Research Article Design and Testing of a Shell-Encapsulated Solar...

Research ArticleDesign and Testing of a Shell-Encapsulated Solar Collector withthe Compound Surface Concentrators

Hongfei Zheng Gang Wu Jing Dai and Yanyan Ma

School of Mechanical Engineering Beijing Institute of Technology Beijing 100081 China

Correspondence should be addressed to Hongfei Zheng 343038311qqcom

Received 23 November 2014 Accepted 31 January 2015

Academic Editor Yuehong Su

Copyright copy 2015 Hongfei Zheng et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents design and testing of a shell-encapsulated solar collector which can be used in north area of China for wall-amounting installationThe designed solar collector is based on the combination of a novel compound curved surface concentratorand an aluminum concentric solar receiver which is contained in a glass evacuated-tube As there is no perforative joint betweenthe double-skin glass evacuated-tube and the aluminum concentric solar receiver the difficulty of vacuum keeping for a glass-metaljoint is avoided The cavity shell provides an additional thermal insulation to reduce heat loss of the designed solar collector Theworking principle of the compound curved surface concentrator is described The ray-tracing results are given to show the effectof deviation angle of the concentrator on its optical efficiency hence determining its maximum acceptance angle A prototype ofthe designed solar collector has been constructed and tested under the sunny winter weather condition The experimental resultsindicate that the hot water temperature higher than 80∘C with a daily average efficiency of about 45sim50 has been achieved at theaverage ambient temperature below 0∘C so the designed solar collector can produce hot water at a useful temperature in winter

1 Introduction

Generically there are two types of solar collectors beingused widely that is conventional flat plate collectors andrecently-developed glass evacuated tube collectorsThey havetheir individual advantage and disadvantage The flat platesolar collectors have the advantages of bearing mechanicalstress no immediate leaking once partly damaged and easierarchitectural integration while their disadvantages are lowoperating temperature in winter and being subject to theproblem of freezing damage Reversely the glass evacuatedtube collectors can maintain a sufficiently high operatingtemperature at the ambient temperature below the freezingpoint in winter for example at the outdoor temperaturehigher than ndash10∘C the collection temperature can exceed45∘C However they have the disadvantage of easily beingdamaged under mechanical stress especially for the largescale systemThe evacuated tube solar collectors have signifi-cantly higher efficiency than the flat plate collectors at highercollection temperature or lower ambient temperature owingto vacuum thermal insulation Zambolin and Del Col [1] had

experimentally compared these two types of solar collectorsand found that the evacuated tube collector could maintainan efficiency of above 50 at the average hot water tem-perature of about 60∘C ambient temperature of 20∘C andsolar irradiance of 700Wm2 Solar concentrators could beused to enhance the thermal performance of the evacuatedtube collectors for higher operating temperature applicationor the situation of low solar irradiation The concentration-type solar collector designed by Snail et al [2] has an opticalefficiency of 65 and a thermal efficiency of better than50 at fluid temperatures of 200∘C without tracking thesun In comparison Rabl et al [3] had studied combinationof nonevacuated solar collectors with compound parabolicconcentrators (CPC) Li and Wang [4] have investigated acombined trough parabolic concentrator and evacuated tubesolar collector system and measured an efficiency of about70 at the outlet water temperature of 105∘C Although theproduction of CPC optical surfaces can be done only byexpensive single-point machining techniques it is possible toapproximate the complex surfaces of the CPC by means of alimited number of simpler shapes without severe efficiency

Hindawi Publishing CorporationInternational Journal of PhotoenergyVolume 2015 Article ID 130187 10 pageshttpdxdoiorg1011552015130187

2 International Journal of Photoenergy

losses [5] Adsten et al [6] have proposed a so-calledMaReCodesign of solar concentrators for stationary installationNorton et al [7] gave many researches to symmetric andasymmetric linear compound parabolic concentrators whichis very useful for us to design some novel concentrators

On the other hand in some situation the collector needsbe mounted on the wall For example in very high buildingthe users hope to fix their solar collector on the south wall ifit is available Ji et al [8] described a wall-mounted hybridphotovoltaicwater-heating collector The evacuated tubesolar collectors are particularly suitable for wall-mountinginstallation in the area of high latitude [9] However thevacuum tube collector is cram with water which adds its heatmass so that it gives very low temperature hot water in winterIn order to get higher temperature thermal energy Adstenet al (2005) evaluated various asymmetric CPC designs forstand-alone roof or wall-mounted installations Mills et al[10] also researched the characteristics of asymmetric CPCsolar collectors with tubular receiver and indicated that theycan be used in some special occasion

In addition the receiver used in the compound parabolicconcentrator is very important Mills et al [10] discussedthe problems about evacuated tube solar receivers mountedin special concentrator Tripanagnostopoulos et al [11] alsodiscussed the problem about CPC solar collectors couplingwith flat bifacial absorbers All of the previous work is topursuit the higher working temperature of the collector or letthe collectors be able to operate in winter

This study will present design and testing of a new-typesolar collector based on incorporation of a novel compoundcurved surface concentrator with an aluminum concentricsolar receiver enclosed in a glass evacuated tubeThedesignedsolar collector would be suitable for wall-mounting installa-tion in the area of high latitude

2 Design of the System

Theuse of a novel compound curved surface solar concentra-tor is a key element in the design of a new-type solar collectorhot water system for wall-mounting installation Combinedwith the glass evacuated tube solar receiver the solar collectorsystem would be able to provide hot water at the temperatureof above 70∘C in the winter The detailed innovative design isdescribed as follows

21 Design of the Compound Curved Surface ConcentratorThe key component of the proposed new-type solar collectorsystem is a novel trough-type compound curved surfaceconcentrator the cross-section of which is shown in Figure 1The compound concentrator consists of two upper parabolicmirrors formed from a paraboloid ldquo1rdquo two plane mirrors ldquo2rdquoand a parabolic mirror ldquo3rdquo at the base The heights of thetwo upper parabolic mirrors are not equal to give a tiltedaperture the angle of which is associated with geographiclatitude The central line of a tubular receiver ldquo4rdquo overlapswith the focus line of the paraboloid ldquo1rdquo while it may slightlybe above the focus line of the paraboloid ldquo3rdquo The incomingrays within a certain angle to the symmetrical axis of theconcentrator are mainly reflected by the upper parabolic

2120575A

2120575A

A

d

4

1

DE

O

2 F1F2 G

C

3

2120575B

2120575B

B120572

B998400y

x

Figure 1 A cross-sectional view of the compound curved surfaceconcentrator

mirrors to the receiver ldquo4rdquo and the rest are reflected by theplane mirrors and the base parabolic mirror which may re-reflect the reflected rays from the mirrors ldquo1rdquo to the receiverldquo4rdquo

211 Design Considerations On the cross-section of theconcentrator as shown in Figure 1 119860119863 and 119861119862 are the leftand right sections of the parabolic curve ldquo1rdquo with its focus onthe point 119865

