Applied Energy 119 (2014) 467–475

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Applied Energy

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Theoretical analysis of a novel, portable, CPC-based solar thermalcollector for methanol reforming

0306-2619/$ - see front matter � 2014 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.apenergy.2014.01.033

⇑ Corresponding author. Address: RMIT University, School of Mechanical andManufacturing Engineering, 115 Queensberry St., Carlton, VIC 3053, Australia. Tel.:+61 3 99258020.

E-mail address: gary.rosengarten@rmit.edu.au (G. Rosengarten).

Xiaoguang Gu a, Robert A. Taylor a,b, Graham Morrison a, Gary Rosengarten c,⇑a School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney 2052, Australiab School of Photovoltaic and Renewable Energy Engineering, The University of New South Wales, Sydney 2052, Australiac School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Melbourne, Australia

h i g h l i g h t s

� A new concentrating micro solar collector with vacuum insulation is proposed.� Optical and thermal theoretical analyses of the collector have been presented.� The collector can provide heat at 250 �C with an efficiency of approximately 70%.� The collector may be used to drive endothermic reactions such as methanol reforming.

a r t i c l e i n f o

Article history:Received 11 October 2013Received in revised form 23 December 2013Accepted 12 January 2014Available online 5 February 2014

Keywords:Solar energyFuel cellHydrogen productionCPCHigh temperature

a b s t r a c t

In this paper we propose a new solar thermal collector which is suitable for providing heat for endother-mic chemical reactions. The particular reaction that is considered is hydrogen production by mentholreforming. The design presented here is based on CPC (compound parabolic concentrator) technology,which can operate without complicated (and costly) tracking systems. It consists of a small, double-sidedselective surface receiver in a vacuum envelope comprised of CPC reflectors and a glass aperture cover.Heat absorbed by the receiver is transferred to the working fluid inside micro tubes where the chemicalreaction is occurring. This design, to the best of our knowledge, represents the first time that a vacuumpackage (which creates thermal concentration) has been combined with a CPC-based optical concentra-tor for thermo-chemical applications. This collector design can convert over 78% of incident solar radia-tion into heat with a concentration ratio of 1.75, allowing for a high solar-to-fuel efficiency in chemicalreactions. This study establishes both the optical and thermal models needed to predict the performanceof this type of collector. The results show that the collector stagnates at very high temperatures (up to600 �C), and can provide solar heat in the form of a small collector for a variety of portable applications– e.g. methanol reforming that requires temperatures of around 250 �C.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction [6] reported a small, rooftop solar concentrating collector based

It is widely accepted that energy generation in the future can nolonger rely on fossil-fuel resources. Thus, various renewable andmore sustainable means of energy resources are under develop-ment around the world [1–3]. Solar energy is a huge renewableresource, with recent work aiming to decease the cost whileimproving the efficiency of ‘macro’ scale solar systems (i.e.>100 W in size), both for photovoltaic and thermal solar collectors[4,5]. However, few studies about ‘micro’ solar thermal collectors(i.e. <100 W) have been published. Micro-concentrating solarthermal systems are particularly underdeveloped. Sultana et al.

on small Fresnel reflectors, which is designed to deliver heat attemperatures up to 200 �C. Zimmerman et al. [7] proposed a newportable solar energy application device which can provide energyfor hydrogen production by methanol reforming in a flat vacuuminsulated receiver. Zimmerman’s work [7] is also notable as itwas the first time that solar energy had been proposed to producehydrogen for PEM (proton exchange membrane) fuel cells.

The most commonly used reactors for methanol reformingrequire temperatures between 250 �C and 300 �C in the presenceof a catalyst [8,9]. A challenge for incorporating renewable isthat it is important to achieve and maintain these temperaturesfor the endothermic reforming reaction to proceed. Conventionalreactors use external power, such as electric heaters to maintainthese conditions [10,11]. An alternative way is to use some ofthe produced hydrogen to provide the power, but the overall

Nomenclature

English lettersA area (m2)C specific heat capacity (J/kg K)Cr concentration ratioE energy (J)F view factorh heat transfer coefficient (W/m2 K)H enthalpy (J/kg)i number of reflections for ‘‘bottom-received’’ raysI solar radiation flux (W/m2)k number of reflections for ‘‘top-received’’ rays_m mass flow rate (kg/s/m2)

