investigation of solar hybrid electric/thermal system with radiation

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2013 Article ID 704087 7 pageshttpdxdoiorg1011552013704087

Research ArticleInvestigation of Solar Hybrid ElectricThermal System withRadiation Concentrator and Thermoelectric Generator

Edgar Arturo Chaacutevez Urbiola and Yuri Vorobiev

CINVESTAV del IPN Unidad Queretaro Libramiento Norponiente 2000 76230 Queretaro QRO Mexico

Correspondence should be addressed to Edgar Arturo Chavez Urbiola echavezqrocinvestavmx

Received 16 October 2012 Revised 8 January 2013 Accepted 1 February 2013

Academic Editor Keith Emery

Copyright copy 2013 E A Chavez Urbiola and Y Vorobiev This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

An experimental study of a solar-concentrating system based on thermoelectric generators (TEGs) was performed The systemincluded an electrical generating unit with 6 serially connected TEGs using a traditional semiconductormaterial Bi

2Te3 which was

illuminated by concentrated solar radiation on one side and cooled by running water on the other side A sun-tracking concentratorwith amosaic set of mirrors was used its orientation towards the sun was achieved with two pairs of radiation sensors a differentialamplifier and two servomotors The hot side of the TEGs at midday has a temperature of around 200∘C and the cold side isapproximately 50∘C The thermosiphon cooling system was designed to absorb the heat passing through the TEGs and provideoptimal working conditions The system generates 20W of electrical energy and 200W of thermal energy stored in water witha temperature of around 50∘C The hybrid system studied can be considered as an alternative to photovoltaicthermal systemsespecially in countries with abundant solar radiation such as Mexico China and India

1 Introduction

Solar hybrid electricthermal systems using photovoltaic(PV) panels combined with a waterair-filled heat extractingunit were designed and studied in many laboratories duringthe last three decades [1ndash10] and now are widely usedthroughout the world (England Canada China GreeceIndia and so forth) Some investigations were made [11ndash16] into the possibilities of using thermoelectric generators(TEGs) in solar hybrid systems with the conclusion thatTEGs can be successfully used in these systems instead ofPV panels or together with them An essential increase inthermoelectric conversion efficiency was achieved during thelast decade [17ndash19] which is quite favorable for this kindof TEGrsquos applications With the traditional thermoelectricmaterial Bi

2Te3 the peak electric efficiency that could be

obtained in such a system is 5 [16]Chavez-Urbiola et al [14] investigated different options of

the construction of hybrid solar energy conversion systemsusing TEGs They showed that these systems can be efficient(and economic in case of industrial production) even withthe use of material and devices that are already available on

the market especially in countries with high solar insolation(Mexico China India etc) Below we describe the construc-tion and detailed experimental investigation of one of thehybrid systems analyzed in the above-mentioned paper [14]namely the system with a solar radiation concentrator TEGand water-filled heat extracting unit Circulation of waterwas achieved by thermosiphon effect The experiments wereperformed in Queretaro Mexico at 20∘ of northern latitudein March 2012

2 Description of the Hybrid System

A schematic of the system is shown in Figure 1 where thesolar radiation flux (1) is concentrated by the mosaic mirror(2) onto the electricthermal generating unit (3) (details ofthe TEG are shown in Figure 2) consisting of a radiationabsorber (hot plate) TEG array and a cooling plate that isin direct contact with water-circulating copper tubes Thethermosiphon water loop includes a water storage thermaltank (4) with tubes for water entrance and output

The radiation-concentrating block consisted of 55 planemirrors each having a size equal to that of the TEG array

2 International Journal of Photoenergy

Hot water output

Cold water inputWater

circulation

4

3

1

2

Figure 1 A schematic of the hybrid system

Hot plateCooling plate

TEG arrayWater flow

Figure 2 Thermoelectric generating (TEG) unit

(8 times 12 cm2) providing a concentration ratio (the number ofmirrors focused on the heating plate multiplied by the mirrorreflecting efficiency) of sim52 and considering a reflectionefficiency of 095 The mirrors were positioned in a paraboliccurve with the focal point over the heating plate of the TEGassembly the angle of the inclination of each mirror wascalculated to achieve this effect The block (mirror holder)was attached to the 2-axis sun-tracking system (see [20] fordetails) equipped with 2 pairs of radiation sensors positionedin such a way that the difference in photo response in eachcouple is zero if the mirror holder is orientated towardsthe sun giving the highest illumination of the absorberhot plate The difference in photo response increases withdisorientation (disorientation signal)This difference signal isapplied to a PIC16F877 microcontroller which monitors thesystem using two geared servomotors

