Initial Analysis of Pcm Integrated Solar Collectors

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L. H. Alva S.Department of Mechanical Engineering,

University of Puerto Rico-Mayagüez,Mayagüez, Puerto Rico 00681-9045

J. E. González1

Department of Mechanical Engineering,Santa Clara University,

CA 95053e-mail: [email protected]

N. DukhanDepartment of Mechanical Engineering,

University of Puerto Rico-Mayagüez,Mayagüez, Puerto Rico 00681-9045

Initial Analysis of PCM IntegratedSolar CollectorsThis paper investigates the technical feasibility of innovative solar collectors. The pro-posed collectors have a phase change material (PCM) integrated into them as the stor-age mechanism. The PCM-integrated solar collector eliminates the need of conventionalstorage tanks, thus reducing cost and space. The present work uses a paraffin-graphitecomposite as the PCM to increase the conductivity of the PCM matrix. The paraffin’smelting point is around 89°C, which is appropriate for use in single-effect absorptionsystems. The mathematical model that describes the thermal process in the PCM ispresented and differs from the analysis of conventional flat plate solar collectors makinguse of the lumped capacitance method which neglects spatial variations. The proposedmodel is calibrated favorably with a more detailed mathematical model that uses finitedifferences and considers temporal and spatial variations. Results for the collectors’thermal performance are presented along with the effects of the composition of the PCM.The results for the PCM integrated collector proposed here are very encouraging. There-fore, there is an indication that conventional storage tanks may be replaced for the PCMintegrated in the solar collector. �DOI: 10.1115/1.2188532�

Keywords: PCM, solar, thermal, collectors, storage, lumped, enthalpy

IntroductionThe residential market in the Caribbean and other tropical lo-

cations represents a great opportunity for solar thermal applica-tions for air conditioning systems. The typical cooling load inthese buildings ranges between 10.5 and 35 kW. However, forsolar driven absorption machines to be considered to satisfy cool-ing needs in the residential and commercial sectors in these re-gions, compact systems must be designed that eliminate the use ofcooling towers and possibly the thermal storage tank. Recently weproposed a compact absorption machine that somehow addressesthis need of downsizing solar absorption machines �1�. The sys-tem proposed in that work is an air-cooled closed absorption ma-chine where the water cooling is replaced by air cooling throughthe use of compact fans, for both the condenser and the absorber.We concluded in that work that the penalty for using air cooling isminimum if extremely compact and efficient heat exchangers areused. The proposed machine was suggested for 10.5, 14.0, and17.5 kW cooling loads.

We now suggest in this work a mechanism to eliminate the useof storage tanks. We propose a flat plate solar collector that incor-porates a phase change material �PCM� as a mechanism for ther-mal storage. We suggest here an analysis for the proposed PCM-solar collector and investigate its thermal performance andtechnical feasibility. The proposed method of analysis is thelumped capacitance method. A computer program is used to simu-late the thermal performance of the PCM under different workingconditions.

The PCM-Solar CollectorIn this work the PCM-solar collector considered is constructed,

as shown in Fig. 1, with a group of tubes immersed inside thePCM. The PCM is confined in separated and insulated rectangularcontainers as shown in Fig. 2. No similar characteristics for asolar collector have been taken in consideration in the previousworks reported in PCM collectors. Bansal et al. �2� and Rabin et

1Corresponding author. Present address: Department of Mechanical Engineering,Santa Clara University, 500 El Camino Real, Santa Clara, CA, 95051.

Contributed by the Solar Energy Division of ASME for publication in the JOUR-

NAL OF SOLAR ENERGY ENGINEERING. Manuscript received November 4, 2003; final
manuscript received December 6, 2005. Reviewed conducted by Karen DenBraven.
Journal of Solar Energy Engineering Copyright © 20

ownloaded 08 Nov 2011 to 14.139.34.2. Redistribution subject to ASME

al. �3� considered an arrangement of tubes over the PCM. Sokolovand Keizman �4� considered a PCM confined between two con-centric tubes �solar pipe�.

