Thermal Model of Cylindrical Trough Collector Receiverparabolic trough solar collector receiver and revealed that the heat transfer achievement of parabolic trough solar receiver show

Thermal Model of Cylindrical Trough Collector

Receiver 1Parvathi Gorantla and

2B. Janarthanan

1Department of Physics, Karpagam Academy of Higher Education,

Eachanari Post, Pollachi Main Road, Coimbatore.

[email protected]

2Department of Physics, Karpagam Academy of Higher Education,

Eachanari Post, Pollachi Main Road, Coimbatore.

Abstract An attempt is made to design, fabricate and analyze a cylindrical trough

solar collector system. An Evacuated Aluminium receiver has been used in

the focal plane of the system to receive the thermal energy and water has been

used as the heat transfer fluid to collect the thermal energy from the present

system. Different heat transfer mechanisms, i.e., the heat transfer mechanism

through convection of the internal receiver, in the circular among the linear

receiver tube and cover glass, from the cover glass tube to the ambience air,

the heat transfer mechanism through glass cover to the linear receiver tube to

cover glass walls, Radiative heat transfer mechanism through Radiation from

the linear receiver tube to glass cover walls and glass cover surfaces to

ambience have been evaluated and interpreted. Thermal modelling for the

proposed system is done and the results are correlated with the empirical

observations intended for validation of the model.

Key Words:Receiver, cylindrical trough solar collector, heat transfer

mechanism.

International Journal of Pure and Applied MathematicsVolume 116 No. 24 2017, 155-171ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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I. Introductory Part

To solve energy crisis problem caused by the consumption of conventional fuels

and the solution of atmospheric problems associated with using of fossil fuels in

recent years, Renewable energy is the one of the leading alternative solution.

Therefore, vital using of solar energy attracts millions of the specialists for a

sustainable development of the human being and reducing the environmental

needs. Solar energy is the one of most cheapest clean energies of the among all

renewable energy sources, because of its zero pollution, the production of green

energy and great scenery in the utilization of different areas such as solar

electricity generation in both thermal and photovoltaic modes, heating, cooling

and solar heating and also on saline water distillation.

The Cylindrical Trough Solar Collector (CTSC) is made by flexing of reflective

material into Cylindrical shape. A metal receiver is painted with mat black color

and to diminish the thermal losses, the metal receiver tube is enclosed by a glass

tube and placed along the focal plane of the collector. To absorb the direct and

reflected sun’s energy, the system is continuously tracked towards the motion of

the Sun. The absorbed and reflected sun’s energy heats the heat transfer fluid

surrounding through the receiver and transfigures the solar energy into useful

heat. In general, the Solar collector is located in an East West path to trace the

solar radiation from the North - South direction or the Collector position located

in the North-South path to track the Solar radiation from East-West direction.

The tracking mode influences the collector faces towards the Sun throughout

the day. However, a North-South field collector absorbs more energy in

summer and East-West located collector absorbs more energy in the winter

throughout the year. So the sense of direction confides on application and

season.

The performance of parabolic solar collector has been refined furthermore and

tested by Omar Behar et al. [1] and studied that the proposed thermal model for

the system predicted the accurate thermal efficiency than engineering equation

solver with an average indefinite of 0.64% correlated to 1.11% for Engineering

Equation solver. The energetic and exegetic comparison of various gas working

fluids in a parabolic trough collector is studied by Eyangelos Bellos [2] and

from the results it has been found that the expected exergetic efficiency is

achieved by the Helium with an operating inlet temperature of 640K and

0.035Kg/s mass flow rate. The investigation of optical and thermal evaluation

of a parabolic collector having a absorber painted with matt black paint and

enclosed with glass cover is performed by Devander Kumar and Sudhir Kumar

[3] and the peak instantaneous thermal efficiency is 66.78% in the month of

July in the horizontal mode, 65.77% in September

International Journal of Pure and Applied Mathematics Special Issue

156

on tending planes of collector. Numerical investigation of thermal

characteristics of the receiver tube of a parabolic collector on laminar stream is

presented by Zeng-Yao Li et al. [4] and the results of the study revealed that the

heat transfer of laminar force through has convection greater than 10%

reflecting the advanced Grashof number than a threshold value. Parabolic

trough collector attached with heat storage tank with heater coupled to Kalina

cycle system has been developed by Milad Ashouri et al. [5] and concluded that

electricity exergy efficiency is increased by 5.24% by the exegetic

developement potential of 62%. Evaluation of optical and thermal performances

of parabolic trough collector’s solar efficiency has been done using engineering

equation solver by Esmail MA Mokheimer et al. [6] and the study revealed that

the maximum and minimum values of optical efficiencies are 73.5% and 61%.