The TEG array includes 6 generating elements of the typeTGM-127-14-25 based on Bi

2Te3(made by Kryotherm Saint

Petersburg Russia each element is 4 times 4 times 05 cm3)The elec-trical characteristics of the elements at different temperaturesof the operation were given in a previous publication [14]

3 Calculation of Thermosiphon Loop

For the thermosiphon solar water heaters the flow rate of thecirculating water is conventionally calculated by equating the

pressure head and the friction head Pressure head is causedby density gradients in the loop and the friction head iscaused by friction in the plumbing arrangement

The pressure head in the thermosiphon causes flow tooccur This flow in the collector is driven by the weight dif-ference between the hot water column in the return pipepassing through the collector and the cold fluid column inthe inlet pipe The temperature conditions are given by theinlet temperature of the fluid 119879

119894= 25∘C and the inner surface

temperature of the hot pipe 119879119904= 40∘C the density variations

in the water along the collector are assumed to be linear forthe calculations [21] The desired maximum temperature inthe cooling plate should be around 50∘C

Imagine an opened thermosiphon loop as a U-tubecontaining a fluid with one column filled with hot fluid andthe other with cold fluid A height difference 119889ℎ results dueto the density differences If instead ofU-tube one has a closedloop this 119889ℎ leads to a driving force that produces the flow inthe loop

The continuity equations under static equilibrium in caseof U-tube can be expressed by

ℎ119888120588119888= ℎℎ120588ℎ (1)

and the corresponding pressure head

119889ℎ = ℎℎminus ℎ119888 (2)

which is a function of the temperature and the total height ofthe columnsWe can rewrite (2) as a function of the cold- andhot-side densities and considering a total length 119871

119889ℎ = 119871(2

120588119888

120588119888+ 120588ℎ

minus 1) (3)

To determine the thermal driving forces it is necessaryto take into account the values of 119879

119894and 119879

119904 Using the desired

values of 119879119894= 25∘C and 119879

119904= 40∘C 119889ℎ = 251mm is ob-

tainedThe friction head flow rate and convective coefficient are

interrelated but they also depend on several physical param-eters that must be defined such as piping type materials andpipe length among others

Using the Bernoulli equation an energy conservationanalysis can be made For a pipe system [21] where 119901

1and

1199012are inlet and outlet pressures 119911

1and 119911

2are heights and

1199071and 1199072are the corresponding flow velocities the following

can be written in terms of energy

1199011

120574

+ 1199111+

1199072

1

2119892

+ ℎ119860minus ℎ119877minus ℎ119871=

1199012

120574

+ 1199112+

1199072

2

2119892

1199072 (4)

whereℎ119860is the added energyℎ

119877is the subtracted energyℎ

119871is

the energy loss (friction head) 119892 is the acceleration of gravityand 120574 is the specific weight of the fluid

On the other hand it is necessary to include the Darcyequation for friction head ℎ

119871

ℎ119871= 119891

119871

119863

1199072

2119892

(5)

International Journal of Photoenergy 3

where119871 is the piping length and119863 is its diameter that dependson the flow rate 119907 As the friction factor 119891 depends on theReynolds number Re for the laminar flow [21]

119891 =

64

Re=

64120583

119907119904119863120588

(6)

for a thermosiphon system the pressure head is equalized tofriction head causing the energy loss

119889ℎ = ℎ119871 (7)

As a consequence it is necessary to take into account theenergy losses due to friction (major losses due to friction andminor losses due to changes in the size and direction of theflow path) in the loop

The friction head can then be expressed for this case interms of the friction factor and the flow rate

ℎ119871= 15

1199072

119904

2119892

+ 3517

1199072

119904

2119892

119891 (8)

The first term corresponds to the sum of losses in the inletand outlet where it is common to use the estimation frictioncoefficient 119896

119891= 119891(119871eq119863) = 15 for systems of this kind [21]

Taking in consideration the laminar flow and equalizing thethermal driving head with the friction head we get

119889ℎ = 15

1199072

119904

2119892

+ 3517

119907119904

2119892

64120583

119863120588

(9)