M mass (kg)q heat flux (W/m2)Q heat transfer rate (W)T temperature (K)x proportion of solar flux trapped by top coating of recei-

ver

Greek lettersa absorptanceq reflectance

s transmittancer Stefan–Boltzman’s constant (W/m2 K4)e emissivityh incident angle (degree)

Subscriptsb bottom of receiverB beam radiationc glass coverconv convectived diffuse radiationin inletinfra radiativem CPC mirrormix water and methanol mixturer receiverrefl reflectives selective coatingsun solar-relatedt top of receiver1 reaching for the first time2 reaching for the second time1 sky

468 X. Gu et al. / Applied Energy 119 (2014) 467–475

chemical reaction efficiency decreases significantly in thisscenario.

Large scale solar collectors (>5 kW) for methanol reforming[12,13] have also been experimentally tested proving that solar en-ergy is a feasible option to drive the endothermic reaction, but thecollectors are not aiming to portable applications. Zimmermanet al. [7] published a theoretical thermal analysis showing that atemperature higher than 250 �C is achievable from a well-engi-neered solar collector by using a vacuum insulated receiver andhigh quality selective surfaces. In this paper, we improve on previ-ous studies [7] by incorporating a compound parabolic concentra-tor (CPC). The advantage of a CPC for our application is that a CPCcan work as a stationary collector (without a complicated trackingsystem) as long as the incident angle is within its extreme half an-gle [14,15]. Additionally, a CPC can concentrate diffuse radiationwhich is normally lost in other optical concentrators. Many CPC-based collectors have been proposed and studied [16,17], but forthis application we investigate a bifacial flat receiver which is themost suitable for combining with vacuum packaging. As such, thisdesign significantly improves on previous work [7] to achieve hightemperatures in a portable micro collector.

2. CPC-based collector

In solar thermal applications, the key design objective is to ab-sorb as much solar energy as possible while minimising heat loss.Radiation heat loss can be suppressed by using a selective surface.Conductive and convective heat loss can be minimised by using avacuum layer between the high temperature receiver and the coldcover. A vacuum pressure lower than 1 Pa, which is achievable bylow cost positive displacement pumps, is required to avoid theeffects of both conductive and convective heat loss [18]. The CPCsystem used in this application concentrates incoming solar fluxinside a vacuum package to a selective coating on the absorber.Thus, this design is used to minimise all modes of heat loss. A sche-matic of the designed collector is shown in Fig. 1.

Two CPC reflectors were milled from easy-to-manufacturematerials (renshape and aluminium) and were put into a stainlesssteel frame as the basic concentration unit. The selective-surface

coated, flat, copper receivers, which are in the evacuated space,serve to absorb solar energy inside the CPC as shown in Fig. 1(b).The width of the receiver is chosen to be 15 mm due to the consid-eration of the proposed collector being less than 1 kg. A high trans-mission glass cover is bonded on top of the SS frame and a vacuumenvironment (below 1 Pa) is generated by pumping gases out ofthe package to significantly reduce convection heat loss from thereceiver to surroundings. In this design, solar energy is first opti-cally concentrated onto the receiver (1000–2500 W/m2). Then,due to the vacuum, a larger temperature difference between fluidand receiver concentrates the energy further, to 3200 W/m2, flow-ing into the reaction tube. In this design the glass is able to with-stand the atmospheric pressure force. Additionally, the CPCrepresents one module (designed for portability) that could be con-nected to other modules in parallel to increase the flow rate, or inseries to increase the chemical reaction zone residence time. In thefollowing sections, the theoretical performance of the proposedCPC is analysed both optically and thermally.

2.1. Optical analysis (short wavelength radiation)

In most CPC applications a tubular receiver or a one-sided flat re-ceiver is used. The limitations of these types of receivers is that theyonly provide a Cr (concentration ratio) in the range of 1–1.5 [19], be-cause the receiver area is relatively large compared to the aperturearea. To overcome these limitations a bifacial flat receiver has beenproposed [20] which reduces the heat loss area for the same concen-tration ratio. To reduce the conductive heat loss from the receiver inthis application there is no contact between the hot receiver and CPCmirror. The proposed CPC design employs both parabolas and semi-circles to trap both the incoming beam and diffuse solar componentswithin an extreme angle of 27.5� (seen in Fig. 1(a)).

To analyse the proposed CPC collector theoretically, the follow-ing assumptions are made:

1. The CPC shape is ideal and free from fabrication errors. Thismeans that within the extreme angle of 27.5�, all solar rayseventually reach the receiver (potentially after 0 or severalreflections).