1 which is described by

2119901

1(119910 minus 119897) = 119909

2

(for upward opening 1199011gt 0) (1)

where 1199011is the focal parameter and 119897 is the vertical distance

from the vertex of the parabolic curve ldquo1rdquo to the 119909-axisThe parabolic curve is truncated with straight line 119860119861

which therefore forms the aperture of the parabolic curveThe tilt angle 120572 of the line 119860119861 may be the same as localgeographic latitude The straight line segments 119863119864 and 119862119866are vertical to the 119909-axis and symmetrical about the 119910-axis The distance between 119863119864 and 119862119866 and their reasonablelengths are chosen in accordance with the diameter of thetubular receiver and also in order tomaximize the acceptanceangle 119864119874119866 is a section of the parabolic curve ldquo3rdquo with itsfocus at the point 119865

2and its vertex on the 119909-axis The 119864119874119866

is described by

2119901

2119910 = 119909

2


where 1199012is the focal parameter Therefore the cross-section

of the compound curved surface comprises of the paraboliccurved segments 119860119863 and 119861119862 straight line segments119863119864 and119862119866 and parabolic curved segment 119864119874119866

212 Geometric Concentration Ratio and Maximum Accep-tance Angle As shown in Figure 1 the two angles 2 sdot 120575

119860and

2 sdot 120575

119861are formed between the tangent lines from the points

International Journal of Photoenergy 3

119860 (119909

119860 119910

119860) and 119861 (119909

119861 119910

119861) to the cross-section circle of the

receiver ldquo4rdquo They are given by

sin 120575119860asymp

1198892

radic(119909

1198651

minus 119909

119860)

2

+ (119910

1198651

minus 119910

119860)

2

=

1198892

radic(119909

1198602119901

1)

2

+ 119901

1

2

sin 120575119861=

1198892

radic(119909

119861minus 119909

1198651

)

2

+ (119910

119861minus 119910

1198651

)

2

=

1198892

radic(119909

1198612119901

1)

2

+ 119901

1

2

(3)

As 1199092119860

gt 119909

2

119861

there is 120575119860lt 120575

119861 It is obvious that angle 120575

119860or

angle 120575119861represents the maximum allowable deviation angle

of the concentratorrsquos symmetrical axis from the incoming raysin order to reflect the rays from point 119860 or point 119861 to thetubular receiver ldquo4rdquo Relative to the normal incidence rays theinclined incoming rays from the left may hardly strike on themirror 119860119863 so 120575

119860may be considered as the lower acceptance

angle of the concentrator All the inclined incoming rays fromthe right at the deviation angle which is no larger than 120575

119860can

be directly reflected to the receiver by the parabolic mirror119860119863 Similarly 120575

119861may be considered as the upper acceptance

angle of the concentrator In fact each point on the parabolicmirrors 119860119863 and 119861119862 has its individual maximum allowabledeviation angle According to (3) the individual maximumallowable deviation angle obviously increases when the pointis moving downTherefore when the deviation angle is largerthan 120575

119860or 120575119861 part of the incoming rays can still be reflected

directly to the receiver by the lower part of the parabolicmirrors 119860119863 and 119861119862 and some other may reach the receiverthrough the second reflection by the plane mirror ldquo2rdquo andbase parabolic mirror ldquo3rdquo For this reason the maximumacceptance angle 120575max could be much larger than 120575

119860and

120575

119861 A little more detail about 120575max will be discussed in the

following section If the tilt angle of the compound curvedsurface concentrator is adjusted to follow the sun the angle120575

119860(lt 120575119861) could be used to determine the time interval for

adjusting the tilt angle In other words this angle can alsorepresent the maximum allowable tracking deviation

The geometrical concentration ratio of the compoundcurved surface concentrator may be defined as

119862 =

119860119861

120587119889

(4)

where 119860119861 is the width of the aperture 119860119861 and 119889 is thediameter of the tubular receiver If using the width of theaperture119860119861 and the diameter of the tubular receiver to definethe geometrical concentration ratio then 119862 is 119862 = 119860119861119889

Equations (1)ndash(4) may be used to determine the accep-tance angle and geometrical concentration ratio of the con-centrator for a given geometry For example assuming thatthe concentrator had the following geometrical parameters119889 = 50mm 119897 = 12mm 119901

1= 44 119901

2= 50 119909

119861= 108mm and

120572 = 265

∘ there is that 120575119860= 6

∘Themaximum receiving angle120575max is 18

∘ and the geometric concentrating ratio 119862 = 184(for the perimeter of the tubular receiver) or 119862 = 58 (for thediameter of the tubular receiver)

D

O

Q

C

120575B

Figure 2 Illustrated diagram of tracking error

40 60 80 100 120 140 1604

8

12

16

20

24

28

32

Trac

king

accu

racy

requ

irem

ent(

∘ )

Distance from original point (mm)

Figure 3 Variation of tracking accuracy requirement with thedistance

213 Tracking Accuracy Requirement Ideally if the troughconcentrator could track the sun accurately all incomingsunlight would be reflected by the trough surface to the focusreaching the receiver However there is a tracking error thatis the symmetrical axis of the trough being deviated fromthe sunlight as shown in Figure 2 For any receiver beingused there is a maximum allowable deviation angle whichmay depend on the position on the trough surface Thisangle actually represents tracking accuracy requirement for acertain point As seen from Figure 2 themaximum deviationangle 120575 changes with the position of point on the troughsurface

For the design parameters described in the previoussection the variation of 120575 with the position of point wascomputed and shown in Figure 3 It is clear that the trackingaccuracy requirement for different point is different Forexample the tracking accuracy was 93∘ when the distancefrom original point is 108mm 53∘ for 1437mm distance


Clockwise deviation by 10∘ Clockwise deviation by 12∘ Clockwise deviation by 17∘

Anticlockwise deviation by 6∘ Anticlockwise deviation by 7∘ Anticlockwise deviation by 15∘

Figure 4 Ray-tracking for various deviation angles of the concentrator

It can be found that the tracking accuracy requirement will behigher when a reflection point is more distant from the focuspoint The minimum value of these calculated maximumallowable deviation angle may be considered as the trackingaccuracy requirement of the whole trough if all incomingsunlight is expected to reach the receiver

214 Ray-Tracing Analysis The compound curved surfaceconcentrator with the above assumed geometrical parameterswas modeled in the 3D design software ProENGINEERand the physical model was saved as IGES format andthen was imported into the optical simulation softwareLightTools for ray-tracing analysis The incident rays wereassumed to be parallel and the number of rays was setat 100 Ray-tracing simulation was performed for variousdeviation angles Figure 4 shows the ray-tracing results forthe clockwise deviation angles of 10∘ 12∘ and 17∘ and theanticlockwise deviation angles of 6∘ 7∘ and 15∘

It is apparent that the deviation angle affected the numberof the rays reaching the receiver In order to comparethis effect between different deviation angles it would beconvenient to define an ideal optical efficiency which isthe ratio of the number of rays reaching the receiver to

the total number of incoming rays According to the resultsof ray-tracing analysis the relationship between the idealoptical efficiency and deviation angle can be obtained andis shown in Figure 5 It can be seen that when the deviationangle of the concentratorrsquos symmetrical axis is between 12∘clockwise and 6∘ anticlockwise all incoming rays can reachthe receiver the ideal optical efficiency is 10 When it is17

∘ clockwise the ideal optical efficiency is 081 and whenit is 17∘ anticlockwise the ideal optical efficiency is only058 The reason for this difference could be explained asfollows as discussed in the previous section the individualmaximum allowable deviation angle of each point on theparabolic mirrors ldquo1rdquo decreases when the point is movingup As the height of the leftward parabolic mirror is largerthan the rightward parabolic mirror the average maximumallowable deviation angle of the leftward parabolic mirror issmaller than the rightward one hence less percentage of theincoming rays are reflected to the receiver when the deviationangle is larger than 120575

