an experimental optimization study on a tube-in-shell latent heat storage

INTERNATIONAL JOURNAL OF ENERGY RESEARCHInt. J. Energy Res. 2007; 31:274–287Published online 9 August 2006 in Wiley InterScience(www.interscience.wiley.com) DOI: 10.1002/er.1249

An experimental optimization study on a tube-in-shell latentheat storage

Orhan Aydın1,*,y, Mithat Akgun1 and Kamil Kaygusuz2

1Department of Mechanical Engineering, Karadeniz Technical University, 61080 Trabzon, Turkey2Department of Chemistry, Karadeniz Technical University, 61080 Trabzon, Turkey

SUMMARY

Thermal energy storage (TES) using phase change materials (PCMs) has recently received considerableattention in the literature, due to its high storage capacity and isothermal behaviour during the storage(melting or charging) and removal (discharging or solidification). In this study, a novel modification on atube-in-shell-type storage geometry is suggested. In the proposed geometry, the outer surface of the shell isinclined and it is the objective of this study to determine the optimum range for the inclination angle of theshell surface. Paraffin with a melting temperature of 58.068C, which is supplied by the Merck Company, isused as the PCM. The PCM is stored in the vertical annular space between an inner tube through which theheat transfer fluid (HTF), hot water, is flowing and a concentrically placed outer shell. At first, thethermophysical properties of this paraffin are determined through the differential scanning calorimeter(DSC) analysis. Temporal behaviour of the PCM undergoing a non-isothermal solid–liquid phase changeduring its melting or charging by the HTF are determined for different values of the inlet temperature andthe mass flow rate of the HTF. The new geometry is shown to respond well with the melting characteristicsof the PCM and to enhance heat transfer inside the PCM for a specific range of the shell inclination angle.Copyright # 2006 John Wiley & Sons, Ltd.

KEY WORDS: PCM; paraffin; thermal energy storage; melting; charging; tube-in-shell geometry

1. INTRODUCTION

Thermal energy storage (TES) has recently become popular as an energy saving method toconserve available energy and to improve its utilization overcoming the imbalance betweenenergy supply or availability and demand through the implementation of a proper energystorage system. Of various thermal energy storage methods, the latent heat thermal energy

*Correspondence to: Orhan Aydın, Department of Mechanical Engineering, Karadeniz Technical University, 61080Trabzon, Turkey.yE-mail: [email protected]

Contract/grant sponsor: Karadeniz Technical University Research Fund; contract/grant numbers: 2001.112.3.2,2002.111.002.4

Received 25 March 2006Revised 20 June 2006Accepted 2 July 2006Copyright # 2006 John Wiley & Sons, Ltd.

storage (LHTES) employing phase change material (PCM) has been widely noticed as aneffective way due to its advantages of high energy storage density (i.e. low volume/energy ratio)and its isothermal operating characteristics (i.e. charging/discharging heat at a nearly constanttemperature) during solidification and melting processes, which is desirable for efficientoperation of thermal systems. In a latent heat storage system, energy is stored during meltingand recovered during solidification of a PCM. The use of the latent heat of a PCM as a thermalenergy storage medium has gained considerable attention recently by finding applications inconservation of energy and natural resources, recovery and use of waste industrial energy, spacecraft, refrigeration and air conditioning systems, solar energy systems, heating and cooling ofbuildings, etc. However, practical difficulties usually arise in applying the latent heat methoddue to the low thermal conductivity, density change, stability of properties under extendedcycling, and sometimes phase segregation and subcooling of the PCMs. During the last 20 years,PCM for storing energy have developed rapidly. Their thermal and physical properties such aslong-term stability and durability have been improved a lot.