A thermal mathematical analysis for a parabolic trough solar collector has been

done by Ibrahim Halil Yılmaz and Mehmet Sait Soylemez [7] and solved using

Engineering equation solver. From the results, it has been found that the

increase in wind speed influence the thermal efficiency of receiver tube related

to vacuum and wind speed effect decreases thermal efficiency greater than bulk

temperature of 150 °C. A detailed model of the optical efficiency of a parabolic

solar collector with the vacuum receiver has been developed by Weidong

Huang et al. [8] and the effects of different errors of the receiver such as optic

installation error, positional error, reflectors optical characterstics, the vacuum

tube receiver Transmittance and absorptivity on the performance of the

proposed trough system fabricated. Yacine Marif et al. [9] have proposed the

optical and thermal efficiencies of a parabolic solar collector under the

atmospheric conditions of the Sahara Algerian and by using computer program,

single dimensional implicative finite difference technique with the energy

balance developed has given thermal efficiency of about 69.73-72.24%. Soteris

A. Kalogirou [10] has presented a comprehensive thermal model of a parabolic

trough collector. Heat transfer mechanism of receiver tube heating by Non

Uniform Heat Flux and the turbulent flow development in receiver tube due to

buoyancy force effect has been developed by Zhen Huang et al. [11]. The

effects of thermal boundary conditions of the Uniform and Non Uniform heat

fluxes at different solar angles 0°,30°,60° and 90° and effects of different

parameters such as Reynolds number (Re), Grashof number (Gr), Richardson

number (Ri) on the thermal analysis of the receiver has been reviewed.

Nomenclatures

a accommodation coefficient of air (-)

Ar Receiver area of the collector (m2)

b interaction coefficient at convection heat transfer (-)

C Heat transfer coefficient through convection(W/m2C)

Cp Water specific heat capacity(J/KgC)

Dirt internal receiver tube diameter (m)

Dort External receiver tube diameter (m)

F Collector efficient factor

firt Receiver inner surface friction factor, (-)

g gravitational constant (=9.8m/s)

hf HTF heat transfer coefficient through convection at Tf(W/m°C)

K Thermal Conduction of water (W/m-°C)

Kf Heat Conduction of the HTF at temperature of the fluid (W/m°C)

Kθ incident angle modifier (-)

m Water mass flow rate (kg/s)


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A numerical investigation of entropy production in a parabolic trough receiver

at different concentric ratios, inlet and outlet temperatures and at different flow

rates has been carried out by Aggrey Mwesigye et al. [12] and the entropy

generation increases with the increase of the concentric ratio of receiver by

using the second law of thermodynamics. Jianfeng Lu et al. [13] have

developed non-uniform heat transfer model and theoretical investigation of the

parabolic trough solar collector receiver and revealed that the heat transfer

achievement of parabolic trough solar receiver show better performance than

non uniform model. Rubén Barbero et al. [14] approached the use of an

analytical expression from the heat balance differential equation and found that

a maximum in efficiency depend on the concentration factor. The effect of

modification of the receiver in low form concentrated solar thermal collector

has been investigated experimentally by Qiyuan Li et al. [15] and the proposed

design suited to industrial and commercial heating applications. The Cylindrical

trough solar collector was most promising solar thermal technology used in the

1970s. The surface of the receiver coated with black paint or selective absorber

coatings for maximum absorption and low thermal emission of solar thermal

radiation. The glass tube is used to diminish the convection heat transfer from

the receiver tube of the collector. The present model considered all the modes of

heat transfer mechanisms ie., heat transfer mechanism through out the Receiver

tube by convection, the annular between receiver tube and the cover glass, from

cover glass to ambient; conduction heat transfer mechanism receiver tube and

the walls of cover glass and the radiation heat transfer mechanism receiver tube

to the surface of cover glass and from the glass tube to ambient.