Fig. 1. The proposed CPC vacuum package: (a) cross section of the collector; (b) a close up of the copper fin receiver tube.

Fig. 2. Material property and flux definitions inside the CPC collector.

X. Gu et al. / Applied Energy 119 (2014) 467–475 469

2. The hybrid non-imaging CPC concentrator does not pro-duce an image of the light source.

3. There is a 1 mm gap between the receiver and the bottomsemi-circle reflector. According to our previous ray-tracingresults [21], the gap here does not have a significant effecton the optical analysis. Thus, we ignore the effects gener-ated by the gap in the theoretical analysis.

4. Infrared radiation emitted by the absorber is reflected bythe CPC concentrator and eventually reaches the top glasscover (potentially after several reflections).

5. We assume that the diffuse radiation can be analysed inde-pendently from the beam radiation inside the collector, butin a similar manner.

In terms of the geometry of a CPC with a bi-facial flat receiver,solar rays can be absorbed by both the top and the bottom of the re-ceiver (seen in Fig. 2). Thus, we define the fraction of the incidentrays absorbed by top of the receiver as x while that received bybottom are defined as (1 � x). We also define Ar as the one-side areaof the receiver and Ac is the area of the glass cover. Then, Ar/Ac

can be used to define x. For our design x = 0.3 – for a solar incidenceangle of 0�. This means 30 percent of the solar rays hit the top of thereceiver while the remaining 70% go to the bottom of thereceiver.

As seen in Fig. 2, the total received beam flux on the receiver qr,B

is the sum of the solar flux absorbed by both the top and bottomselective surfaces and can be described by:

qr;B ¼ qt;B þ qb;B ð1Þ

where qt,B and qb,B are the solar flux absorbed by top and bottomsurfaces of the receiver, respectively. The rays which end up being‘top-received’ rays and ‘bottom-received’ on the double sided

Fig. 4. Characteristic ray paths inside the CPC system.

470 X. Gu et al. / Applied Energy 119 (2014) 467–475

absorber will have significantly different paths through the collec-tor. The potential paths of rays that can arrive at the top and bottomof the receiver are further shown in Fig. 3. For the following analysiswe use the variable k to track the average number of reflectionsafter which rays are absorbed by the top surface and the variablei to track the number of reflections experienced by rays hittingthe bottom surface. After passing through the cover, solar rayscan go directly to the top of the receiver, or can arrive at the top re-ceiver after one reflection from the parabolic mirror, thus the aver-age k should be in the range between 0 and 1. Similarly, the raysabsorbed by the bottom receiver must be reflected at least once,thus, the value of i will be larger than 1. The values of k and i aredependent on the shape of the reflector and on the incident angle.

To simplify the analysis we introduce a view factor between theglass cover and the receiver. For our CPC system, all rays that orig-inate from the receiver can reach the glass cover either directly orwith help of CPC reflector (potentially after several reflections).However, only a fraction (Ar/Ac) of the energy leaving the glass cov-er can get to the receiver [22]. Thus, we set view factors Fr�c andFc�r to 1 and Ar/Ac, respectively, for a perfect reflectivity CPC mirror.Both the defined view factors and imperfect reflectivity are takeninto consideration later in the optical analysis [note: the reflectivityused in optical analysis is for short wavelengths only].

By analysing the total beam flux down to the top of the receiver,the propagation path of the rays is shown in Fig. 4, then we can cal-culate qt,B by:

qt;B ¼ qt=1 þ qt=2 ð2Þ

qt/1 is the flux absorbed by the receiver top surface for solar raysthat reach the receiver. note: the rays reflected by the selective coat-ing (dashed lines) are diffuse due to the optical properties of theselective coating. Taking the optical properties of the cover, CPCmirror and selective coating into consideration (according to thepath in Fig. 4) qt/1 is calculated by:

qt=1 ¼ xIBðhcÞscðhcÞqkmasðhrÞ

Ac

Arð3Þ

It can also be seen in Fig. 4 that the term qt/2 in Eq. (2) is the second-ary flux absorbed by the receiver top surface from solar rays thathave been reflected by the selective coating, subsequently re-re-flected by the glass cover (a notably small quantity) and then landon the receiver top surface. Additionally, due to the properties ofselective coating, the reflected rays are diffuse and hence do notnecessarily follow the same path back to the cover as when theycame down to the receiver. Then, qt/2 can be calculated as:

qt=2 ¼ xIBðhcÞscðhcÞqkm �qs �qcq2k

m�as

Ac

ArFc�r ð4Þ

Subscripts c, t, b, s represent the cover, top surface and bottom sur-face of the receiver, selective coating, respectively. IB is the beamradiation flux. Ar is the area of one side of the receiver. note: the