Solving (9) for 119889ℎ = 251mm a flow rate of 119907119904=

00436ms is obtainedOnce the flow rate is defined the convective coefficient

can be calculated [21] For the laminar region in the circularpipe and the temperature of 25∘C the corresponding Nusseltaverage number is

Nu = 366 + 0065 (119863119871)Re Pr1 + [(119863119871)Re Pr]23

= 5051 119871119905lt 119871

(10)

For a thermal length 119871119905asymp 005 Re Pr119863 = 5047m the

condition 119871119905lt 119871 is satisfied and the convection coefficient

can be calculated as

ℎ119888=

Nu 119896119863

=

5051 sdot 0597 (WmK)001892m

= 15484 (Wm2K) (11)

Once ℎ119888and 119907119904are determined we can take them as initial

values for the design of the heat exchanger which starts withcomputer simulations

4 Design of the Heat Exchanger forElectricThermal Generating Unit

In order to determine the optimal configuration of the heatexchanger several configurations were proposed and evalu-ated using commercial finite elementmethod (FEM) software

(COMSOL Multiphysics 42a) For the flow rate the valueobtained earlier was used 119907

119904= 00436 (ms) The cooling

plate temperature must not exceed 50∘C and the hot platemust be around 200∘CThe solar power transformed into heatin the hot plate is around 200W in an area of 008 times 012m2in correspondence with the 2 times 3 array of TEG elements

The heat exchanger was designed to be as simple aspossible a flat plate attached to the commercial pipes InFigure 3 the modeling results for several configurations arepresented changing parameters like hot plate location pipediameter piping array and welding material among othersIn this same figure simulations from Figure 3(a) to 3(c) arefor 1-inch-diameter and from Figure 3(d) to 3(f) are for 34-inch-diameter type K copper pipe according to ASTM B-88standard The red areas are the hottest and the blue ones thecoldest in accordance with the reference bar in the right sideof each model

After evaluating a wide range of configurations twooptions that best meet the conditions were selected andevaluated and the results are shown in Figure 4 One-inchtypeK cooper pipe [21] was used in (a) obtaining amaximumvalue of 424∘C in the center of the surface (red zone)34-inch type K pipe was chosen for case (b) leading to amaximum value of 394∘C distributed in a more uniform wayalong the center of the surface Thus option (b) was chosenfor the experiment

5 Experimental Results

The actual system studied is shown in the photograph inFigure 5 The positions of the thermocouples are indicatedby the red and blue points The red points also indicate thelocation of the ink injection used to give idea of the actualwater flow rate As can be seen in the image the thermoelec-tric assembly is illuminated by the concentration block

The results of the systemrsquos electrical and thermal charac-terization are presented in Figures 6 and 7 To estimate thesystemrsquos efficiency (both electrical and thermal) the intensityof solar radiation was taken as 950Wm which correspondsto the direct normal irradiance (DNI) in Queretaro Mexicoat 20∘ of northern latitude at the equinox time of the yearFirst the electric power generated by the system duringdaytime is shown in Figure 6 The measurements were takenwith a matched load so the data shown gives the maximumpower availableOne can see that the average powerwas 20Wthus producing 120Wh of electric energy between 10 am and4 pm (the total energy obtained during the day was 175Wh)These results correspond to a maximum electric efficiencyof the system of 5 which agrees well with the estimationsmade in [14] and with the results of modeling [16]

Figure 7 presents the thermal characteristics of the hybridsystemThe average hot water tank temperature was approxi-mately 45∘Cwhich is sufficient for domestic applicationsThevariations in the thermic efficiency 120578therm = (119876therm119876sol) times100 observed during the time of the experiment give inaverage of 50 which is higher than that an traditionalPVthermal systems The corresponding thermal power is200W giving the 12 kWh of energy in the 6 h between 10 am


119911

42974

42

40

38

36

34

32518

02040

0

100

200

300

0

100

200

300

119909

119910

Volume temperature (∘C)

(a)

119911 119909

119910

4106141

40

39

38

37

36

35

34

33

32332

02040300

200

100

0

0

100

200

300


(b)

119911 119909

119910

41

40

39

38

37

36

35

34

02040

0

100

200

300

100

150

200

42488

33843

42


(c)

119911

119909119910

01020

300

200

100

00

50

100

35376

35

34

33

32

31

30

29

28

27

26157


(d)