A number of studies have been performed to examine the overall thermal behaviour andperformance of various LHTES systems in recent years. These studies focused on the melting/freezing problem of the PCM and on the convective heat transfer problem of the heat transferfluid (HTF) used to store (melting) and/or retrieve energy (solidification) from the unit. Readersare referred to see the excellent reference books by Lane (1983), Garg et al. (1985), and Dincerand Rosen (2002) on the topic to have a better view on the studies existing in the literature. Also,some of the review articles are mentioned in the following: Abhat (1983) and Hasnain (1998)presented a review on sustainable thermal energy storage technologies in terms of heat storagematerials and techniques. Faith (1998) assessed solar thermal energy storage technologies. Zalbaet al. (2003) presented a review of the history of thermal energy storage with solid–liquid phasechange focusing on three aspects; materials, heat transfer and applications. Ettouney et al.(2004) studied heat transfer enhancement by use of metal screens/spheres placed inside the PCMin double pipe energy storage system. A paraffin wax is used as the PCM. Farid et al. (2004)reviewed previous work on latent heat storage and provided an insight to recent efforts todevelop new classes of PCMs for use in energy storage focusing his review on PCM materials,encapsulation and applications. Recently, Sharma and Sagara (2005) presented a detailed reviewon latent heat storage materials and systems.

Paraffin wax is an attractive material for heat storage applications. High latent heat storagecapacities over a narrow temperature range can be obtained and these PCM’s are ecologicallyharmless and non-toxic. Paraffin waxes are cheap and have moderate thermal energy storagedensity but low thermal conductivity and, hence, require large surface area. The normalparaffins of type CnH2nþ2 are a family of saturated hydrocarbons with very similar properties.Paraffins between C5 and C15 are liquids, and the rest are waxy solids. Paraffin wax is the most-used commercial organic heat storage PCM (Garg et al., 1985). It consists of mainly straightchain hydrocarbons that have melting temperatures ranging from 23 to 678C (Abhat, 1983).Commercial-grade paraffin wax is obtained from petroleum distillation and is not a puresubstance, but a combination of different hydrocarbons. In general, the longer the averagelength of the hydrocarbon chain, the higher the melting temperature and heat of fusion (Himranet al., 1994). Paraffins are easily available from many manufacturers and are usually lessexpensive than some salt hydrates. Recently, several works have been carried out in order tostudy the thermal characteristics of paraffins during solidification and melting processes (Banuet al., 1998; Velraj et al., 1999; Cho and Choi, 2000; Hong and Xin-Shi, 2000; Enibe, 2002;

TUBE-IN-SHELL LATENT HEAT STORAGE 275

Copyright # 2006 John Wiley & Sons, Ltd. Int. J. Energy Res. 2007; 31:274–287

DOI: 10.1002/er

He and Setterwall, 2002; Sharma et al., 2002; Sarı, 2004; Trp, 2005). Their studies show thatcommercial-grade paraffin wax and other pure paraffins have stable properties after 1000–2000cycles. Paraffin wax did not show regular degradation in thermal properties after repeatedmelting/freezing cycles. Paraffin waxes are safe and non-reactive. They are compatible with allmetal containers and easily incorporated into heat storage systems. Care should be taken whenusing plastic containers as paraffins have a tendency to infiltrate and soften some plastics.

In this study, we aimed at experimentally investigating a novel tube-in-shell-type storagegeometry for PCMs. The storage geometry is constructed as the annular space between a tubethrough which the HTF (water) is flowing and a conical shell. Both the tube and the shell areplaced concentrically. The surface of the shell, conical, is motivated by the structure of themelting behaviour of the PCM in the annular space between a tube and an outer concentricallyplaced shell. Optimum angle of the shell is defined following the determination of the thermalperformance of the PCM during the melting process for each angle.

2. EXPERIMENTAL STUDY

2.1. Heat storage material

In the present study, paraffin (P1, C26H54) supplied from the Merck Company is used as a latentheat energy storage material. Paraffin is an attractive, chemically stable and non-toxic materialwithout regular degradation and it has high latent heat storage capacities over a narrowtemperature range. In terms of the thermal energy storage capacity, the latent heat storagecapacity, the melting point temperature and the density are the important parameters, whosevalues are shown to be 250 kJ kg�1, 58.068C and 880 kgm�3, respectively, by a differentialscanning calorimeter (DSC) technique for the PCM under study.