The Paraffin-Graphite CompositeThe PCM considered is the composite proposed and reported

by Py et al. �5�, which has a high thermal conductivity and astable thermal capacitance. The composite is formed of two com-ponents: paraffin as the PCM and compressed expanded naturalgraphite �CENG�. To form the composite, graphite powders arepoured into a mold of aluminum and then pressed to obtain theporous graphite matrix with the desired bulk density �5�. Then thematrix is soaked into melted paraffin and regularly weighted untilmaximum load is reached. In terms of capacity, and depending onbulk graphite density, the CENG/paraffin composites present aweight percentage ranging from 65% to 95% �5�, which is therange used in this work. Figure 3 shows the maximum paraffinweight loading versus bulk graphite matrix density, consideringthe loaded total porosity. Figure 3 also presents the thermal stor-age capacity ratio versus the CENG matrix density. It can be notedthe heat storage capacity decreases with the CENG matrix density.The final effective material properties used for the paraffin at89°C were �6�: density �� 900 kg/m3; latent heat �L� 179 kJ/kg;specific heat �c� 1770 J /kg K; and thermal conductivity �k�0.2 W/m K.

Thermal Analysis for the PCMFor the solution of the phase change problem, the basic as-

sumption is that the sensible heat is negligible compared to thelatent heat �Stefan number is assumed zero�, and consequently allthe heat is assumed to drive the phase-change �7�. This lumpedapproach is compared with a second method in which the energyequation is discretized by finite differences and that considers spa-tial and temporal variations. This second method is commonlyreferred as the “enthalpy method” �7�, and the results are shownlater in this document.

Lumped Capacitance MethodA lumped approach was used to investigate the PCM collector

along the following assumptions:

MAY 2006, Vol. 128 / 17306 by ASME

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�1� Phase transition occurs at a single fixed temperature.�2� Heat transfer inside the PCM matrix is restricted to the

conduction mode.�3� No density change occurs while phase change is occurring.�4� Physical properties are temperature independent.�5� The local interface is assumed planar and sharp �a surface

separating the phases�, at the phase-change temperature.�6� Surface tension and curvature effects at the interface are

assumed insignificant.

Energy and mass balances were established for the PCM usingthe lumped capacitance method and the resulting equations arepresented here. For the absorber plate, conduction in a surfacewith negligible thermal mass is considered as the heat transportmechanism to the PCM. The expression for the heat conductionthrough the absorber plate is

S − UT�TP − Ta� −k

��TP − T̄PCM� = 0 �1�

The above expression is solved at each time interval for theplate temperature using the secant method simultaneously with thePCM temperature whose solution is described below. The value ofUT is found using the relationship suggested by Duffie and Beck-man �8� for mean plate temperatures between ambient and 200°Cto within ±0.3 W/m2°C:

UT = � N

C

TP�TP − Ta

N + f�e

+1

hw�−1

+��TP + Ta��TP

2 + Ta2�

��P + 0.00591Nhw�−1 +2N + f − 1 + 0.133�P

�g− N

�2�

where:

N is the number of glass covers,f is �1+0.089hw−0.1166hw�P��1+0.07866N�,C is 520�1−0.000051�2� for 0° ��70°,e is 0.43�1−100/TP�,� is the collector tilt �degrees�; �20° in this work�,�g is the emittance of glass; �0.9 in this work�, and�P is the emittance of plate; �0.09 in this work�.

Fig. 1 Schematic of the PCM solar collector

Fig. 2 PCM element configuration

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No Collector Flow, Sensible Heating Case. For the analysis ofthe PCM during sensible heating all the mass of the PCM is as-sumed at the same temperature and energy is balanced over theentire control volume. Note that at this stage no melting of thePCM or fluid flow through the tubes is considered. The energybalance for this case is

mc

A

PCM

dTPCM

dt= S − UT�TP − Ta� − k

�

INS�TPCM − Ta� �3�

No Collector Flow, Melting the PCM Case. A melting stagefor the PCM can be considered with no fluid flow through thetubes. During this stage the liquid and the solid phases are con-sidered both to be at the melting temperature and the interface isconsidered planar. At this stage the position of the interface intothe PCM is an important parameter and is represented by x�t�. Theenergy balance during melting is