119911

119909119910

100

50

0

300

200

100

0

01020

3908939

38

37

36

35

34

33

32

31

3014


(e)

119911

119909119910

01020

300

200

100

0

0

50

100

37553

37

36

35

34

33

32

31

30

29021


(f)

Figure 3 Computer simulations for different configurations (see text) the colors show the temperature distribution

and 4 pm It can also be seen that the flow rate correlates withthe thermal efficiencymdashhigher flow is accompanied by higherefficiencymdashalthough the water temperature in the tank islower

The cost-efficiency estimation made in our previouspublication for the hybrid system studied [14] showed that atindustrial production (in quantities of hundreds of systems)the cost of the electric energy generation could be 3-4 USdollars per watt peak which is almost the same as the costof the energy generated by PV panels This is in contrastwith the typical case where the cost of energy production

in hybrid systems is usually 50 higher than that in theindividual devices The cost of thermal energy in our systemwith TEGs is lower than that in the traditional PVthermalsystems because of the larger thermal power

6 Conclusions

Performance of the designed hybrid system in the conditionsat Queretaro Mexico at the equinox time of the year hasrevealed that a systems electrical efficiency of 5 and thermalefficiency of 50 with the estimated cost of the electric


200

100

150

4239742

41

40

39

38

37

36

35

3433855

300

200

100

0119911119909

119910


(a)

0

50

100

300

200

100

0

0102039396

39

38

37

36

35

34

33

32

3130818

119911

119909119910


(b)

Figure 4 Computer simulations results for (a) 110158401015840 pipes and (b) 3410158401015840 pipes

Electricthermalgenerating unit

Concentrationblock

Figure 5 Photograph of the system

energy production are practically equal to those of thetraditional photovoltaicthermal systems Thus we concludethat the solar hybrid system with the concentrator and thethermoelectric generator even with the existing componentscan be considered as a reasonable alternative to the traditionalelectricthermal solar hybrid system Taking into account therapid progress in the development of newnanostructured andhighly efficient thermoelectric materials we can expect thatin the near future performance of the TEG-based systemscan surpass that of the traditional solar hybrid systems inparticular in the solar-rich regions having relatively lowlatitude

Nomenclature

119860119904 Effective flow area of the piping m119862119901 Specific heat capacity JKgsdot∘C119863 Piping diameter m119889ℎ Pressure head (thermal driving head) m

119891 Friction factor119892 Gravity msℎ Height mℎ119860 Energy added to the fluid Jℎ119888 Cold fluid column height mℎ119888 Average convection coefficient Wmsdot∘Cℎℎ Hot fluid column height mℎ119871 Friction head inside the piping mℎ119877 Energy removed to the fluid J119896119891 Friction coefficient119896 Thermal conductivity WmK119871 Piping length m119871eq Equivalent pipig length of theminor lossesm119871119905 Thermic inlet length m Mas flow KgsNu Average Nusselt number1199011 Inlet pressure Nm1199012 Outlet pressure Nm

Pr Prandtl number Heat flux W119876sun Solar heat input W119876out Bottoming heat transfer W119876therm Heat transfer to running water WRe Reynolds number119879119890 Outlet temperature in the fluid of the heating

pipe ∘C119879119894 Inlet temperature in the fluid of the heating

pipe ∘C119879119904 Inner surface temperature of the hot pipe ∘C119907 Flow velocity inside the piping ms1199071 Inlet velocity of the fluid ms1199072 Outlet velocity of the fluid ms1199111 Height at the inlet point m1199112 Height at the outlet point m120578therm Thermic efficiency120588 Fluid density kgm120588119888 Cold fluid density kgm120588ℎ Hot fluid density kgm120574 Specific weight of the fluid Nm120583 Dynamic viscosity Kgmsdots


10 11 12 13 14 15 1616

17

18

19

20

21

22

Electric power

Pow

er (W

)

Time (h)

(a)

110 120 130 140 150 160 170 18016

17

18

19

20

21

22

Electric power

Pow

er (W

)

Temperature difference (K)

(b)

Figure 6 Electric power generation as a function of time of day (a) and as a function of the temperature difference between the TEG plates(b)

10 11 12 13 14 15 1620

25

30

35

40

45

50

Mean tank temperature

Tem

pera

ture

(∘C)

Time (h)

(a)

10 11 12 13 14 15 160

10

20

30

40

50

60

70

80

90

100

Thermic efficiencyFlow rate

Time (h)