119860and 120575

119861 It can be also expected that

the complete curve of the ideal optical efficiency would lookalmost symmetrical crossing the vertical line 119886119887which passesthrough the clockwise deviation angle about 25∘ shown as inFigure 5 But actually the rightward section of curve is slightly


0 5 10 15 20055

060

065

070

075

080

085

090

095

100

Opt

ical

effici

ency

Deviation angle

Clockwise Anticlockwise

a

bminus20 minus15 minus10 minus5

Figure 5 The relationship between the ideal optical efficiency anddeviation angle of the concentrator

steeper than the leftward section The two end points of theflat section of the curve are corresponding to the upper andlower acceptance angleThemaximum acceptance angle maybe determined by extending the efficiency curve to interceptwith the 0 efficiency line It is worthwhile to mention thatFigure 5 would look somewhat different if a fixed densityof rays instead of a given number is chosen for ray-tracinganalysis

22 Design of the Sun Tracking System Seen from Figure 5the designed compound surface concentrator has a clockwiseacceptance angle of 135∘ and anticlockwise acceptance angleof 95∘ in which the optical efficiency is more than 90 Itwill give an overall acceptance angle of 23∘ So sun trackingis necessary in order that the concentrator could collect thedirect solar radiation as much as possible For the wall-mounting installation if the biggest solar altitude angle is 90∘then the daily adjustment number for tracking the sun is only9023 asymp 4 times In winter it mostly need not adjust the anglebecause the solar altitude angle is small For the designedsolar collector it was intended to use a single-axis automaticsolar tracking system with the tracking accuracy of about 2∘and the tracking time interval of thirtyminutes in accordancewith the anticlockwise acceptance angle of 95∘ This tracingsystem adopts the light-operated excitation mode

23 Design of the Receiver The solar receiver is another keycomponent A double-skin glass evacuated tube incorporatedwith a concentric aluminum pipe was used as the solarreceiverThe outer dimension of the glass evacuated tube was58mm times 2100mm The concentric aluminum pipe includestwo layers as shown in Figure 6 The outer aluminum has adiameter of 42mm and a length of 1900mm and its outersurface was coated by an oxidation film to form an effectivetubular solar absorption surface Compared with the conven-tional finned U-tube solar absorbers the concentric absorberhas an annular water channel on the inside of the tubularsolar absorption surface so the thermal resistance could beminimized In addition the double-skin glass evacuated tube

does not have any perforative junction with the aluminumconcentric pipe hence the possibility of vacuum leakagecould also be minimized

24 Design of the Shell-Encapsulated Solar Collector Theschematic structure and experimental prototype of thedesigned solar collector are shown in Figure 7 The solar col-lector is comprised of an encapsulation shell ldquo1rdquo a combinedmanual and automatic tracking mechanism ldquo2 and 3rdquo severalsmall-size trough-type compound curved surface concentra-tors ldquo4rdquo a glass cover ldquo5rdquo and several glass evacuated tubesolar receivers ldquo6rdquoTheworking principle of the solar collectoris as follows (1) the solar rays are incident on the compoundcurved surface collector ldquo4rdquo through the glass cover ldquo5rdquo (2)the rays are reflected to the surface of the receiver ldquo6rdquo (3) thesolar radiation is transformed into heat through absorptionby the selective coating on the outer aluminum pipe (4) theheat transfer fluid enters the inner tube of the concentricaluminum pipe and then it flows into the annular channelbetween the middle pipe and outer pipe where it absorbsheat and its temperature increases along the channel (5) theheat transfer fluid transports heat to the hot water storagetank through the circulation line and it releases heat to waterthrough the immerged coil heat exchanger to increase thewater temperature Compared with the common evacuatedtube solar collectors the designed concentration-type solarcollector uses less number of evacuated tubes for the samesolar collection area so the overall amount of heat transferfluid in the tubes could be reduced This may help reducethe overall thermal inertia and hence lead to a fast thermalresponse Due to the use of solar concentration the solarcollectormay be able to provide a usable water temperature inthe coldwinter and is not subject to the frosting problem so itis especially suitable for the high-latitude regions and winterwith a smaller solar elevation angle

The dimension of the prototype wall-mounting solarcollector was 23mtimes20mtimes03mThe inside of the encapsu-lation shell was attached with a cystosepiment board of about20mmthick and a thin layer of glasswool as the thermal insu-lation layer to reduce heat loss The solar collector includedfour trough-type compound curved surface concentratorsThe tracking system was behind the trough concentratorsso it was seen from outside Each trough concentrator had awidth of 260mmand a length of 1900mm to give an aperturearea of 0494m2 The reflecting surface of the concentratorshad about 92 reflectance with the diffuse reflectance lessthan 10 and specular reflectance equaling 88 The glasscover and encapsulation shell was jointed to form an enclosedcavity The glass cover was a 4mm thick low-iron float flatglass with the light transmittance of 088 that exceeds therequirement of GB 11614-2009 (Chinarsquos Nation Standard andProfession Standard for flat glass) Although the glass coverreduces the amount of solar radiation entering the solarcollector it provides dust-proof for the concentrators andthe enclosed cavity could help reduce heat loss from theevacuated tube solar receiver


Medium outlet

Glass vaccum tube Medium inlet

58mm

Figure 6 An aluminum concentric pipe receiver comprising of a glass evacuated tube

12

3 4

5

6

(1) Packaging shell(2) Manual regulation tracker(3) Draw bar

(4) Compound curved surface concentrators(5) Glass cover(6) Glass evacuated-tube collector

Figure 7 The schematic structure and photo of the prototype shell-encapsulated solar collector

3 Performance Testing of the PrototypeSolar Collector

31 Experimental System As shown in Figures 7 and 8 theexperimental system included a prototype wall-mountingshell-encapsulated solar collector a water tank a circulationpump a feed container a heat exchange coil and a circulationpipe A 20mm thick thermal insulation layer was applied tothe circulation line and water tank to reduce heat loss Theworking principle of the experimental system is as followsthe incoming solar radiation is concentrated and collected bythe solar collector to heat up the heat transfer fluid insidethen the heated working fluid flows to the water tank where

its heat is released to the waterThe cooled working fluid afterheat release is circulated by the pump to the solar collectorto be heated again With the process continuing the watertemperature in thewater tank gradually risesWhen it reachesto a certain degree it is ready to be used

The performance testing was conducted in Beijing(N39∘571015840E116∘191015840) with the ambient temperature in therange of minus1sim minus9∘C The volume of the water tank was 80 Lwith an initial water temperature at 116∘C In the experimentthe solar irradiance was automatically recorded by a TRM-2solar test system (including the TBQ-DI solar radiation table)with the accuracy plusmn5The calibrated k-type thermocoupleswere used to measure temperatures at various points on


1

2

34

5

678

(1) A novel compound curved surface concentrator(2) Circulating pipe(3) Water outlet(4) Water tank(5) Heat exchange coil(6) Water inlet(7) Oil tank(8) Pump

Figure 8 Schematic experimental system for testing the prototypeshell-encapsulated solar collector

the system The data were recorded by a TT-12 temperaturedata logger in which reading interval could be adjusted