�L��PCMdx

dt= S − UT�TP − Ta� − k

�

INS�TM − Ta� �4�

Collector Flow, Melting of PCM Case. A simultaneous stagecan be simulated in which solar radiation is available and a fluid iscirculating through the solar collector, such that energy is beingremoved and added simultaneously from and to the PCM. Equa-tion �5� below is used for the final temperature of the PCM, whichresults from the application of an energy balance �only when tem-perature of the PCM is above the melting temperature�,

dTPCM

dt= A

mc

PCM�S − UT�TP − Ta� − k

�

INS�TPCM − Ta��

−QCONV

�mc�PCM�5�

where QCONV is the heat transfer rate to the collector.For this simultaneous stage when the temperature falls to the

melting temperature and solidification begins around the collectortube, a radial configuration is considered similar to that shown inFig. 4, and Eq. �6� is used for the position of the interface at eachtime interval,

dR

dt= 1

2��L�l�PCM 1

R�QCONV + A�UT�TP − Ta� + k

�

INS

�TPCM − Ta� − S�� 6�

For the charging stage all the PCM is considered to be solidified,solar energy is transmitted to the composite by the absorbingplate, and no energy is removed inside the tubes, thus energy istransmitted from the upper side to the bottom. For this case a flatinterface is assumed. During the simultaneous stage all the PCMis considered to be melted, heat is being removed inside the tubes,

Fig. 3 Maximum paraffin weight „in percentage… and reducedstorage thermal capacity versus density of the graphite matrix„loaded total porosity… †6‡

and solar radiation is available. Therefore solidification is ex-

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pected to occur around the tubes and a radial configuration can beassumed for the interface. There is no conflict in this approachbecause charging and simultaneous stages are assumed to takeplace at different times.

Collector Fluid/Tube Analyses. The output fluid temperatureand the energy removed from the solar collectors by forced con-vection are calculated under the assumption of a constant PCMtemperature along the collector tubes. For the collector’s outletfluid temperature a differential element is considered inside thetube. The integration along the axis z direction of the collectortube gives

TOUT�z� = Ti + e−z�TIN − Ti� �7�where

=2h

RINV�c

The expression for the convective heat flux is given by �9�

QCONV = ASh�Ti − TOUT� − �Ti − TIN�

lnTi − TOUT

Ti − TIN �8�

The inside wall temperature of the copper tube can be expressedas

Ti =TPCM + �TIN

1 + ��9�

and

� = ASh

ln RO

RIN

2�lkc

e−l − 1

− l�10�

The Biot number used in this work represents the ratio of theconvective effects to the spatial conduction and is an importantparameter to observe when using the lumped capacitance method.Its value should be less than 0.1 for the lumped capacitancemethod to be valid �9�. It is defined as

Bi =hrc

k�11�

where rc is the characteristic length �see Fig. 4�, h is the convec-tion coefficient inside the tube, and k is the thermal conductivityof the composite.

Validation: The Enthalpy MethodThe method used to validate the results obtained with the

lumped capacitance method is referred as the enthalpy method �7�.The enthalpy method is based on the conservation of energy ex-pressed in terms of enthalpy and temperature. The energy conser-vation applied to a one-dimensional problem is expressed in the

Fig. 4 Schematic representation of the PCM material for thesimultaneous stage

following:

Journal of Solar Energy Engineering


tn

tn+1 �

�tA xj−1/2

xj+1/2

E�x,t�dxdt = − tn

tn+1

A xj−1/2

xj+1/2

qx�x,t�dxdt

�12�

Here the enthalpy E is the sum of sensible and latent heats of thePCM. Proceeding with the discretization of the control volume ina finite number of nodes, a backward-in-time and central-in-spacedifference formulation is used. The following expressions are ob-tained for the enthalpy of each node:

Ejn+1 = Ej

n +�tn

�xj�qj−1/2

n + qj+1/2n � �13�

The heat flux between nodes is

qj−1/2n = −

T jn − T j−1

n

Rj−1/2�14�

The temperature of the nodes is

Solid �Ejn � 0� . . . T j

n = TM +Ej

n

�cS�15�

Interface �0 � Ejn � �L� . . . T j

n = TM �16�

Liquid �Ejn � �L� . . . T j

n = TM +Ej

n − �L

�cL�17�

The PCM element was divided vertically into five sections �Fig.5� with the node at the center of each section. The first node isconsidered to be placed in the section under the absorber plate andthe fifth node in the section immediately over the bottom insula-tion. Results obtained from the enthalpy method are presented inthe next sections and are compared with those obtained with thelumped capacitance method.