Fig. 3. Characteristic paths of rays reach

bar appearing above several symbols in the equations signify prop-erties which correspond to average angular surface properties. Theterm Ac/Ar represents the one-side concentration ratio – which is3.5 in this design. The symbol h following each term representsits dependency with incident angle.

As mentioned above, the view factor Fc�r in Eq. (4) indicates thatonly a fraction of the rays that leave the glass cover reach the recei-ver. In this design, there are multiple reflections between the glasscover and flat receiver. However, due to the relatively high absorp-tion (>90%) of the receiver in the presence of selective coatings, theincident flux is assumed to a negligible level after several reflec-tions. Thus, we only considered 2 reflections and make no attemptto track the flux afterward.

After qt/1 and qt/2 are numerically calculated, the total amount ofsolar flux can be calculated by combining Eqs. (2)–(4), which gives:

qt;B ¼ xIBðhcÞscðhcÞqkm asðhrÞ þ �qs �qcq2k

m�asFc�r

� �Ac

Arð5Þ

Similarly, to find the flux absorbed on the bottom surface, weuse the proportion factor (1�x) instead of x in Eq. (5), and as dis-cussed above, the reflection number i will be different for rays thatreach the top surface, so we replace k with i. Then, the fluxabsorbed by bottom receiver coating qb,B is described as Eq. (6):

qb;B ¼ qb=1 þ qb=2

¼ ð1� xÞIBðhcÞscðhcÞqim asðhrÞ þ �qs �qcq2i

m�asFc�r

� �Ac

Arð6Þ

As there is heat transfer between the glass cover and the recei-ver, the solar radiation absorbed by glass cover for the short wave-length also needs to be analysed. Referring to Fig. 2 we can write anet beam radiation flux for the glass cover as shown in Eq. (7):

qc;B ¼ qc=1 þ qc;t=2 þ qc;b=2 ð7Þ

where qc,B is the total solar radiation absorbed by the glass cover. qc/1

is the incident solar flux absorbed by the cover directly it comes intoCPC for the first time, and can be calculated in Eq. (8):

ing top and bottom of the receiver.

X. Gu et al. / Applied Energy 119 (2014) 467–475 471

qc=1 ¼ IBðhcÞacðhcÞ ð8Þ

Additionally, qc,t/2, qc,b/2 are the solar radiation componentsreflected by the top and bottom of the receiver, respectively, whichare then absorbed by the glass cover. Based on the ray path inFig. 2, qc,t/2 can be numerically derived by taking the average reflec-tivity of selective surface �qs and CPC mirror qm into considerationand can, in terms of the ray path, be described as:

qc;t=2 ¼ xIBðhcÞscðhcÞ�qsq2km

�acAc

ArFr�c ð9Þ

Similarly, qc,b/2 is given by:

qc;b=2 ¼ ð1� xÞIBðhcÞscðhcÞ�qsq2im

�acAc

ArFr�c ð10Þ

Substituting Eqs. (8)–(10) into (7), we get qc,B as:

qc;B¼ IBðhcÞ acðhcÞþ xscðhcÞ �qsq2km

�acþð1�xÞscðhcÞ �qsq2im

�ac� �Ac

ArFr�c

� �ð11Þ

By introducing view factors in the preceding analysis, Eqs.(5)–(11) match Hsieh’s work well [23]. Our work uses a graphicalapproach and consider the top-received and bottom-received raysseparately, Eq. (11) differs from Hsieh’s Eq. (4) [23] only in the xterm and the view factor. This difference is the result of using a flatreceiver instead of tubular receiver.