Ther

mic

effici

ency

()

8

10

12

14

16

18

Flow

rate

(gs

)

(b)

Figure 7 Hot water tank temperature (a) and calculated thermal efficiency of the system and the flow rate in the thermosiphon (b)

Conflict of Interests

Noneof the authors of the presentwork have direct or indirectfinancial relation with the commercial identity ldquoCOMSOLMultiphysics 42ardquo that might lead to a conflict of interests ofany kind for any of the authors

Acknowledgments

The authors are grateful to CONACYT for financial sup-port of the project and for the PhD scholarship of E AChavez-Urbiola They would also like to thank Dr MikeBoldrick of the US Peace Corps for his review of the paper

References

[1] E C Kern Jr and M C Russell ldquoCombined photovoltaic andthermal hybrid collector systemsrdquo inProceedings of the 13th ISESPhotovoltaic Specialists pp 1153ndash1115 Washington DC USAJune 1978

[2] P Raghuraman ldquoAnalytical predictions of liquid and air pho-tovoltaicthermal flat-plate collector performancerdquo Journal ofSolar Energy Engineering vol 103 no 4 pp 291ndash298 1981

[3] H PThomas S JHayter R LMartin and LK Pierce ldquoPV andPVHybrid products for buildingsrdquo in Proceedings of the 16thEuropean Photovoltaic Solar Energy Conference and Exhibitionvol 2 pp 1894ndash1897 Glasgow UK May 2000


[4] H A Zondag D W De Vries W G J Van Helden R J CVan Zolingen and A A Van Steenhoven ldquoThe thermal andelectrical yield of a PV-thermal collectorrdquo Solar Energy vol 72no 2 pp 113ndash128 2002

[5] J Aschaber C Hebling and J Luther ldquoRealistic modelling ofTPV systemsrdquo Semiconductor Science and Technology vol 18no 5 pp S158ndashS164 2003

[6] Y Tripanagnostopoulos ldquoAspects and improvements of hybridphotovoltaicthermal solar energy systemsrdquo Solar Energy vol81 no 9 pp 1117ndash1131 2007

[7] H A Zondag ldquoFlat-plate PV-Thermal collectors and systems areviewrdquo Renewable and Sustainable Energy Reviews vol 12 no4 pp 891ndash959 2008

[8] S Dubey and G N Tiwari ldquoThermal modeling of a combinedsystem of photovoltaic thermal (PVT) solar water heaterrdquo SolarEnergy vol 82 no 7 pp 602ndash612 2008

[9] A IbrahimM Y OthmanMH Ruslan SMat and K SopianldquoRecent advances in flat plate photovoltaicthermal (PVT)solar collectorsrdquoRenewable and Sustainable Energy Reviews vol15 no 1 pp 352ndash365 2011

[10] Y Vorobiev J Gonzalez-Hernandez P Vorobiev and L BulatldquoThermal-photovoltaic solar hybrid system for efficient solarenergy conversionrdquo Solar Energy vol 80 no 2 pp 170ndash1762006

[11] S A Omer and D G Infield ldquoDesign optimization of ther-moelectric devices for solar power generationrdquo Solar EnergyMaterials and Solar Cells vol 53 no 1-2 pp 67ndash82 1998

[12] P Li L Cai P Zhai X Tang Q Zhang and M Niino ldquoDesignof a concentration solar thermoelectric generatorrdquo Journal ofElectronic Materials vol 39 no 9 pp 1522ndash1530 2010

[13] D Kraemer L Hu A Muto X Chen G Chen and MChiesa ldquoPhotovoltaic-thermoelectric hybrid systems a generaloptimization methodologyrdquo Applied Physics Letters vol 92 no24 Article ID 243503 2008

[14] E A Chavez-Urbiola Y Vorobiev and L P Bulat ldquoSolar hybridsystems with thermoelectric generatorsrdquo Solar Energy vol 86no 1 pp 369ndash378 2012

[15] W G J H M V Sark ldquoFeasibility of photovoltaic-thermoelec-tric hybrid modulesrdquo Applied Energy vol 88 no 8 pp 2785ndash2790 2011

[16] D Kraemer K McEnaney M Chiesa and G Chen ldquoModelingand optimization of solar thermoelectric generators for terres-trial applicationsrdquo Solar Energy vol 86 no 5 pp 1338ndash13502012