II. Energy Model of Receiver

The energy balance of the proposed system for the temperature components has

been written to predict the collector’s performance. The equations have been

solved for the analytical expressions for the temperature elements and it

confides on the ambient condition and cylindrical collector’s optical properties.

The schematic diagram of the receiver tube enclosed with cover glass tube

along with heat transfer fluid flowing through the receiver tube in Figure. 1 (a).

Figure. 1 (b) presents the thermal resistance model attained from the energy

balance of the receiver tube. It has been assumed that the temperature, heat flux

and thermodynamic radiation is consistent around the boundary of the receiver

tube.

Figure 1(a): Schematic diagram of the receiver tube


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Figure 1(b): Thermal resistance Model for the cross section of the receiver tube of

collector

Energy balance equations of the receiver are derived by applying law of

conservation of energy at the receiver tube area of crosssection and are

(1)

(2)

(3)

(4)

(5)

A. Heat Transfer Mechanism through Convection between the Heat Transfer Fluid Along with the Receiver Tube

By applying Newton’s law of cooling, the heat transfer through convection from

the receiver tube inner surface area to the Heat transfer fluid is

h A(Ts-Tα) and for the proposed system it can be written as

(6)

and the heat transfer Coefficient trough Convection for the internal surface

of the receiver is

(7)

where

- Heat transfer through Convection (W/m-°C)

-Convectional heat transfer coefficient through Convection.

The Receiver tubes Heat transfer Area

T Rec- Internal surface temperature of the Receiver tube (°C)

–Heat transfer fluids mean temperature of the (°C)

–Thermal conductivity of the heat transfer fluid in the receiver at

(W/m-°C)

Nu- Nusselt number

– Inner diameter of the receiver tube (m)

TRec and THTF are to be considered self-sufficiently for both the directions such

as angular and longitudinal directions of receiver tube. Nusselt number used for

convectional heat transfer coefficient has been chosen with considering the type

of flow of heat transfer fluid passing through the receiver tube. It has been

considered that during sunshine hours, the flow is turbulent in heat transfer fluid

flow and laminar flow at off sunshine hours. For laminar stream of thermic fluid

in the receiver tube, Reynolds number seems to be less than 2300 and greater


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than 2300 used for turbulent flow. The correspondence for Nusselt number

advanced by Gnielinski [16] has been used for the calculation of convectional

heat transfer mechanism as of the receiver tube to heat transfer fluid.

(8)

For

With (9)

where Prandtl number evaluate by the Heat Transfer Fluid

temperature,

Prandtl number evaluate by the receiver tube inner surface

temperature,

B. Heat Transfer Mechanism during Conduction at the Walls of the Receiver Tube

From Fourier’s equation for thermal conduction, the heat transfer mechanism

through conduction through the walls of receiver of a vacant cylinder [Incropera

and DeWitt 1990] [17] has been found by

(10)

- Thermal conductance of the receiver at the average receiver temperature

is given by

(W/m-°C)

- Internal receiver temperature (°C)

–Outer receiver temperature(°C)

-Internal receiver diameter (m)

-Outer receiver diameter (m)

Thermic conductivity for the receivers made of copper, aluminium and stainless

steel are 385W/mK, 205 W/mK and 16.3 W/mK and calculated using the

equations as

= (Davis [17])

= (Davis [17])

C. Heat Transfer Mechanism from the Receiver Tube to the Outer Glass Tube

Both convection and radiation heat transfer mechanisms occurred among

receiver tube and outer glass tube and depend on the annulus pressure.

Convection heat transfer exists at low pressures (<1 torr) due to molecular

conduction and free convection at high pressures (>1 torr). The temperature

difference between the inner receiver tube with inner surface of the cover glass

envelop led to the radiation heat transfer mechanism and assumed that the glass

cover is translucent to infrared emission and grey surface.