As mentioned above, CPCs can also take advantage of diffuse so-lar radiation. To analyse diffuse radiation, a similar procedure wasemployed to calculate the diffuse radiation absorbed by each com-ponent. We substitute Id to Eq. (11) and change incident-angle-dependent variables to average values. Then, the diffuse lightabsorbed by glass cover, the top and bottom of the receiver arederived analogically to Eqs. (11), (5), and (6) respectively. Afterrearranging the terms, the corresponding absorbed heat flux isshown in Eqs. (12)–(14). [Note: the approach is simplified since dif-fuse irradiance spreads in all directions uniformly – i.e. Id is notincident angle dependent.]

qc;d ¼ Id �ac 1þ x�sc �qsq2km þ ð1� xÞ�sc �qsq

2im

� �Ac

ArFr�c

� �ð12Þ

qt;d ¼ xId�scqkm

�as 1þ �qs �qcq2km Fc�r

� �Ac

ArFc�r ð13Þ

qb;d ¼ ð1� xÞId�scqim

�as 1þ �qs �qcq2imFc�r

� �Ac

ArFc�r ð14Þ

2.2. Thermal analysis

In addition to the short wavelength (solar) analysis, a thermalradiation analysis is needed where long wavelength radiation ex-change can be considered. The combination of these will allow usto determine temperatures and calculate thermal efficiency forvarious conditions in the collector.

A schematic of the (1-D) thermal model of the micro solar col-lector is shown in Fig. 5. With a vacuum layer, the main heat loss isdue to thermal radiation from the receiver, radiation from the cov-er, and convection between the cover and the surroundings. Anyremaining heat can be carried away by the working fluid, whichwe assume to be a methanol/water mixture.

We assume that there is a negligible temperature difference be-tween the top and bottom of the receiver and thus Tt and Tb areequal, and are expressed by the receiver temperature Tr. Basedon the preceding optical analysis, the incoming flux absorbed bythe receiver can be calculated from Eqs. (5), (6), (13), and (14).The same geometry described in the optical analysis (above)

applies to the following thermal analysis as well. Thus, the radia-tion network for the CPC collector is similar with that of a surfaceinside an enclosure. Additionally, using the same method in Hsieh’swork [23] we assume that the CPC reflector also has a unity reflec-tivity for the infrared. The equivalent resistance network betweenthe whole receiver and the glass cover is shown in Fig. 6.

In Fig. 6, 2Ar represents the whole area of the receiver includingboth top and bottom surface. Based on this, the radiation balanceequation between the receiver and the cover can be establishedas follows:

Qr=c ¼rðT4

r � T4c Þ

1� es

es2Arþ 1

2ArFr�cþ 1� ec

ecAc

ð15Þ

where Qr/c is the heat transfer between the receiver and the glasscover. Dividing Eq. (15) through by 2Ar gives:

qr=c ¼rðT4

r � T4c Þ

1esþ 2Ar

Acð1ec� 1Þ

ð16Þ

Based on the heat flux qr/c derivation in Eqs. (1)–(16), we canwrite an energy balance for glass cover:

Mc

AcCc@Tc

@t¼ qr=c þ qc;B þ qc;d � recðT4

c � T41Þ � hcðTc � T1Þ ð17Þ

where qc,B and qc,d are the energy absorbed from Eqs. 11 and 12. Mc

is the mass of the glass cover and Cc is the specific heat capacity ofthe glass cover. At thermal steady state, both sides of the equationshould be equal to zero.

Following the same logic, a similar equation can be written forthe receiver:

Mr

ArCr@Tr

@t¼ qt;B þ qb;B þ qt;d þ qb;d � qr=c � hr�inðTr � TinÞ ð18Þ

Note that the subscript ‘‘in’’ indicates the working fluid inlettemperature. For a reacting flowing fluid, we can add anotherequation to specify the last term in Eq. (17) using the definitionof enthalpy:

hr�inðTr � TinÞ ¼ _mZ Tr

Tin

CmixdT þ Hmix þ E

!ð19Þ

Eq. (19) takes into account the energy associated with heating thefluid up to boiling, the change of phase from liquid to a vapourthrough the enthalpy, Hmix, and the heat required to drive thereforming reaction, E.