32 Experimental Results and Analysis

321 Efficiency Testing In order to validate the designedsolar collector for application in winter two days with lowerambient temperature were chosen for the experiment Theprototype solar collector was placed vertically to simulatethe wall-mounting installation The system was in automatictracingmodelThe ambient andwater temperatures and solarirradiance on vertical plane were recorded every 20min Therecorded data are shown in Figures 9 and 10

It can be seen from the solar irradiance values in Figure 9that two chosen days for testing were sunny and cloudlessbut the ambient temperature was below minus1∘C As shown inFigure 10 the prototype solar collector had heated the storagewater up to nearly 80∘C by 300 pm so it could fully meet therequirement of domestic hot water in winter in colder areasThe water temperature almost increased linearly with timeat the beginning and exceeded 65∘C at around 200 pm andthen the rate of temperature rise began to decrease becausethe solar radiation started to decrease in the afternoon whilethe heat loss of the system continued to increase with theincreasing water temperature It can also be seen that theenclosed cavity generally had a temperature of above 20∘CThis would clearly help to reduce heat loss to the ambientcompared with the situation of exposing the evacuated tubesolar receivers to the ambient temperature of below 0∘C in thewinter

0900 1000 1100 1200 1300 1400 1500 1600350400450500550600650700750800850900950

23012501

Local time (hhmm)

0

5

10

15

20

25

30

minus10

minus5

Am

bien

t tem

pera

ture

(∘C)

Sola

r irr

adia

tion

(Wm

2 )

Figure 9 Change of the solar irradiance and ambient temperaturewith local time

0900 1000 1100 1200 1300 1400 1500 16000

10

20

30

40

50

60

70

80

Internal temperature of shell

23012501

Local time (hhmm)

Average temperature

of water

Tem

pera

ture

(∘C)

Figure 10 Change of water temperature and shell inside tempera-ture with local

The daily average efficiency is a key parameter to charac-terize a solar collector and it may be defined as follows

120578

119889=

119872119862

119901(119905

119890minus 119905

119904)

119860

119888119867

(5)

where 120578119889is the daily average efficiency 119872 and 119862

119901are the

amount and specific heat of water 119905119904is the initial average

temperature of the water tank (∘C) 119905119890is the final temperature

of the water tank (∘C) 119867 is the daily cumulative solarradiation exposure (MJm2) and 119860

119888is the aperture area of

the solar collector which was 247m2Substituting the experimental data into (5) gives the daily

average efficiency of 513 for the 23rd of January and 501


003 006 009 012 015020

025

030

035

040

045

050

055

060

065

This workGlass vaccum tube collector with heat pipe Flat plate collector

Normalization temperature difference ((m2middotK)W)

Uns

tead

y st

ate e

ffici

ency

(120578)

Figure 11 Unsteady-state efficiency curves for three types of solarcollectors

for the 25th of January respectively The small difference inthe efficiencies for these two daysmay be due to the differencein the average operating temperatures

The transient efficiency is a reflection of thermal conver-sion efficiency changing with time and it may be defined as[12]

120578 =

119872119862

119901(119905

119894+1minus 119905

119894)

119860

119888(119867

119894+1minus 119867

119894)

(6)

where 120578 is the transient efficiency119872 is the water mass in thewater tank (kg) 119860

119888is the aperture area of the solar collector

(m2) 119862119901is the specific heat of water (kJ sdot kgminus1 sdot ∘Cminus1) 119905 is

the average water temperature in the water tank (∘C) 119867 isthe cumulative solar irradiation (MJm2) and the subscripts119894 + 1 and 119894 stand for the start state and end state of each timeinterval

By inserting the experimental data into (6) the transientefficiency 120578 at different time can be obtained and plottedagainst the normalized temperature difference (119905

119898minus 119905

119886)119868

as shown in Figure 11 The transient efficiency displays anapproximate quadratic relationshipwith the normalized tem-perature difference The least square regression of the data inFigure 11 gave the following formula

120578 = 0632 minus 0983119879

lowast

119894

minus 5084119879

lowast

119894

2

(7)

Figure 11 also shows the transient efficiency curves for anefficient flat solar collector [13] and an evacuated tube heat-pipe solar collector for comparison [14] It can be seen thatwhen the water temperature equals the ambient temperaturethat is (119905

119898minus 119905

119886)119868 = 0 the 119910 intercept of the transient

efficiency curve of the designed solar collector is 0632 whichis higher than the other two solar collectors This indicates

0900 1000 1100 1200 1300 1400 1500 1600 1700

300

400

500

600

700

800

900

1000

Local time (hhmm)

06112311

20

30

40

50

60

70

80

90

Wat

er te

mpe

ratu

re (∘

C)

Sola

r irr

adia

tion

(Wm

2 )

Figure 12 The change trend of solar irradiance and water tempera-ture with local time

that the heat loss of the designed solar collector might beconsiderably reduced due to the use of the solar concentratorand cavity shell The transient efficiency curves of three solarthermal collectors are in a common trend that is with therise of the operating temperature their efficiencies decrease atdifferent slopes amongwhich the efficiency curve of flat solarcollector has the steepest slope The slope of the efficiencycurve of the designed solar collector is similar to that ofthe common evacuated tube heat-pipe solar collector but isslightly lower at higher temperature This is mainly becausethe thermal insulation of the designed solar collector is not asgood as that of the common evacuated tube solar collectorthus a considerable amount of heat is lost at the water tankand circulation pipe

The system was also tested in the nontracking mode forcomparison in which the trough was fixed during a day testBut the tilt angle (between the symmetrical axis of the troughand the ground) was adjusted between different days Forexample the angle was 50∘ on 6th of November and 40∘ on23rd of November respectively Other conditions were thesame as that of automatic tracing mode

The experimental results on two typical shiny days aregiven in Figure 12 Based on the data the daily efficiency iscalculated to be 445 and 38 respectively This indicatesthat the tilt angle has important influence on the efficiencyCompared with the efficiency of about 50 for the trackingmode it can be seen that use of sun-tracking is important forobtaining a high efficiency

The measuring error of experiment was analyzed Thedifferential operation is used in solving (5) Variation ofefficiency gave the following formula

Δ120578

=

119862

119901

119860

119888

[

119872

119867

Δ119905

119890+

119872

119867

Δ119905

119904+

(119905

119890minus 119905

119904)

119867

Δ119872 +

119872(119905

119890minus 119905

119904)

119867

2

Δ119867]

(8)


1000 1100 1200 1300 1400 1500 16000

200

400

600

800

1000

Local time (hhmm)

07112101

2201

Sola

r irr

adia

tion

(Wm

2 )

Figure 13 Change of solar irradiation with local time

Bringing these parameters into efficiency error equationerror can be worked out The relative uncertainty is 26 Byerror analysis the validity of the above method is proved

322 Testing of Hot Water Displacement at a Controlled Tem-perature The experiment was also conducted to investigatethe thermal performance of the prototype solar collectorwith a periodical displacement of hot water at a controlledtemperature The system was in nontracking mode Theconcentrating troughwas fixed with the tilt angle of 50∘ in theexperiment Such testingwasmade on several shiny dayswiththe setting temperature of 45∘C at which the cold water wasfed into the tank to displace hot waterWhen the temperatureof the outflow water reached a certain degree (40∘C or 35∘C)thewater feedwas halted Figures 13 and 14 show the recordedvalues of solar irradiance and water temperature