ResultsData of the PCM conductivity for materials with a paraffin

content of less than 65% are not available �6� and are not consid-ered in this work. Figure 6 shows the variation of the thermalconductivity of the 65% composite material with paraffin weightpercentage. The overall thermal conductivity of the composite issimilar to that of the sole porous graphite matrix �7� where thethermal conductivity is mainly in the perpendicular direction tothe composite surface. In this work we consider uniform thermal

Fig. 5 Node arrangement used in the enthalpy method

conductivity along the thickness of the PCM.

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To compare the lumped capacitance and the enthalpy methodsdescribed above, simulations were conducted for a constant am-bient temperature of 30.74°C and an incident solar irradiation of526 W/m2. The dimensions of the PCM element considered are0.056 m in width and 3.583 m in length. Figure 7 presents theresults for the warming process of the PCM from the ambienttemperature to the PCM’s melting temperature �89°C� for bothmethods. As described, five nodes through the depth of the PCMwere considered for the case of the enthalpy method. As can beobserved results from both methods are very similar. The PCMreaches the melting temperature in 196.3 min using the lumpedcapacitance method and in 160.5 min with the enthalpy method.The time both methods take to melt the PCM is shown in Fig. 8,where the fractional melted volume for both methods is presentedas a function of time. Here the lumped capacitance method pre-dicts that the PCM will melt completely in 524.3 min, while theenthalpy method predicts it will occur in 512.5 min. Thus, theremaining results presented here make use of the lumped capaci-tance method.

To find practical values of PCM volume and dimensions for theintegrated collector a range between 0.06 and 0.04 m of PCMwidth was found to be acceptable to avoid excessive melting forgiven mass flow rates while maintaining a uniform melting asindicated by the small values of the Biot number. These valueswere found by optimization using the thermal efficiency and amaximum solidification rate of 80% as controlling parameters.The corresponding mass flow rates inside the tube that can beallowed for this range of PCM material were between 0.001 and0.002 kg/s per element. Higher values of mass flow rates mayinduce faster solidification of the PCM.

Figure 9 shows the minimum 65%-paraffin composite area, cor-

Fig. 6 Composite conductivity versus paraffin weightpercentage

Fig. 7 Comparison of the warming process of the PCM ele-ment for results given by the lumped capacitance method andthe enthalpy method using five nodes

176 / Vol. 128, MAY 2006


responding to a maximum solidification allowed of approximately80%, with respect to the maximum mass flow rate per tube fordifferent constant flow inlet temperatures. The maximum solidifi-cation is considered when the interface diameter equals the depthof the composite. Composite areas lower than the values shownmay result in PCM solidification rates in excess of 80%, andconsequently the PCM-collector may not work appropriately. Itcan also be noted that the composite material has a linear trendwith respect to the mass flow rate, with a zero intercept. The valuefor the minimum composite area corresponding to an assumedmass flow rate and inlet temperature is a design parameter to beconsidered when sizing the total area of PCM collectors neededfor a specific application. The mass flow rate and the collectorinput temperature under actual working conditions may be differ-ent than those used here.

Figure 10 shows the width and length of a composite elementversus the mass flow rate per tube, corresponding to the minimumcomposite area and a maximum solidification of 80%, for the caseof a constant inlet temperature of 80°C. It can be noted from thefigure that as the mass flow rate per tube increases the width of theelement decreases, and the length increases. The area of the com-posite is the product of the composite’s width and length. Sincethe widths used �0.04–0.06 m� to find practical dimensions of theproposed PCM integrated collector correspond to the maximumpermitted, then the results for the lengths correspond to mini-mums, as can be observed from Fig. 10.

Figure 11 shows the total collector area and the collector effi-ciency versus the composite’s width, for an element with a con-stant mass flow rate of 0.00142 kg/s. This mass flow rate wasselected arbitrarily in order to work with a small collector area. Inthe case shown in Fig. 11, the maximum collector efficiency andthe minimum total collector area are reached for a composite’swidth in the range of 0.049 and 0.056 m.