In order to calculate the efficiencies using the above analysis,we must constrain some parameter values around our specific de-sign. It should be noted, however, that the approach is a generalone and could be applied to other designs. For our design, theone-side concentration ration (Ac/Ar), is 3.5 and the ambient tem-perature is fixed at 25 �C. The proportion factor x is somewhatdependent on the incident angle, but previous research [21] showsthat the overall gained flux does not vary dramatically with inci-dent angle (up to the acceptance angle) [21]. The aperture areain this design is almost three and a half times the area of one sideof the receiver, thus, the value of x at 0� is 0.3, which is the ratio ofAr/Ac. Also, we assume that after 1 and 2 reflections, the incomingsolar radiation reaches the top and bottom of the receiver, respec-tively. Therefore, we make the assumption that k and i are 1 and 2,respectively. As one of the possible applications for this CPC is toprovide hydrogen for PEMFC (proton exchange membrane fuelcell), we assume the flow rate of methanol is between 1.7 � 10�4

and 2.2 � 10�4 kg/s/m2 – based on reported fuel cell operationspecifications [24,25]. Although the enthalpy Hmix changes slightlywith temperature, we assume that Hmix and E are 50.8 kJ/mol and

Fig. 5. 1D thermal model of designed CPC collector.

Fig. 6. Thermal resistance network between the receiver and the glass cover.

Fig. 7. Stagnation temperature as a function of absorptance and emittance of thereceiver (assumes: IB = 900 W/m2 and Id = 100 W/m2, T1 = 25 �C, hc = 10 W/m2 K,ac ¼ �ac ¼ 0:05, ec = 0.85, �qc ¼ 0:05, sc = 0.9, �qs ¼ 0:06, qm = 0.95).

Fig. 8. Stagnation temperature as a function of solar flux and external convectiveheat transfer coefficient (assumes: Id = 100 W/m2, T1 ¼ 25 �C, ac ¼ �ac ¼ 0:05,ec = 0.85, �qc ¼ 0:05, sc = 0.9, �qs ¼ 0:06, qm = 0.95, TiNOx es = 0.04, �as ¼ as ¼ 0:94).

472 X. Gu et al. / Applied Energy 119 (2014) 467–475

59.5 kJ/mol, respectively. Note: these values correspond to the onlydata point available in literature at a fixed temperature of 250 �C[26]. The following section shows our results for calculations basedon the equations defined above and these assumptions.

3. Results

To get a high level view of the potential performance of thistype of CPC collector, a sensitivity analysis of critical parametersis carried out. The performance of the receiver’s selective surfaceis one of the most important aspects of this design. Different typesof selective surfaces were assessed for this design – including blackchrome (Cr–Cr2O3), nickel (Ni)-pigmented alumina (Al2O3) andTiNOx. Since these surfaces can vary in terms of their short wave-length (<3 lm) absorptance (0.97–0.85) and long wavelength(>3 lm) emittance (0.04–0.09), the choice of selective coating sig-nificantly affects the performance of the CPC collector. The systemof non-linear Eqs. (1)–(19) is solved using Matlab to predict thestagnation temperature (no flow, e.g., _m ¼ 0) with different es

and as. The reflectivity and absorptance of the glass cover andthe CPC reflective surface are taken from material datasheets.

The heat transfer coefficient between the glass cover and ambientair is set to 10 W/m2 K for normal weather without strong winds.The results are shown in Fig. 7.

Fig. 7 shows that the temperature is more sensitive to longwavelength emissivity than to short wavelength absorptance.Based on these results, we chose to use TiNOx as our final selectivecoating with average emittance and absorptance of 0.04 and 0.94respectively [7]. The calculated stagnation temperatures shownin Fig. 7 indicate temperatures of up to 610 �C are achievable withvacuum insulation (however these results do not include axial con-duction losses). Our previous thermal test results show that thestagnation temperature (without a vacuum) is 118 �C [21]. Thus,the results in Fig. 7 indicate a large temperature increase by usingvacuum packaging. To check the structural integrity of the vacuumpackage, an FEA model was built to check the stresses in the glasscover – the maximum stress was 15 MPa which is well below thetensile strength 78 MPa of 3 mm toughened glass [26].

Another important factor is the external heat transfer coeffi-cient as for a portable thermal source it should be robust enoughto work at higher coefficients. In order to find out the sensitivityto the external heat transfer coefficient and solar flux level, Eqs.(1)–(19) are solved for a range of values of IB and hc. As the beamflux has a more significant effect on the working temperature thanthe diffuse flux we assume that the diffuse flux is constant at100 W/m2. The results are shown in Fig. 8.

Fig. 8 shows how the stagnation temperature changes as a func-tion of solar flux and external heat transfer coefficient. It can beseen that when the heat transfer coefficient is under 10 W/m2 K,which represents low wind conditions, the temperature has a

X. Gu et al. / Applied Energy 119 (2014) 467–475 473

marginal dependence on the convective heat transfer coefficient hc.However, above a heat transfer coefficient of 10 W/m2 K the stag-nation temperature is not very sensitive to increases in hc.