According to (5) the daily average thermal efficiency ofthe prototype solar collector hot water system on the 22nd ofJanuary may be calculated as follows

120578

119889=

119862

119901sdot sum

119894

Δ119905

119894sdot 119898

119894

119860

119888sdot 119867

= 052 (9)

whereΔ119905119894is the change of average water temperature between

the 119894th displacement and the (119894 minus 1)th displacement and 119898119894

is the amount of water for the 119894th displacement It is clearthat the thermal efficiency of the system with a periodicaldisplacement of hot water is slightly larger than that with aclosed water tank The reason is that the prototype systemin the former situation operated at a lower temperaturehence less heat lost to the ambient In the same way theefficiency on both 7th of November and 21st of January can beobtained being 45 and 48 It can be found easily that theefficiency in the controlled temperature mode is bigger dueto its operation temperature being lower and heat loss beingless

1000 1100 1200 1300 1400 1500 160025

30

35

40

45

50

Local time (hhmm)

07112101

2201

Wat

er te

mpe

ratu

re (∘

C)

Figure 14 Change of water temperature with local time

4 Conclusions

In order to overcome the drawback of conventional solarcollectors in winter that is its unavailability due to low watertemperature or even freezing this paper has presented a newdesign of solar collectors based on combination of a novelcompound curved surface concentrator and an aluminumconcentric solar receiver contained in a double-skin glassevacuated tube A prototype solar collector has been con-structed and encapsulated in a glass-covered shell the cavitywhich provides an additional thermal insulationThe perfor-mance of the prototype has been tested for a sunny winterweather condition and with wall-mounting installation Theexperimental results indicate that when the average ambienttemperature was below 0∘C the water temperature can beheated up to 80∘C with a daily average efficiency of about50 Therefore the designed solar collector could produceuseful hot water in winter The designed solar collector hasthe following advantages

(1) The designed solar collector employs a novel com-pound curved surface concentrator the number of evacuatedtubes used per unit of solar collection area is reduced andso does the amount of heat transfer fluid inside the solarcollector Therefore the thermal response of the systemwould be fast This would be beneficial for application inwinter when the period of sunshine is short and the ambienttemperature is low

(2) A heat transfer fluid which can operate betweenndash30∘C and 200∘C is used to transport the collected solarheat to the water tank through a circulation pump and a heatexchange coil The heat transfer fluid has a low freezing pointand would help to prevent the solar collector from crackingand explosion due to the potential freezing in winter

(3) The solar collector uses an aluminum concentricpipe as the solar receiver The fluid channel is directly onthe inside of the solar absorption surface so heat transferwould be fast and efficient In addition there is no joint


between the evacuated tube and the aluminum concentricsolar receiver so this has avoided the difficulty of vacuumkeeping for a glass-metal joint

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This work is supported by the National Natural ScienceFoundation of China (no U1261119)

References

[1] E Zambolin and D Del Col ldquoExperimental analysis of thermalperformance of flat plate and evacuated tube solar collectors instationary standard and daily conditionsrdquo Solar Energy vol 84no 8 pp 1382ndash1396 2010

[2] K A Snail J J OrsquoGallagher and R Winston ldquoA stationaryevacuated collector with integrated concentratorrdquo Solar Energyvol 33 no 5 pp 441ndash449 1984

[3] A Rabl J OrsquoGallagher and R Winston ldquoDesign and testof non-evacuated solar collectors with compound parabolicconcentratorsrdquo Solar Energy vol 25 no 4 pp 335ndash351 1980

[4] M Li and L L Wang ldquoInvestigation of evacuated tube heatedby solar trough concentrating systemrdquo Energy Conversion andManagement vol 47 no 20 pp 3591ndash3601 2006

[5] D Jafrancesco E Sani D Fontani et al ldquoSimple methodsto approximate CPC shape to preserve collection efficiencyrdquoInternational Journal of Photoenergy vol 2012 Article ID863654 7 pages 2012

[6] M Adsten A Helgesson and B Karlsson ldquoEvaluation of CPC-collector designs for stand-alone roof or wall installationrdquo SolarEnergy vol 79 no 6 pp 638ndash647 2005

[7] B Norton P C Eames and Y P Yadav ldquoSymmetric andasymmetric linear compound parabolic concentrating solarenergy collectors the state-of-the-art in optical and thermo-physical analysisrdquo International Journal of Ambient Energy vol12 no 4 pp 171ndash190 1991

[8] J Ji J Han T-T Chow et al ldquoEffect of fluid flow and pack-ing factor on energy performance of a wall-mounted hybridphotovoltaicwater-heating collector systemrdquoEnergy and Build-ings vol 38 no 12 pp 1380ndash1387 2006

[9] W M Shen ldquoBalcony wall type solar water heaters promotethe combination of solar water heaters and building energyefficiencyrdquo Transactions of the CSAE vol 22 pp 194ndash198 2006

[10] D R Mills A Monger and G L Morrison ldquoComparison offixed asymmetrical and symmetrical reflectors for evacuatedtube solar receiversrdquo Solar Energy vol 53 no 1 pp 91ndash104 1994

[11] Y Tripanagnostopoulos P Yianoulis S Papaefthimiou and SZafeiratos ldquoCPC solar collectors with flat bifacial absorbersrdquoSolar energy vol 69 no 3 pp 191ndash203 2000

[12] H Zinian ldquoStudy on unsteady-state efficiency equations forsolar water heatersrdquo Journal of Acta Energiae Solaris Sinica vol13 pp 1ndash7 1992

[13] J H Li and Q Jiang ldquoExperimental research on a high efficientflat plate solar collectorrdquo Journal of Acta Energiae Solaris Sinicavol 22 no 2 pp 131ndash135 2001

[14] S-Y Yan R Tian S Hou and L-N Zhang ldquoAnalysis onunsteady state efficiency of glass evacuated solar collector withan inserted heat piperdquo Journal of Engineering Thermophysicsvol 29 no 2 pp 323ndash326 2008

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


Carbohydrate Chemistry

International Journal of


Journal of

Chemistry


Advances in

Physical Chemistry

Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

Journal of

Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Medicinal ChemistryInternational Journal of


Chromatography Research International


Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


losses [5] Adsten et al [6] have proposed a so-calledMaReCodesign of solar concentrators for stationary installationNorton et al [7] gave many researches to symmetric andasymmetric linear compound parabolic concentrators whichis very useful for us to design some novel concentrators

On the other hand in some situation the collector needsbe mounted on the wall For example in very high buildingthe users hope to fix their solar collector on the south wall ifit is available Ji et al [8] described a wall-mounted hybridphotovoltaicwater-heating collector The evacuated tubesolar collectors are particularly suitable for wall-mountinginstallation in the area of high latitude [9] However thevacuum tube collector is cram with water which adds its heatmass so that it gives very low temperature hot water in winterIn order to get higher temperature thermal energy Adstenet al (2005) evaluated various asymmetric CPC designs forstand-alone roof or wall-mounted installations Mills et al[10] also researched the characteristics of asymmetric CPCsolar collectors with tubular receiver and indicated that theycan be used in some special occasion