[17] R Venkatasubramanian E Siivola T Colpitts and B OrsquoQuinnldquoThin-film thermoelectric devices with high room-temperaturefigures of meritrdquo Nature vol 413 no 6856 pp 597ndash602 2001

[18] A Tavkhelidze G Skhiladze A Bibilashvili et al ldquoThermionicconverter with quantum tunnelingrdquo in Proceedings of the IEEE22th International Conference on Thermoelectrics pp 435ndash438August 2002

[19] L P Bulat V T Bublik I A Drabkin et al ldquoBulk nanostruc-tured polycrystalline p-Bi-Sb-Te thermoelectrics obtained bymechanical activation method with hot pressingrdquo Journal ofElectronic Materials vol 39 no 9 pp 1650ndash1653 2010

[20] P Vorobiev and Y Vorobiev ldquoAutomatic Sun tracking solar elec-tric systems for applications on transportrdquo in Proceedings of 7thInternational Conference on Electrical Engineering ComputingScience and Automatic Control (CCE rsquo10) pp 66ndash70 ChiapasMexico September 2010

[21] R L Mott Applied Fluid Mechanics Macmillan New York NYUSA 4th edition 1994

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CatalystsJournal of


Hot water output

Cold water inputWater

circulation

4

3

1

2

Figure 1 A schematic of the hybrid system

Hot plateCooling plate

TEG arrayWater flow

Figure 2 Thermoelectric generating (TEG) unit

(8 times 12 cm2) providing a concentration ratio (the number ofmirrors focused on the heating plate multiplied by the mirrorreflecting efficiency) of sim52 and considering a reflectionefficiency of 095 The mirrors were positioned in a paraboliccurve with the focal point over the heating plate of the TEGassembly the angle of the inclination of each mirror wascalculated to achieve this effect The block (mirror holder)was attached to the 2-axis sun-tracking system (see [20] fordetails) equipped with 2 pairs of radiation sensors positionedin such a way that the difference in photo response in eachcouple is zero if the mirror holder is orientated towardsthe sun giving the highest illumination of the absorberhot plate The difference in photo response increases withdisorientation (disorientation signal)This difference signal isapplied to a PIC16F877 microcontroller which monitors thesystem using two geared servomotors

The TEG array includes 6 generating elements of the typeTGM-127-14-25 based on Bi

2Te3(made by Kryotherm Saint

Petersburg Russia each element is 4 times 4 times 05 cm3)The elec-trical characteristics of the elements at different temperaturesof the operation were given in a previous publication [14]

3 Calculation of Thermosiphon Loop

For the thermosiphon solar water heaters the flow rate of thecirculating water is conventionally calculated by equating the

pressure head and the friction head Pressure head is causedby density gradients in the loop and the friction head iscaused by friction in the plumbing arrangement

The pressure head in the thermosiphon causes flow tooccur This flow in the collector is driven by the weight dif-ference between the hot water column in the return pipepassing through the collector and the cold fluid column inthe inlet pipe The temperature conditions are given by theinlet temperature of the fluid 119879

119894= 25∘C and the inner surface

temperature of the hot pipe 119879119904= 40∘C the density variations

in the water along the collector are assumed to be linear forthe calculations [21] The desired maximum temperature inthe cooling plate should be around 50∘C

Imagine an opened thermosiphon loop as a U-tubecontaining a fluid with one column filled with hot fluid andthe other with cold fluid A height difference 119889ℎ results dueto the density differences If instead ofU-tube one has a closedloop this 119889ℎ leads to a driving force that produces the flow inthe loop

The continuity equations under static equilibrium in caseof U-tube can be expressed by

ℎ119888120588119888= ℎℎ120588ℎ (1)

and the corresponding pressure head

119889ℎ = ℎℎminus ℎ119888 (2)

which is a function of the temperature and the total height ofthe columnsWe can rewrite (2) as a function of the cold- andhot-side densities and considering a total length 119871

119889ℎ = 119871(2

120588119888

120588119888+ 120588ℎ

minus 1) (3)

To determine the thermal driving forces it is necessaryto take into account the values of 119879

119894and 119879

119904 Using the desired

values of 119879119894= 25∘C and 119879

119904= 40∘C 119889ℎ = 251mm is ob-

tainedThe friction head flow rate and convective coefficient are

interrelated but they also depend on several physical param-eters that must be defined such as piping type materials andpipe length among others