Previous CFD simulations [27] showed that the mass flow ratewould have a large impact on the fluid mixture temperature distri-bution along the tube. Zimmerman et al. showed that for global solarradiation of 1000 W/m2, a maximum flow rate of 3 � 10�4 kg/s/m2

for a working temperature of 250 �C can be used without concentra-tion [7]. By solving Eqs. (1)–(19), operating temperatures for differ-ent mass flow rates and heat fluxes are analysed and the results areshown in Fig. 9.

The results in Fig. 9, show the solar flux level required toachieve a required working temperature as a function of mass flowrate. Since the feed rate of current fuel cells is between 1.7 � 10�4

and 2.2 � 10�4 kg/s/m2 [11,24,25], temperatures higher than400 �C are achievable using this collector when the heat flux isabove 900 W/m2. In the methanol reforming fuel cell in Zimmer-man’s work [26], a power density of 0.1875 W/cm2 is typical fora flow rate of 2.2 � 10�4 kg/s/m2.

The one-dimensional heat loss model presented here (with noconduction between the tube and the frame) is compared with3D CFD modelling results for two operating conditions of a collectorwith similar boundary conditions to the collector analysed here.The CFD model developed in our previous research [27] was runfor a convective heat transfer coefficient, hc, of 10 W/m2 K and anemissivity of the receiver of 0.04 (e.g. TiNOx). A glass tube withthermal conductivity of 1.4 W/m K is modelled as the working fluidconduit. note: in the present design, an aluminium tube is the pro-posed option. However, by using Kapton tubes with low conductiv-ity (0.12 W m�1 K�1 [28]) as the end connectors we believe theconductive end heat loss can be minimised further. As the hot recei-ver is suspended in a vacuum environment, the convective heattransfer coefficient of the top and bottom surfaces is set to 0.

The mean fluid temperatures, defined in Eq. (20), for the twocases are 381 and 383 �C (results shown in Fig. 9).

Tmean ¼1L

Z L

0TlocalðlÞdl ð20Þ

where Tmean is the mean temperature of the fluid along the tube andTlocal(l) is the local fluid temperature at l (m) position along the tubedirection. L is the length of the tube and is set to 100 mm in our

Fig. 9. Theoretical water/methanol mixture temperature as a function of solar fluxand flow rate with comparison to our previous simulation results [27] (assumesId = 100 W/m2, T1 ¼ Tin ¼ 25 �C, hc = 10 W/m2K, ac ¼ �ac ¼ 0:05, ec = 0.85, �qc ¼ 0:05,sc = 0.9, �qs ¼ 0:06, qm = 0.95, TiNOx es = 0.04, �as ¼ as ¼ 0:94).

model. The drop of the temperature is mainly due to the conductionbetween the tubes and the frame as mentioned above. In solarapplications, the solar flux is significantly dependent on weatherconditions. Thus, in order to find the correlation between tempera-tures and flow rate at certain heat fluxes, Eqs. (1)–(19) are solved fordifferent solar fluxes as shown in Fig. 10.

Fig. 10 shows mass flow rates less than about 2 � 10�4 kg/s/m2

the temperature drops dramatically with increasing flow rate,which means that in the low flow range, temperature is more sen-sitive to the mass flow rate. However, when continuously increas-ing the flow rate to more than 3 � 10�4 kg/s/m2, the temperaturecurves become relatively flat, which means the collector is lesssensitive to flow rate at higher flow rates. For a steady state flowrate of 2 � 10�4 kg/s/m2 with a beam and diffuse of 500 and100 W/m2, respectively, Eq. (19) indicated that the total input fluxto the receiver tube is 1632 W/m2. Of this, 354 W/m2 is lost as heat,710 W/m2 is used for heating the incoming fluid, and 568 W/m2 isavailable to drive the chemical reaction.