160

Heat Transfer Mechanism through Convection

The two thermal systems deliberated into the present section are heat transfer

mechanism through convection within receiver tube and the wall of glass

tube(Cirt-igt, conve ), Those are the gratis molecular and natural convectional

mechanisms [18]. These pressure annulus and molecular annulus are tested

separately.

Heat Transfer mechanism through Convection of the Annulus at Vacuum

At vacuum annulus (pressure ), the heat transfer through convection

among the inner temperature of the receiver and the glass tube developed by

gratis molecular convection and is given by [19]

(11)

where (12)

for

and

This correspondence slightly over estimates the heat transmit for low

pressures(< 1torr). The air molecule diameter, is attained from [19] and is

identical to 3.55X10-8

Cm, Air’s thermal conductivity is 0.02551W/m°C, the

value of coefficient of interaction is 1.571, molecular collision average free

path is 88.67Cm, and the fraction of the annulus air specific heat is 1.39. The

above mentioned are for the typical temperature of fluid 300°C and pressure is

equivalent to 1torr.

Convection Heat Transfer Mechanism of Pressure in Annulus

The Receivers annulus is vanished or if the receiver is fill with ambient air or

receiver tube is partly crammed with ambient air (pressure is greater than 1torr),

then the heat transfer mechanism through convection involving receiver tube

and cover glass tube developed by usual convection process. For this Raithby

and Holland’s relation in annulated space involving in the cylinder is used [19]

(13)

for 0.7

(14)

(15)


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The critical length in the above equations is given by

Where l conduction heat transfer of annulus gas at Tort-igt (W/m°C)

Prandtl number for gas evaluated at

= Reyleigh number calculated at

at this relationship estimates long, straight and concentric cylinder at

standardized temperatures. All physical characteristics are calculated at the

average temperature (Tort+Tigt) /2.

D. Heat Transfer Mechanism through Radiation

For the derivation of Radiation heat transfer mechanism, few expectations were

made. gas in annulus is Non-participating , The surface area is in grey color,

circulate reflection and irradiation of isothermal lengthy cylinders, the glass

tube is difficult to infrared emission, All these assumptions are not totally

precise. In the case, neither the glass tube nor the selective coating is not grey,

and the glass tube is not absolutely hazy for the complete thermal emission

spectrum [20]. All these errors related with the expectations are tiny. Then the

heat transfer through radiation between the receiver tube and the glass tube is

following with the equation λ.

(16)

E. Heat Transfer through Conduction in the Glass Tube

The Heat transfer mechanism through conduction of the glass tube adapted the

similar equation as the heat transfer mechanism through conduction of the

Receiver tube wall is represented in the section 2.2. The anti reflective

behaviour of the inner and outer glass tube is considered no thermal resistance

or no effect on the emissivity of glass. Because by chemical etching not include

other elements on the glass cover. For this temperature circulation at glass tube

is imagined to be linear. For that the thermal conductivity of glass is imagined.

From [20] the value of thermal conductivity of glass is 1.04.

F. Heat Transfer Mechanism from the Cover Glass Tube to the Ambient

Air

The heat transfer mechanism from the glass tube to the Ambient air by

convection and radiation mechanisms. The convection heat transfer mechanism

will be either unnatural or natural, Due to difference in temperature between the

glass tube and Ambient the radiation heat loss developed in the presence of

wind.


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Convectional Heat Transfer

Based on the Nusselt number the heat transfer mechanism through Convection

is influential. On the base of Nusselt number, the type of convective heat

transfer determined. The convection is natural the Nusselt number is less than

2300 or greater than 2300 the convection is forced. From Newton’s law of

cooling the convectional heat transfer from the glass tube to the atmosphere in

the presence of wind.