Using the Bernoulli equation an energy conservationanalysis can be made For a pipe system [21] where 119901

1and

1199012are inlet and outlet pressures 119911

1and 119911

2are heights and

1199071and 1199072are the corresponding flow velocities the following

can be written in terms of energy

1199011

120574

+ 1199111+

1199072

1

2119892

+ ℎ119860minus ℎ119877minus ℎ119871=

1199012

120574

+ 1199112+

1199072

2

2119892

1199072 (4)

whereℎ119860is the added energyℎ

119877is the subtracted energyℎ

119871is

the energy loss (friction head) 119892 is the acceleration of gravityand 120574 is the specific weight of the fluid

On the other hand it is necessary to include the Darcyequation for friction head ℎ

119871

ℎ119871= 119891

119871

119863

1199072

2119892

(5)



119891 =

64

Re=

64120583

119907119904119863120588

(6)


119889ℎ = ℎ119871 (7)



ℎ119871= 15

1199072

119904

2119892

+ 3517

1199072

119904

2119892

119891 (8)




119889ℎ = 15

1199072

119904

2119892

+ 3517

119907119904

2119892

64120583

119863120588

(9)




Nu = 366 + 0065 (119863119871)Re Pr1 + [(119863119871)Re Pr]23

= 5051 119871119905lt 119871

(10)




ℎ119888=

Nu 119896119863

=

5051 sdot 0597 (WmK)001892m

= 15484 (Wm2K) (11)















119911

42974

42

40

38

36

34

32518

02040

0

100

200

300

0

100

200

300

119909

119910


(a)

119911 119909

119910

4106141

40

39

38

37

36

35

34

33

32332

02040300

200

100

0

0

100

200

300


(b)

119911 119909

119910

41

40

39

38

37

36

35

34

02040

0

100

200

300

100

150

200

42488

33843

42


(c)

119911

119909119910

01020

300

200

100

00

50

100

35376

35

34

33

32

31

30

29

28

27

26157


(d)

119911

119909119910

100

50

0

300

200

100

0

01020

3908939

38

37

36

35

34

33

32

31

3014


(e)

119911

119909119910

01020

300

200

100

0

0

50

100

37553

37

36

35

34

33

32

31

30

29021


(f)





6 Conclusions



200

100

150

4239742

41

40

39

38

37

36

35

3433855

300

200

100

0119911119909

119910


(a)

0

50

100

300

200

100

0

0102039396

39

38

37

36

35

34

33

32

3130818

119911

119909119910


(b)



Concentrationblock



Nomenclature







10 11 12 13 14 15 1616

17

18

19

20

21

22

Electric power

Pow

er (W

)

Time (h)

(a)

110 120 130 140 150 160 170 18016

17

18

19

20

21

22

Electric power

Pow

er (W

)


(b)


10 11 12 13 14 15 1620

25

30

35

40

45

50


Tem

pera

ture

(∘C)

Time (h)

(a)

10 11 12 13 14 15 160

10

20

30

40

50

60

70

80

90

100


Time (h)

Ther

mic

effici

ency

()

8

10

12

14

16

18

Flow

rate

(gs

)

(b)




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



119891 =

64

Re=

64120583

119907119904119863120588

(6)


119889ℎ = ℎ119871 (7)



ℎ119871= 15

1199072

119904

2119892

+ 3517

1199072

119904

2119892

119891 (8)




119889ℎ = 15

1199072

119904

2119892

+ 3517

119907119904

2119892

64120583

119863120588

(9)




Nu = 366 + 0065 (119863119871)Re Pr1 + [(119863119871)Re Pr]23

= 5051 119871119905lt 119871

(10)




ℎ119888=

Nu 119896119863

=

5051 sdot 0597 (WmK)001892m

= 15484 (Wm2K) (11)















119911

42974

42

40

38

36

34

32518

02040

0

100

200

300

0

100

200

300

119909

119910


(a)

119911 119909

119910

4106141

40

39

38

37

36

35

34

33

32332

02040300

200

100

0

0

100

200

300


(b)

119911 119909

119910

41

40

39

38

37

36

35

34

02040

0

100

200

300

100

150

200

42488

33843

42


(c)

119911

119909119910

01020

300

200

100

00

50

100

35376

35

34

33

32

31

30

29

28

27

26157


(d)