Fig. 8 Comparison of the fraction of volume melted resultsgiven by the lumped capacitance method and the enthalpymethod

Fig. 9 Minimum composite area versus maximum mass flow
rate for different inlet temperatures
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ConclusionsThe following specific conclusions can be drawn from this

work:

• The lumped capacitance method was compared with a one-dimensional enthalpy method that used finite differences.The results for warming and melting of the PCM were verysimilar from the two methods. Therefore, the results ob-tained using the lumped capacitance method are acceptableand representative of the process presented here.

• The paraffin-graphite composite with 65% of paraffin inweight was found to work best mainly because of the high-est conductivity obtained. Data for higher paraffin fractionsis not available, but should be investigated further.

• A minimum composite-element area was found for which amaximum solidification of approximately 80% was permit-ted to occur. This area depended strongly on the elementmass flow rate and the collector input temperature.

• The results for this PCM integrated collector proposed hereare very encouraging. Therefore, there is an indication thatconventional storage tanks may be replaced for the PCMintegrated in the solar collector.

• The performance of a collector as described in this paperdepends strongly on an operational design point. Variationsfrom this design point �other insulation rates, charging/discharging durations� may affect the storage performance.

AcknowledgmentThe authors recognize the valuable editorial suggestions by

Prof. Jeffrey Morehouse of University of South Carolina, whichresulted in significant improvements of the final manuscript.

NomenclatureA PCM total area �m2�c specific heat �J/kg K�

Fig. 10 Width and length of the composite material as func-tion of mass flow rate „for constant inlet temperature of 80°C…

Fig. 11 Collector area and collector efficiency versus width ofthe PCM material „for a mass flow rate equal to 0.00142 kg/s…

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E enthalpy �J /m3�h heat transfer coefficient �W/m2 K�k thermal conductivity �W/m K�L latent heat �J/kg�l tube longitude �m�

m mass �kg�Q heat flux �W�q heat flux per area �W/m2�qt top losses due convection and radiation

�W/m2�R tube radius �m�, thermal resistance �K m2/W�rc characteristic length �m�S absorbed solar radiation �W/m2�T temperature �K�t time �s�

UT top loss coefficient from the absorber plate toambient �W/m2 K�

V fluid velocity �m/s�x distance �m�z horizontal axis, collector tube length

Greek Symbols� change, insulation thickness �m�� density �kg/m3�� plate thickness �m�� Stefan Boltzmann constant� characteristic length

Superscriptsn time stepa ambientb bottom losses

CONV convectivec copperi inside

IN inletINS insulation

j node numberL liquid

M meltingO outside

OUT outletPCM phase change material

P absorber plateS solids lateral area

w wind

References�1� Alva, L. H., and González, J. E., 2002, “Simulation of an Air-cooled Solar-

assisted Absorption Air Conditioning System,” ASME J. Sol. Energy Eng.,124, pp. 276–282.

�2� Bansal, N. K., and Buddhi, D., 1992, “Performance of a Cum Storage Sys-tem,” Sol. Energy, 48, pp. 185–194.

�3� Rabin, Y., Bar-Niv, I., Korin, E., and Mikic, B., 1995, “Integrated Solar Col-lector Storage System Based on a Salt-hydrate Phase-change Material,” Sol.Energy, 55, pp. 435–444.

�4� Sokolov, M., and Keizman, Y., 1991, “Performance Indicators for Solar Pipeswith Phase Change Storage,” Sol. Energy, 47, pp. 339–346.

�5� Py, X., Olives, R., and Mauran, S., 2001, “Paraffin/Porous-Graphite-MatrixComposite as a High and Constant Power Thermal Storage Material,” Int. J.Heat Mass Transfer, 44, pp. 2727–2737.

�6� Hoogendoorn, C. J., and Bart, G. C. J., 1992, “Performance and Modeling ofLatent Heat Stores,” Sol. Energy, 48, pp. 53–58.

�7� Alexiades, V., and Solomon, A. D., 1993, Mathematical Modeling of Meltingand Freezing Processes, Hemisphere, Washington.

�8� Duffie, J. A., and Beckman, W. A., 1991, Solar Engineering of Thermal Pro-cesses, Wiley, New York.

�9� Incropera, F. P., and DeWitt, D. P., 1996, Fundamentals of Heat and MassTransfer, Wiley, New York.

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Initial Analysis of Pcm Integrated Solar Collectors