(17)

(18)

Where = Heat transfer coefficient from convection of air at

(W/m2°C)

Air’s thermal conductivity (W/m°C)

= Mean Nusselt number based on the outer glass tube diameter

No wind Or Forced Convection

When absence of Wind case, the heat transfer mechanism through convection

from the glass tube to the surroundings developed by natural convection and

equation is given by

(19)

(20)

=Rayleigh number apply for air on the diameter of outer glass tube,

= Air’s thermal diffusivity (m2/sec)

=Prandt l number of air at

Kinematic viscosity of air at (m2/sec)

This relation determines a linear heimel isothermal cylinder and all

characteristics of the fluid at represented film temperature

Convection Heat Transfer in the Presence of Wind

At no wind case, the forced convection developed between the glass cover and

environment. The Nusselt number in present case is approximated with the

relationship for outside forced convectional flow to isothermal cylinder [21]

.7 (21)


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Where C and m are the constants from [23], whereas the value of the constant n

is equivalent to 0.37 for Pr 10 = 0.36 for Pr ˃ 10. All the fluid characteristics

are calculated at temperature Ta, expect Progt calculated at outer glass tube

temperature.

Radiation Heat Transfer Mechanism

The beneficial incoming solar radiation is included in the solar absorption

terms. The heat transfer mechanism through radiation between the glass tube

and sky develops because of the temperature variation between the cover glass

tube and sky. Then the net radiative heat transfer among the cover glass tube to

sky is given by

(22)

The sky is in the Non clear condition and it does not act as a blackbody. In

practice by using of efficient sky temperature to balance the difference, for

simplifying the model, the useful sky temperature is assumed as Ta-8°C

Absorption of Solar irradiation

In the present exemplary, the optical efficiency is predicted and the optical

efficiency terms are estimated and connected to form an develop efficient

optical efficiency, which is ultimately used to conclude the optical loss and

absorption of solar radiation. The different optical properties are used in the

present model are

=Shadowing of the Receiver, 0.974

= Tracking error of collector 0.994

= Geometry error of collector, 0.98

= Reflectance of mirror, 0935

= Dust of mirrors ( :0.88-0.93

= Dust on the receiver,

= Unaccounted 0.96

The terms , , are predicts, by using value of the reflectance of

the mirror and the dirt of mirror and receiver , these dirt

parameters are applicable only for normal solar irradiance. To caluculate

incident angle losses incident angle modifier is taken in to account, which used

for shading the trough, reflection and refraction losses, and coating of receiver

tube incident angle effects.

The above parameters account for collector geometric effects, mirror and glass

envelope effects and a parameter for difference between the data’s of field test

and model. The incident angle modifier is used to account when solar irradiance

is not normal to the collector aperture and it is a function of the solar incident

angle (θ) to normal to the collector aperture.


164

(24)

For the calculation of optical losses optical properties of selective coating

absorptance and emittance are appropriated. The glass tube absorptance and

emmitance are constant and independent of type of selective coating. The glass

tube transmittance, metal tube selective coating absorptance and emittance

depends on the coating type. Both the glass tube transmittance and selective

coating absorptance are constants.

Glass envelope transmittance=0.935(-)

Absorptance of selective coating=0.92 (-)

Selective coating emittance=At 100°C the value is 0.06 and 0.15 at 400°C the

value is 0.15(-)

Selective coating emittance, =0.000327(T+273.15)-0.065971

The Glass Envelope of Solar Irradiance Absorption

The absorption of solar energy in to the glass tube is considered as heat flux and

this heat generation depends on the thickness of the glass. It is an irrelevant

error since the glass tube wall is moderately thin and solar absorption

coefficient is moderately minute and optical efficiency is calculated by

(25)

is estimated by the multiplication of the direct normal solar radiation by the

projected normal absorbed surface area of the collector. ie., collectors aperture

area, and dividing the surface length of collector.

(26)

In the above equation, the incident angle modifier is taken from the above list.

In both the equations every term is temperature independent.

G. Solar Absorption of the Receiver Tube

The sun energy captivated by the receiver tube develops at the surface of the

receiver and considered as heat fluctuation. The equation for the solar

consumption in the receiver tube is given by

(27)

where

In the above equation, the terms are temperature independent and the efficient

optical efficiency of the glass tube, attained from the equalization.