119911

119909119910

100

50

0

300

200

100

0

01020

3908939

38

37

36

35

34

33

32

31

3014


(e)

119911

119909119910

01020

300

200

100

0

0

50

100

37553

37

36

35

34

33

32

31

30

29021


(f)





6 Conclusions



200

100

150

4239742

41

40

39

38

37

36

35

3433855

300

200

100

0119911119909

119910


(a)

0

50

100

300

200

100

0

0102039396

39

38

37

36

35

34

33

32

3130818

119911

119909119910


(b)



Concentrationblock



Nomenclature







10 11 12 13 14 15 1616

17

18

19

20

21

22

Electric power

Pow

er (W

)

Time (h)

(a)

110 120 130 140 150 160 170 18016

17

18

19

20

21

22

Electric power

Pow

er (W

)


(b)


10 11 12 13 14 15 1620

25

30

35

40

45

50


Tem

pera

ture

(∘C)

Time (h)

(a)

10 11 12 13 14 15 160

10

20

30

40

50

60

70

80

90

100


Time (h)

Ther

mic

effici

ency

()

8

10

12

14

16

18

Flow

rate

(gs

)

(b)




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


119911

42974

42

40

38

36

34

32518

02040

0

100

200

300

0

100

200

300

119909

119910


(a)

119911 119909

119910

4106141

40

39

38

37

36

35

34

33

32332

02040300

200

100

0

0

100

200

300


(b)

119911 119909

119910

41

40

39

38

37

36

35

34

02040

0

100

200

300

100

150

200

42488

33843

42


(c)

119911

119909119910

01020

300

200

100

00

50

100

35376

35

34

33

32

31

30

29

28

27

26157


(d)

119911

119909119910

100

50

0

300

200

100

0

01020

3908939

38

37

36

35

34

33

32

31

3014


(e)

119911

119909119910

01020

300

200

100

0

0

50

100

37553

37

36

35

34

33

32

31

30

29021


(f)





6 Conclusions



200

100

150

4239742

41

40

39

38

37

36

35

3433855

300

200

100

0119911119909

119910


(a)

0

50

100

300

200

100

0

0102039396

39

38

37

36

35

34

33

32

3130818

119911

119909119910


(b)



Concentrationblock



Nomenclature







10 11 12 13 14 15 1616

17

18

19

20

21

22

Electric power

Pow

er (W

)

Time (h)

(a)

110 120 130 140 150 160 170 18016

17

18

19

20

21

22

Electric power

Pow

er (W

)


(b)


10 11 12 13 14 15 1620

25

30

35

40

45

50


Tem

pera

ture

(∘C)

Time (h)

(a)

10 11 12 13 14 15 160

10

20

30

40

50

60

70

80

90

100


Time (h)

Ther

mic

effici

ency

()

8

10

12

14

16

18

Flow

rate

(gs

)

(b)




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


200

100

150

4239742

41

40

39

38

37

36

35

3433855

300

200

100

0119911119909

119910


(a)

0

50

100

300

200

100

0

0102039396

39

38

37

36

35

34

33

32

3130818

119911

119909119910


(b)



Concentrationblock



Nomenclature







10 11 12 13 14 15 1616

17

18

19

20

21

22

Electric power

Pow

er (W

)

Time (h)

(a)

110 120 130 140 150 160 170 18016

17

18

19

20

21

22

Electric power

Pow

er (W

)


(b)


10 11 12 13 14 15 1620

25

30

35

40

45

50


Tem

pera

ture

(∘C)

Time (h)

(a)

10 11 12 13 14 15 160

10

20

30

40

50

60

70

80

90

100


Time (h)

Ther

mic

effici

ency

()

8

10

12

14

16

18

Flow

rate

(gs

)

(b)




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


10 11 12 13 14 15 1616

17

18

19

20

21

22

Electric power

Pow

er (W

)

Time (h)

(a)

110 120 130 140 150 160 170 18016

17

18

19

20

21

22

Electric power

Pow

er (W

)


(b)


10 11 12 13 14 15 1620

25

30

35

40

45

50


Tem

pera

ture

(∘C)

Time (h)

(a)

10 11 12 13 14 15 160

10

20

30

40

50

60

70

80

90

100


Time (h)

Ther

mic

effici

ency

()

8

10

12

14

16

18

Flow

rate

(gs

)

(b)




Acknowledgments


References
































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

investigation of solar hybrid electric/thermal system with radiation

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