In addition the receiver used in the compound parabolicconcentrator is very important Mills et al [10] discussedthe problems about evacuated tube solar receivers mountedin special concentrator Tripanagnostopoulos et al [11] alsodiscussed the problem about CPC solar collectors couplingwith flat bifacial absorbers All of the previous work is topursuit the higher working temperature of the collector or letthe collectors be able to operate in winter

This study will present design and testing of a new-typesolar collector based on incorporation of a novel compoundcurved surface concentrator with an aluminum concentricsolar receiver enclosed in a glass evacuated tubeThedesignedsolar collector would be suitable for wall-mounting installa-tion in the area of high latitude

2 Design of the System

Theuse of a novel compound curved surface solar concentra-tor is a key element in the design of a new-type solar collectorhot water system for wall-mounting installation Combinedwith the glass evacuated tube solar receiver the solar collectorsystem would be able to provide hot water at the temperatureof above 70∘C in the winter The detailed innovative design isdescribed as follows

21 Design of the Compound Curved Surface ConcentratorThe key component of the proposed new-type solar collectorsystem is a novel trough-type compound curved surfaceconcentrator the cross-section of which is shown in Figure 1The compound concentrator consists of two upper parabolicmirrors formed from a paraboloid ldquo1rdquo two plane mirrors ldquo2rdquoand a parabolic mirror ldquo3rdquo at the base The heights of thetwo upper parabolic mirrors are not equal to give a tiltedaperture the angle of which is associated with geographiclatitude The central line of a tubular receiver ldquo4rdquo overlapswith the focus line of the paraboloid ldquo1rdquo while it may slightlybe above the focus line of the paraboloid ldquo3rdquo The incomingrays within a certain angle to the symmetrical axis of theconcentrator are mainly reflected by the upper parabolic

2120575A

2120575A

A

d

4

1

DE

O

2 F1F2 G

C

3

2120575B

2120575B

B120572

B998400y

x

Figure 1 A cross-sectional view of the compound curved surfaceconcentrator

mirrors to the receiver ldquo4rdquo and the rest are reflected by theplane mirrors and the base parabolic mirror which may re-reflect the reflected rays from the mirrors ldquo1rdquo to the receiverldquo4rdquo

211 Design Considerations On the cross-section of theconcentrator as shown in Figure 1 119860119863 and 119861119862 are the leftand right sections of the parabolic curve ldquo1rdquo with its focus onthe point 119865

1 which is described by

2119901

1(119910 minus 119897) = 119909

2


where 1199011is the focal parameter and 119897 is the vertical distance

from the vertex of the parabolic curve ldquo1rdquo to the 119909-axisThe parabolic curve is truncated with straight line 119860119861

which therefore forms the aperture of the parabolic curveThe tilt angle 120572 of the line 119860119861 may be the same as localgeographic latitude The straight line segments 119863119864 and 119862119866are vertical to the 119909-axis and symmetrical about the 119910-axis The distance between 119863119864 and 119862119866 and their reasonablelengths are chosen in accordance with the diameter of thetubular receiver and also in order tomaximize the acceptanceangle 119864119874119866 is a section of the parabolic curve ldquo3rdquo with itsfocus at the point 119865

2and its vertex on the 119909-axis The 119864119874119866

is described by

2119901

2119910 = 119909

2


where 1199012is the focal parameter Therefore the cross-section

of the compound curved surface comprises of the paraboliccurved segments 119860119863 and 119861119862 straight line segments119863119864 and119862119866 and parabolic curved segment 119864119874119866

212 Geometric Concentration Ratio and Maximum Accep-tance Angle As shown in Figure 1 the two angles 2 sdot 120575

119860and

2 sdot 120575

119861are formed between the tangent lines from the points


119860 (119909

119860 119910

119860) and 119861 (119909

119861 119910



sin 120575119860asymp

1198892

radic(119909

1198651

minus 119909

119860)

2

+ (119910

1198651

minus 119910

119860)

2

=

1198892

radic(119909

1198602119901

1)

2

+ 119901

1

2

sin 120575119861=

1198892

radic(119909

119861minus 119909

1198651

)

2

+ (119910

119861minus 119910

1198651

)

2

=

1198892

radic(119909

1198612119901

1)

2

+ 119901

1

2

(3)

As 1199092119860

gt 119909

2

119861

there is 120575119860lt 120575


119860or





119860can






119860and

120575






119862 =

119860119861

120587119889

(4)



1= 44 119901

2= 50 119909

119861= 108mm and

120572 = 265

∘ there is that 120575119860= 6



D

O

Q

C

120575B


40 60 80 100 120 140 1604

8

12

16

20

24

28

32

Trac

king

accu

racy

requ

irem

ent(

∘ )














119860and 120575




0 5 10 15 20055

060

065

070

075

080

085

090

095

100

Opt

ical

effici

ency

Deviation angle


a










Medium outlet


58mm


12

3 4

5

6









1

2

34

5

678







0900 1000 1100 1200 1300 1400 1500 1600350400450500550600650700750800850900950

23012501

Local time (hhmm)

0

5

10

15

20

25

30

minus10

minus5

Am

bien

t tem

pera

ture

(∘C)

Sola

r irr

adia

tion

(Wm

2 )


0900 1000 1100 1200 1300 1400 1500 16000

10

20

30

40

50

60

70

80


23012501

Local time (hhmm)

Average temperature

of water

Tem

pera

ture

(∘C)



120578

119889=

119872119862

119901(119905

119890minus 119905

119904)

119860

119888119867

(5)


119901are the








003 006 009 012 015020

025

030

035

040

045

050

055

060

065



Uns

tead

y st

ate e

ffici

ency

(120578)




120578 =

119872119862

119901(119905

119894+1minus 119905

119894)

119860

119888(119867

119894+1minus 119867

119894)

(6)






119898minus 119905

119886)119868


120578 = 0632 minus 0983119879

lowast

119894

minus 5084119879

lowast

119894

2

(7)


119898minus 119905



0900 1000 1100 1200 1300 1400 1500 1600 1700

300

400

500

600

700

800

900

1000

Local time (hhmm)

06112311

20

30

40

50

60

70

80

90

Wat

er te

mpe

ratu

re (∘

C)

Sola

r irr

adia

tion

(Wm

2 )






Δ120578

=

119862

119901

119860

119888

[

119872

119867

Δ119905

119890+

119872

119867

Δ119905

119904+

(119905

119890minus 119905

119904)

119867

Δ119872 +

119872(119905

119890minus 119905

119904)

119867

2

Δ119867]

(8)


1000 1100 1200 1300 1400 1500 16000

200

400

600

800

1000

Local time (hhmm)

07112101

2201

Sola

r irr

adia

tion

(Wm

2 )





120578

119889=

119862

119901sdot sum

119894

Δ119905

119894sdot 119898

119894

119860

119888sdot 119867

= 052 (9)




1000 1100 1200 1300 1400 1500 160025

30

35

40

45

50

Local time (hhmm)

07112101

2201

Wat

er te

mpe

ratu

re (∘

C)


4 Conclusions









Acknowledgment


References
























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


119860 (119909

119860 119910

119860) and 119861 (119909

119861 119910



sin 120575119860asymp

1198892

radic(119909

1198651

minus 119909

119860)

2

+ (119910

1198651

minus 119910

119860)

2

=

1198892

radic(119909

1198602119901

1)