Heat Elimination Factor

The fraction between the real useful energy advance with the captivating

surface at the partial fluid temperature


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(28)

is the collector performance factor

(29)

The factor reffers collector heat loss coefficient is the sum of coefficients for

heat transfer mechanism through conduction of the glass cover, convection heat

transfer through convection from the outer receiver tube to the annular and

space to ambient, and the heat transfer mechanism through radiation from outer

receiver tube to the sky.

III. Result and Discussions

Thermal analysis has been carried out for the present Cylindrical trough solar

concentrator system in the Department of Physics, KAHE, Coimbatore, India.

The conduction heat transfer coefficient for the proposed system has been found

for one of the typical days of the January, 2017. Fig.2 shows the variation of

heat transfer through conduction among inner and external layers of the receiver

tube and inner and outside layers of the outer glass tube. From the graph, it has

been found that the heat transfer through conduction between the inside and

outside layers of the receiver pipe increases from morning hours and reaches the

maximum value at 12.30pm.

Figure 2: Graph between time, heat transfer coefficient through conduction

between inside to the outside glass tubes and Conduction heat transfer coefficient

among inside and outside of the receiver tube

along with gradually decreases at evening hours. The maximum value of the

Conduction heat transfer reaches at 12.30pm is 105.7072W/m2°C. Because the

sun is shining in the morning, hours and the sun shine decreases gradually at

evening hours. The same trend is in the heat transfer through conduction among

the inner and outer glass tube. In Conduction heat transfer between the two

layers of the outer glass tube the maximum value reaches at 1.00pm and

maximum value of the heat transfer through Conduction in outside and inside

layers of the receiver tube are 178.3185 W/m2°C.


166

Figure 3: Graph between heat transfer coefficient through convection between

heat transfer fluid in receiver and inside receiver tube, heat transfer through

Convection between outer receiver tube to the inner glass tube and

Convectional heat transfer coefficient among glass tube to the Ambient with

respect to time.

Fig.3 displays the heat transfer mechanism through convection between Heat

transfer fluid to the Inside receiver tube, Outer receiver tube to the inside cover

glass tube and outside of the glass tube to the ambient. The Solar radiation

transmitted partially reflected by the glass tube. The reflected solar radiation is

transmitted to the outside receiver tube to the heat transport fluid. The

Convectional heat transfer increases gradually in the morning hours and reaches

maximum value at 12.30pm to 1pm afterwards it gradually decreases and

reaches the minimum value.

Figure 4: Graph between heat transfer coefficient through Radiation among

Outside receiver tube and inside the glass tube with respect to Time

Maximum value of the convectional heat transfer coefficient from the heat

transport fluid to the inside receiver tube is 112.1584 W/m2°C, the maximum

value convection heat transfer fluid between outside the receiver tube to the

inside glass tube is 38.74334 W/m2°C, and maximum convection heat transfer

from outer glass tube to the ambient air is 53.97574 W/m2°C. Fig.4 shows the

Graph of Radiation heat transfer coefficient between Outer receiver tube and


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Inner glass tube overtime. The radiation of the increases from morning hours

and reaches maximum value at 1.30pm at afternoon and again it decreases. The

radioactive heat transfer increases from morning hours and reaches the optimum

value at 1.30PM and afterwards again it decreases. The maximum value of the

radiative heat transfer value is 119.2628W/m2°C and the

minimum value is

31.8103 W/m2°C

IV. Conclusion

In the present paper, a thermic representation of a cylindrical trough solar

collectors receiver is explored. The present representation is incorporated by all

the modes of heat transfer mechanisms such as Convectional heat transfer

mechanism, Conductional heat transfer mechanism and radiational heat transfer

mechanism with reference to the time period and heat transfer by convection

through the Receiver tube, in the annular involving the receiver tube and the

cover glass tube and the cover glass to Ambient air, conduction mechanism

through the metal receiver tube and glass walls and the radiation from metal

receiver tube to glass cover and from the glass tube to the ambient. Theoretical

results are in good concurrence with the investigational observations with least

error and the thermal model can be utilized to simulate the system for

optimizing design parameters for the large scale installations.

References

[1] Omar B., Abdallah K., Kamal M., A novel parabolic trough solar collector model–Validation with experimental data and comparison to Engineering Equation Solver (EES), Energy Conversion and Management 106 (2015), 268–281.

