–54.2Syltherm XLT 0.8755 34.3.4–68.5Marlotherm SH 0.9660 1–10.4Marlotherm X 2.5635 0.4–3.9Santotherm 59 0.6470 1.5–15.5Santotherm LT 0.0775 12.9–129Therminol D12 0.5427 1.8–18.4

5.2. Effect of the nature of HTF

In the second part of results, a comparison between the outlettemperature profile of different thermal oils used as heat transferfluids is carried out. The HTF considered in this study are: Syltherm

800, Syltherm XLT, Therminol D12, Santotherm LT, Santotherm 59,Marlotherm SH, and Marlotherm X [50].

The thermal oils considered in this study are not only highlystable but also designed for high temperature liquid phase opera-tion with good heat transport and transfer properties. The fluidsexhibit low potential for fouling and can often remain in servicefor many years. HTFs are also suitable for use in heating and cool-ing systems with good thermal stability in application range andnon-corrosive to materials of construction.

This comparison is considered for the case of winter and sum-mer in daylight period for clear sky. The results are reported inFigs. 12 and 13.

The curves in the above mentioned figures reveal that each typeof fluid has a range of recommended operating temperatures. Thehighest peak of temperature is related to the Syltherm 800 whichexceeds 700 K in December and 750 K in June. The temperatureof the three thermal oils; Marlotherm SH, Therminol D12 an Santo-therm 59 exceed 700 K in June and reach 650 K in December.Whereas Santotherm LT, Marlotherm X and Syltherm XLT showedthe lowest temperature between 600 K and 700 K. We can explainthese differences in HTFs temperatures by considering the evolu-tion of HTFs physical properties (density, heat capacity conductiv-ity and viscosity) reported in Figs. 14–17. We noticed from thesefigures that the four physical properties influence the temperatureevolution of each fluid. Thus, the three fluids (Syltherm 800, Marlo-therm SH and Santotherm 59) which have maximum range of tem-perature have the most important density, conductivity andviscosity and have lowest heat capacity.

A preliminary economic analysis was carried out to comparethe thermal energy cost of the different heat transfer fluids consid-ered in this paper. The cost of the thermal oils represents a fluctu-ation and a remarkable difference from a fluid to another. The costof the oils silicones (Syltherm) varies between 30 and 60 US $/kg.Whereas various aromatic synthetic oils (Marlotherm, Santotherm,and Therminol) are less expensive from about 1 to 10 US $/kg [51].In particular, this preliminary economic analysis makes it possibleto calculate the daily thermal energy cost of the HTFs. Table 3shows the main results of this comparison. We note from theresults that the specific thermal energetic cost of the HTF shows

0

1 1011

2 1011

3 1011

4 1011

5 1011

6 1011

OranSyltherm 800Marlotherm SHSantotherm 59Therminol D12

Mon

thly

mea

n da

ily h

eat g

ain

(J/m

/day

)

Month

0

1 1011

2 1011

3 1011

4 1011

5 1011

6 1011

AlgiersSyltherm 800Marlotherm SHSantotherm 59Therminol D12

Mon

thly

mea

n da

ily h

eat g

ain

(J/m

/day

)

Month

0

1 1011

2 1011

3 1011

4 1011

5 1011

6 1011

AnnabaSyltherm 800Marlotherm SHSantotherm 59Therminol D12

Mon

thly

mea

n da

ily h

eat g

ain

(J/m

/day

)

Month

0

1 1011

2 1011

3 1011

4 1011

5 1011

6 1011

GhardaiaSyltherm 800Marlotherm SHSantotherm 59Therminol D12

Mon

thly

mea

n da

ily h

eat g

ain

(J/m

/day

)

Month

0

1 1011

2 1011

3 1011

4 1011

5 1011

6 1011

BecharSyltherm 800Marlotherm SHSantotherm 59Therminol D12

Mon

thly

mea

n da

ily h

eat g

ain

(J/m

/day

)

Month

0

1 1011

2 1011

3 1011

4 1011

5 1011

6 1011

9 10 11 121 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12 1 2 53 4 6 7 8 9 10 11 12

1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12

TamanrassetSyltherm 800Marlotherm SHSantotherm 59Therminol D12

Mon

thly

mea

n da

ily h

eat g

ain

(J/m

/day

)

Month

Fig. 18. Monthly mean daily heat gain of thermal oils for different locations in Algeria.

200 M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201

its maximum value for the Santotherm LT (129 US $/kW h/day) dueto the lower thermal energy capacity E (0.0775 kW h/day). More-over, the lowest thermal energetic cost corresponds to MarlothermX with a maximum cost of 3.9 US $/kW h/day.

5.3. Effect of the Algerian climatic regions

In this part, the monthly mean daily heat gain of the variousthermal oils under consideration is determined for six Algerianlocations in Fig. 18.

Fig. 18 reveals that the selection of HTF affects heat gain and theHCE thermal performance in the different locations. On the otherhand, the monthly mean daily heat gain is influenced by the cli-matic conditions of each site like the DNI, the ambient temperatureand the wind speed. We observe also from Fig. 18 that the heat

gain received by the Syltherm 800 HTF is the best overall the yearfor the most studied locations. It is noticed that the summer season(high DNI) has the most important monthly mean daily heat gainfor the different fluids in the six selected sites. In addition, the mostimportant heat gain is collected in the South of Algeria for Ghar-daia, Bechar and Tamanrasset.

6. Conclusions

Against increasing energy demand and growing environmentalproblems in Algeria due to the use of fossil fuels, parabolic troughsolar thermal power plants technologies offer interesting opportu-nities for the country. Algeria has favorable climatic conditions forthe construction of parabolic trough solar thermal power plants.The prediction of the monthly mean daily direct solar radiation

M. Ouagued et al. / Energy Conversion and Management 75 (2013) 191–201 201

reveals that the most important DNI potential is found in the Saharafor Ghardaia between 20 MJ/m2/day and 35 MJ/m2/day, Béchar be-tween 23 MJ/m2/day and 37 MJ/m2/day and the best in Tamanras-set between 28 MJ/m2/day and 38 MJ/m2/day. Numerical modelhas been presented in this paper by simulation of the HTF temper-ature change, HTF heat gain and PTC heat loss during the period ofdaylight for typical days. The results show that increase in HTF andabsorber temperature generates increase of heat loss as well as thedecrease of heat gain. The HTFs thermal oils performances havebeen estimated in the Algerian climatic conditions. Each type offluid has a range of recommended operating temperatures. The Syl-therm 800 can reach a temperature between 700 K and 800 K;while the temperature of Marlotherm SH, Therminol D12 andSantotherm 59 varies between 600 K and 750 K. Concerning Santo-therm LT, Marlotherm X and Syltherm XLT, the temperatures do notexceed 700 K. A comparison was also carried out to evaluate theinfluence of HTF price on the thermal energy cost. The maximumvalue of the HTF thermal energetic cost was found for the Santo-therm LT with 129 US $/kW h/day. The estimation of the monthlymean heat gain using different thermal oils in the six locations se-lected from the Algerian territory shows the influence of the solarradiation on HCE performance. The best monthly heat gain was ob-served in increasing direct solar radiation locations which is noticedin the south of the country. Syltherm 800 represents the best ther-mal capacity over all the year for the studied locations compared tothe other heat transfer fluids. Also, temperature range, cost andavailability could dictate which HTF to use.

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