2

+ 119901

1

2

sin 120575119861=

1198892

radic(119909

119861minus 119909

1198651

)

2

+ (119910

119861minus 119910

1198651

)

2

=

1198892

radic(119909

1198612119901

1)

2

+ 119901

1

2

(3)

As 1199092119860

gt 119909

2

119861

there is 120575119860lt 120575


119860or





119860can






119860and

120575






119862 =

119860119861

120587119889

(4)



1= 44 119901

2= 50 119909

119861= 108mm and

120572 = 265

∘ there is that 120575119860= 6



D

O

Q

C

120575B


40 60 80 100 120 140 1604

8

12

16

20

24

28

32

Trac

king

accu

racy

requ

irem

ent(

∘ )














119860and 120575




0 5 10 15 20055

060

065

070

075

080

085

090

095

100

Opt

ical

effici

ency

Deviation angle


a










Medium outlet


58mm


12

3 4

5

6









1

2

34

5

678







0900 1000 1100 1200 1300 1400 1500 1600350400450500550600650700750800850900950

23012501

Local time (hhmm)

0

5

10

15

20

25

30

minus10

minus5

Am

bien

t tem

pera

ture

(∘C)

Sola

r irr

adia

tion

(Wm

2 )


0900 1000 1100 1200 1300 1400 1500 16000

10

20

30

40

50

60

70

80


23012501

Local time (hhmm)

Average temperature

of water

Tem

pera

ture

(∘C)



120578

119889=

119872119862

119901(119905

119890minus 119905

119904)

119860

119888119867

(5)


119901are the








003 006 009 012 015020

025

030

035

040

045

050

055

060

065



Uns

tead

y st

ate e

ffici

ency

(120578)




120578 =

119872119862

119901(119905

119894+1minus 119905

119894)

119860

119888(119867

119894+1minus 119867

119894)

(6)






119898minus 119905

119886)119868


120578 = 0632 minus 0983119879

lowast

119894

minus 5084119879

lowast

119894

2

(7)


119898minus 119905



0900 1000 1100 1200 1300 1400 1500 1600 1700

300

400

500

600

700

800

900

1000

Local time (hhmm)

06112311

20

30

40

50

60

70

80

90

Wat

er te

mpe

ratu

re (∘

C)

Sola

r irr

adia

tion

(Wm

2 )






Δ120578

=

119862

119901

119860

119888

[

119872

119867

Δ119905

119890+

119872

119867

Δ119905

119904+

(119905

119890minus 119905

119904)

119867

Δ119872 +

119872(119905

119890minus 119905

119904)

119867

2

Δ119867]

(8)


1000 1100 1200 1300 1400 1500 16000

200

400

600

800

1000

Local time (hhmm)

07112101

2201

Sola

r irr

adia

tion

(Wm

2 )





120578

119889=

119862

119901sdot sum

119894

Δ119905

119894sdot 119898

119894

119860

119888sdot 119867

= 052 (9)




1000 1100 1200 1300 1400 1500 160025

30

35

40

45

50

Local time (hhmm)

07112101

2201

Wat

er te

mpe

ratu

re (∘

C)


4 Conclusions









Acknowledgment


References
























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










119860and 120575




0 5 10 15 20055

060

065

070

075

080

085

090

095

100

Opt

ical

effici

ency

Deviation angle


a










Medium outlet


58mm


12

3 4

5

6









1

2

34

5

678







0900 1000 1100 1200 1300 1400 1500 1600350400450500550600650700750800850900950

23012501

Local time (hhmm)

0

5

10

15

20

25

30

minus10

minus5

Am

bien

t tem

pera

ture

(∘C)

Sola

r irr

adia

tion

(Wm

2 )


0900 1000 1100 1200 1300 1400 1500 16000

10

20

30

40

50

60

70

80


23012501

Local time (hhmm)

Average temperature

of water

Tem

pera

ture

(∘C)



120578

119889=

119872119862

119901(119905

119890minus 119905

119904)

119860

119888119867

(5)


119901are the








003 006 009 012 015020

025

030

035

040

045

050

055

060

065



Uns

tead

y st

ate e

ffici

ency

(120578)




120578 =

119872119862

119901(119905

119894+1minus 119905

119894)

119860

119888(119867

119894+1minus 119867

119894)

(6)






119898minus 119905

119886)119868


120578 = 0632 minus 0983119879

lowast

119894

minus 5084119879

lowast

119894

2

(7)


119898minus 119905



0900 1000 1100 1200 1300 1400 1500 1600 1700

300

400

500

600

700

800

900

1000

Local time (hhmm)

06112311

20

30

40

50

60

70

80

90

Wat

er te

mpe

ratu

re (∘

C)

Sola

r irr

adia

tion

(Wm

2 )






Δ120578

=

119862

119901

119860

119888

[

119872

119867

Δ119905

119890+

119872

119867

Δ119905

119904+

(119905

119890minus 119905

119904)

119867

Δ119872 +

119872(119905

119890minus 119905

119904)

119867

2

Δ119867]

(8)


1000 1100 1200 1300 1400 1500 16000

200

400

600

800

1000

Local time (hhmm)

07112101

2201

Sola

r irr

adia

tion

(Wm

2 )





120578

119889=

119862

119901sdot sum

119894

Δ119905

119894sdot 119898

119894

119860

119888sdot 119867

= 052 (9)




1000 1100 1200 1300 1400 1500 160025

30

35

40

45

50

Local time (hhmm)

07112101

2201

Wat

er te

mpe

ratu

re (∘

C)


4 Conclusions









Acknowledgment


References
























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


0 5 10 15 20055

060

065

070

075

080

085

090

095

100

Opt

ical

effici

ency

Deviation angle


a










Medium outlet


58mm


12

3 4

5

6









1

2

34

5

678







0900 1000 1100 1200 1300 1400 1500 1600350400450500550600650700750800850900950

23012501

Local time (hhmm)

0

5

10

15

20

25

30

minus10

minus5

Am

bien

t tem

pera

ture

(∘C)

Sola

r irr

adia

tion

(Wm

2 )


0900 1000 1100 1200 1300 1400 1500 16000

10

20

30

40

50

60

70

80


23012501

Local time (hhmm)

Average temperature

of water

Tem

pera

ture

(∘C)



120578

119889=

119872119862

119901(119905

119890minus 119905

119904)

119860

119888119867

(5)


119901are the








003 006 009 012 015020

025

030

035

040

045

050

055

060

065



Uns

tead

y st

ate e

ffici

ency

(120578)




120578 =

119872119862

119901(119905

119894+1minus 119905

119894)

119860

119888(119867

119894+1minus 119867

119894)

(6)






119898minus 119905

119886)119868


120578 = 0632 minus 0983119879

lowast

119894

minus 5084119879

lowast

119894

2

(7)


119898minus 119905



0900 1000 1100 1200 1300 1400 1500 1600 1700

300

400

500

600

700

800

900

1000

Local time (hhmm)

06112311

20

30

40

50

60

70

80

90

Wat

er te

mpe

ratu

re (∘

C)

Sola

r irr

adia

tion

(Wm

2 )






Δ120578

=

119862

119901

119860

119888

[

119872

119867

Δ119905

119890+

119872

119867

Δ119905

119904+

(119905

119890minus 119905

119904)

119867

Δ119872 +

119872(119905

119890minus 119905

119904)