[2] Evangelos B., Christos T., Kimon A.A., Ilias D., The use of gas working fluids in parabolic trough collectors-An energetic and exergetic analysis, Applied Thermal Engineering 109 (2016), 1–14.

[3] Kumar D., Kumar S., Year-round performance assessment of a solar parabolic trough collector under climatic condition of Bhiwani, India: A case study, Energy Conversion and Management 106 (2015), 224–234.

[4] Zeng-Yao L., Zhen H., Wen-Quan T., Three-dimensional numerical study on fully-developed mixed laminar convection in parabolic trough solar receiver tube, Energy 113(2016), 1288-1303.

[5] Ashouri M., Vandani A.M.K., Mehrpooya M., Ahmadi M.H., Abdollahpour A., Techno-economic assessment of a Kalina cycle driven by a parabolic Trough solar collector, Energy Conversion and Management 105 (2015), 1328-1339.


168

[6] Mokheimer E.M., Dabwan Y.N., Habib M.A., Said S.A., Al-Sulaiman F.A., Techno-economic performance analysis of parabolic trough collector in Dhahran, Saudi Arabia, Energy Conversion and Management 86 (2014), 622-633.

[7] Yılmaz I.H., Soylemez M.S., Thermo-mathematical modeling of parabolic trough collector, Energy Conversion and Management. 88 (2014), 768–784.

[8] Huang W., Hu P., Chen Z., Performance simulation of a parabolic trough solar collector, Solar Energy 86 (2012), 746–755.

[9] Marif Y., Benmoussa H., Bouguettaia H., Belhadj M.M., Zerrouki M., Numerical simulation of solar parabolic trough collector performance in the Algeria Saharan region, Energy Conversion and Management 85 (2014), 521–529.

[10] Huang Z., Li Z.Y., Tao W.Q., Numerical study on combined natural and forced convection in the fully-developed turbulent region for a horizontal circular tube heated by non-uniform heat flux, Applied Energy, 2194-2208.

[11] Xu R., Wiesner T.F., Closed-form modeling of direct steam generation in a parabolic trough solar receiver, Energy 79 (2015), 163-176.

[12] Mwesigye A., Bello-Ochende T., Meyer J.P., Numerical investigation of entropy generation in a parabolic trough receiver at different concentration ratios, Energy 53 (2013), 114-127.

[13] Lu J., Ding J., Yang J., Yang X., Nonuniform heat transfer model and performance of parabolic trough solar receiver, Energy 59 (2013), 666-675

[14] Barbero R., Rovira A., Montes M.J., Val J.M.M., A new approach for the prediction of thermal efficiency in solar receivers, Energy Conversion and Management 123 (2016), 498–511.

[15] Li Q., Zheng C., Mesgari S., Hewkuruppu Y.L., Hjerrild N., Crisostomo F., Rosengarten G., Scott J.A., Taylor R.A., Experimental and numerical investigation of volumetric versus surface solar absorbers for a concentrated solar thermal collector, Solar Energy 136 (2016), 349-364.

[16] Gnielnski V., New equations for heat and mass transfer in turbulent pipe and channel flow, International Chemical Engineering 562 (2) (1976), 359-63.

[17] Davis J.R., Alloy digest, sourcebook, stainless steels. Materials Park, OH: ASM, 2000


169

[18] Bejan A., Convection Heat Transfer, Second Edition, New York, NY: John Wiley & Sons, 1995.

[19] Touloukian Y.S, DeWitt D.P., Radiative properties, nonmetalic solids, thermophysical properties of matter, New York: Plenum Publishing, 1972.

[20] Incropera F., DeWitt D., Fundamentals of Heat and Mass Transfer, Third Edition, New York, NY: John Wiley and Sons, 1990.

[21] Incropera F., DeWitt D., Bergman T.L., Lavine A.S., Fundamentals of heat and mass transfer, 6th ed. New York: John Wiley and Sons, 2007.


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Thermal Model of Cylindrical Trough Collector Receiverparabolic trough solar collector receiver and revealed that the heat transfer achievement of parabolic trough solar receiver show