To determine the total thermal performance of the designedCPC collector as a methanol reformer, it is necessary to calculateefficiencies as a function of mass flow rate. To do this, we takeout E (the chemical enthalpy) from the equations, and use900 W/m2 and 100 W/m2 for the beam and diffuse fluxes respec-tively. The overall efficiency of the CPC collector is then definedas Eq. (21):

g ¼_mR Tr

TinCmix dT þ Hmix

� �CrðIB þ IdÞ

ð21Þ

By solving Eq. (21) based on the optical and thermal analysisabove, and after determining the mean receiver temperature Tr,the efficiency with different weather conditions (changing solarfluxes) can be calculated. As the clearness of the sky affects theproportion of diffuse in global irradiance, Eq. (21) was solved todetermine the efficiency variation with global irradiance at 1000and 700 W/m2. Additionally, for 1000 W/m2, the beam flux wasset to 900 and 500 W/m2 while the corresponding diffuse inputwas 100 and 500 W/m2. Similarly, for the 700 W/m2 irradiance,the beam flux was set to 500 and 350 W/m2 and the correspondingdiffuse is 200 and 350 W/m2. The results with the 4 conditions areshown in Fig. 11.

Fig. 10. Theoretical water/methanol mixture outlet temperature as a function ofsolar flux (assumes Id = 100 W/m2, T1 ¼ Tin ¼ 25 �C, hc = 10 W/m2 K, ac ¼ �ac ¼ 0:05,ec = 0.85, �qc ¼ 0:05, sc = 0.9, �qs ¼ 0:06, qm = 0.95, choosing TiNOx and es = 0.04,�as ¼ as ¼ 0:94).

Fig. 11. Efficiency of the designed collector at different global irradiance (assumesT1 ¼ Tin ¼ 25 �C, hc = 10 W/m2 K, ac ¼ �ac ¼ 0:05, ec = 0.85, �qc ¼ 0:05, sc = 0.9,�qs ¼ 0:06, qm = 0.95, choosing TiNOx and es = 0.04, �as ¼ as ¼ 0:94).

Fig. 12. Efficiency of the designed collector for two reflectivity values as comparedwith other evacuated collectors [30,31] (assumes IB = 900 W/m2, Id = 100 W/m2,T1 ¼ Tin ¼ 25 �C, hc = 10 W/m2 K, ac ¼ �ac ¼ 0:05, ec = 0.85, �qc ¼ 0:05, sc = 0.9,�qs ¼ 0:06, qm = 0.95, choosing TiNOx and es = 0.04, �as ¼ as ¼ 0:94).

474 X. Gu et al. / Applied Energy 119 (2014) 467–475

It can be seen from Fig. 11 that for various beam fluxes, the pro-posed collector is able to provide heat for methanol reforming at itsrequired working temperature from 250 �C to 300 �C (grey area inFig. 11), although at a lower efficiency. Fig. 11 also shows, however,that beam flux is the dominant factor that determines the workingtemperature since only 1/Cr diffuse (in this case 57%) can be ab-sorbed by the receiver with the help of CPC. Based on Bureau ofMeteorology solar data for a typical clear day in Sydney, Australia[29], we set beam and diffuse at 900 and 100 W/m2 in Eq. (21). Thecharacteristic efficiency curve compared to various collectors isshown in Fig. 12.

In Fig. 12, a vacuum package, solar flat plate developed by aSwiss company, TVP Solar SA, is shown for comparison. This collec-tor utilizes a high vacuum to obtain stagnation temperatures up to200 �C higher than normal flat plate collectors. The efficiency curveof the CPC developed by Snail et al. is also compared with our workin Fig. 12. As can be seen in Fig. 12, our proposed concentrated CPCcollector achieves higher efficiency at high temperature than eitherconventional evacuated tubes or the evacuated TVP flat plate col-lector. In addition, the optical efficiency of 78% is also higher fora reflectivity of 0.95. When the reflectivity decreases to 0.90, boththe optical efficiency and the stagnation temperature are reduced

slightly, but the operational temperature range is still better thanalternative collectors – as seen in Fig. 12. For methanol reforming,the collector needs to work with temperatures from 250 �C to300 �C and the corresponding efficiencies in this temperaturerange are from 65% to 71% for reflectivity of 0.95.

4. Conclusion

In this paper, a new portable CPC collector is proposed. Bothoptical and thermal modelling analysis have been presented. Theresults show that this kind of CPC collector can achieve high work-ing temperatures (300–500 �C) by using vacuum insulation andselective coatings. It can also provide high efficiency of 65–71%to drive methanol reforming with temperature from 250 �C to300 �C. Thus, the proposed design is suitable to work as a portablepower supply to provide energy for methanol reforming in fuelcells where a working temperature of 250 �C is required. Thus,the combination of the designed CPC collector and fuel cells is aviable way to generate portable clean power.

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