119867

2

Δ119867]

(8)


1000 1100 1200 1300 1400 1500 16000

200

400

600

800

1000

Local time (hhmm)

07112101

2201

Sola

r irr

adia

tion

(Wm

2 )





120578

119889=

119862

119901sdot sum

119894

Δ119905

119894sdot 119898

119894

119860

119888sdot 119867

= 052 (9)




1000 1100 1200 1300 1400 1500 160025

30

35

40

45

50

Local time (hhmm)

07112101

2201

Wat

er te

mpe

ratu

re (∘

C)


4 Conclusions









Acknowledgment


References
























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


Medium outlet


58mm


12

3 4

5

6









1

2

34

5

678







0900 1000 1100 1200 1300 1400 1500 1600350400450500550600650700750800850900950

23012501

Local time (hhmm)

0

5

10

15

20

25

30

minus10

minus5

Am

bien

t tem

pera

ture

(∘C)

Sola

r irr

adia

tion

(Wm

2 )


0900 1000 1100 1200 1300 1400 1500 16000

10

20

30

40

50

60

70

80


23012501

Local time (hhmm)

Average temperature

of water

Tem

pera

ture

(∘C)



120578

119889=

119872119862

119901(119905

119890minus 119905

119904)

119860

119888119867

(5)


119901are the








003 006 009 012 015020

025

030

035

040

045

050

055

060

065



Uns

tead

y st

ate e

ffici

ency

(120578)




120578 =

119872119862

119901(119905

119894+1minus 119905

119894)

119860

119888(119867

119894+1minus 119867

119894)

(6)






119898minus 119905

119886)119868


120578 = 0632 minus 0983119879

lowast

119894

minus 5084119879

lowast

119894

2

(7)


119898minus 119905



0900 1000 1100 1200 1300 1400 1500 1600 1700

300

400

500

600

700

800

900

1000

Local time (hhmm)

06112311

20

30

40

50

60

70

80

90

Wat

er te

mpe

ratu

re (∘

C)

Sola

r irr

adia

tion

(Wm

2 )






Δ120578

=

119862

119901

119860

119888

[

119872

119867

Δ119905

119890+

119872

119867

Δ119905

119904+

(119905

119890minus 119905

119904)

119867

Δ119872 +

119872(119905

119890minus 119905

119904)

119867

2

Δ119867]

(8)


1000 1100 1200 1300 1400 1500 16000

200

400

600

800

1000

Local time (hhmm)

07112101

2201

Sola

r irr

adia

tion

(Wm

2 )





120578

119889=

119862

119901sdot sum

119894

Δ119905

119894sdot 119898

119894

119860

119888sdot 119867

= 052 (9)




1000 1100 1200 1300 1400 1500 160025

30

35

40

45

50

Local time (hhmm)

07112101

2201

Wat

er te

mpe

ratu

re (∘

C)


4 Conclusions









Acknowledgment


References
























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


1

2

34

5

678







0900 1000 1100 1200 1300 1400 1500 1600350400450500550600650700750800850900950

23012501

Local time (hhmm)

0

5

10

15

20

25

30

minus10

minus5

Am

bien

t tem

pera

ture

(∘C)

Sola

r irr

adia

tion

(Wm

2 )


0900 1000 1100 1200 1300 1400 1500 16000

10

20

30

40

50

60

70

80


23012501

Local time (hhmm)

Average temperature

of water

Tem

pera

ture

(∘C)



120578

119889=

119872119862

119901(119905

119890minus 119905

119904)

119860

119888119867

(5)


119901are the








003 006 009 012 015020

025

030

035

040

045

050

055

060

065



Uns

tead

y st

ate e

ffici

ency

(120578)




120578 =

119872119862

119901(119905

119894+1minus 119905

119894)

119860

119888(119867

119894+1minus 119867

119894)

(6)






119898minus 119905

119886)119868


120578 = 0632 minus 0983119879

lowast

119894

minus 5084119879

lowast

119894

2

(7)


119898minus 119905



0900 1000 1100 1200 1300 1400 1500 1600 1700

300

400

500

600

700

800

900

1000

Local time (hhmm)

06112311

20

30

40

50

60

70

80

90

Wat

er te

mpe

ratu

re (∘

C)

Sola

r irr

adia

tion

(Wm

2 )






Δ120578

=

119862

119901

119860

119888

[

119872

119867

Δ119905

119890+

119872

119867

Δ119905

119904+

(119905

119890minus 119905

119904)

119867

Δ119872 +

119872(119905

119890minus 119905

119904)

119867

2

Δ119867]

(8)


1000 1100 1200 1300 1400 1500 16000

200

400

600

800

1000

Local time (hhmm)

07112101

2201

Sola

r irr

adia

tion

(Wm

2 )





120578

119889=

119862

119901sdot sum

119894

Δ119905

119894sdot 119898

119894

119860

119888sdot 119867

= 052 (9)




1000 1100 1200 1300 1400 1500 160025

30

35

40

45

50

Local time (hhmm)

07112101

2201

Wat

er te

mpe

ratu

re (∘

C)


4 Conclusions









Acknowledgment


References
























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


003 006 009 012 015020

025

030

035

040

045

050

055

060

065



Uns

tead

y st

ate e

ffici

ency

(120578)




120578 =

119872119862

119901(119905

119894+1minus 119905

119894)

119860

119888(119867

119894+1minus 119867

119894)

(6)






119898minus 119905

119886)119868


120578 = 0632 minus 0983119879

lowast

119894

minus 5084119879

lowast

119894

2

(7)


119898minus 119905



0900 1000 1100 1200 1300 1400 1500 1600 1700

300

400

500

600

700

800

900

1000

Local time (hhmm)

06112311

20

30

40

50

60

70

80

90

Wat

er te

mpe

ratu

re (∘

C)

Sola

r irr

adia

tion

(Wm

2 )






Δ120578

=

119862

119901

119860

119888

[

119872

119867

Δ119905

119890+

119872

119867

Δ119905

119904+

(119905

119890minus 119905

119904)

119867

Δ119872 +

119872(119905

119890minus 119905

119904)

119867

2

Δ119867]

(8)


1000 1100 1200 1300 1400 1500 16000

200

400

600

800

1000

Local time (hhmm)

07112101

2201

Sola

r irr

adia

tion

(Wm

2 )





120578

119889=

119862

119901sdot sum

119894

Δ119905

119894sdot 119898

119894

119860

119888sdot 119867

= 052 (9)




1000 1100 1200 1300 1400 1500 160025

30

35

40

45

50

Local time (hhmm)

07112101

2201

Wat

er te

mpe

ratu

re (∘

C)


4 Conclusions









Acknowledgment


References
























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


1000 1100 1200 1300 1400 1500 16000

200

400

600

800

1000

Local time (hhmm)

07112101

2201

Sola

r irr

adia

tion

(Wm

2 )





120578

119889=

119862

119901sdot sum

119894

Δ119905

119894sdot 119898

119894

119860

119888sdot 119867

= 052 (9)




1000 1100 1200 1300 1400 1500 160025

30

35

40

45

50

Local time (hhmm)

07112101

2201

Wat

er te

mpe

ratu

re (∘

C)


4 Conclusions









Acknowledgment


References
























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of





Acknowledgment


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

Research Article Design and Testing of a Shell-Encapsulated Solar...

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