2.2. Experimental apparatus and procedure

A general view of the experimental set-up designed is shown in Figure 1. It mainly consists of aconstant-temperature water bath, a circulation pump, the PCM storage container, HTF tube,T-type thermocouples wiring, data acquisition unit, and a PC for data analysis. Water is used asthe HTF. The PCM is kept in the annular space between an inner tube and a concentricallyplaced outer shell. The tube is made of the copper while the outer shell is made of the stainlesssteel. Five different values for the inclination angles of the shell are examined in the study:f ¼ 08; 58, 108, 158 and 208. The PCM container is filled with paraffin. As it is shown, the hotwater flows from the constant-temperature bath to the HTF tube. The hot water releases itssensible heat to the PCM. The cooler water is routed back to the water bath. The constant-temperature water bath controlling the inlet temperature of the HTF has a temperature range of20–1708C with accuracy of � 0.18C. The unit can deliver up to 0.5 kg s�1 of hot water.A detailed view of the test section with the locations where the thermocouples are inserted isshown in Figure 2. Thermocouple wires are used to measure the temperature field in the PCM.All the thermocouples are calibrated before use and they are observed to have a measuringrange of �10 to 2008C and an accuracy of � 0.28C. A number of thermocouples are distributedin an order in the PCM (see Figure 2). The placement of the thermocouples for eachmeasurement has been tabulated in Table I. Other temperature measurements include the inlet/outlet HTF temperatures and the ambient temperature. A 32-channel data logger is used to

O. AYDIN, M. AKGUN AND K. KAYGUSUZ276


DOI: 10.1002/er

collect the temperature measurements. It stores the entire temperature set once every minute.The experimental data are simultaneously transferred to a PC. The flow rate is measured by arotameter with a degree of calibration within � 1% accuracy. The charging process is startedby flowing the hot water through the HTF tube. This process is assumed to finish when all thetemperature recordings in the PCM region present higher values than the melting temperatureof the PCM. No sooner does the charging process end than the stored energy is extracted bypassing the cold water. The charging and discharging processes are run for different mass flowrates and the inlet temperatures of the water. For the charging or melting experiments, the inlettemperatures of the water are prescribed at values higher than the melting temperature of thePCM, while setting them to lower temperatures for discharging or solidification processes.

3. RESULTS AND DISCUSSION

Charging (i.e. melting) and discharging (i.e. freezing) characteristics of the paraffin are examinedby conducting the experiments described above. Experiments are repeated for the five differentvalues of the inclination angle of the shell, which are: f ¼ 08; 58, 108, 158 and 208. Theexperiments are performed for different inlet temperatures and mass flow rates of the HTF,water. For brevity, only the results of the charging experiments are included. Four differentvalues for the inlet temperature of the water have been tested, which are all set to be above themelting temperature of the paraffin under consideration: Tg ¼ 70; 75, 80 and 858C. Threedifferent values of the flow rate of water are examined: ’m ¼ 4; 6 and 8 kgmin�1.

118

109

7

6

5

4

3

2

1

Cold water inlet

a

b

c

i

f

j

keh

dg

Figure 1. Schematic representation of the experimental set-up.



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At all times, the temperature field presented a symmetric shape around the HTF tube. Figure 3shows typical transients of the temperatures at different points given in Figure 2 for Tg ¼ 858Cand ’m ¼ 8 kgmin�1 for each value of the shell inclination angle. The other values of Tg and ’msuggest similar results. As inferred from the changes of the temperature at different points bytime, melting starts in the below region close to the inner wall and, in the following, moltenPCM ascends to the top part of the PCM container as a result of natural convection boundarylayers existing near the tube wall. Then, two regions coexist during the charging processes,which are the melted PCM region in the liquid phase and the non-melted PCM region in thesolid phase. In the solid region, the conduction inside the solid matrix of the PCM is responsiblefor the heat transfer process inside and this region receives heat from the melted part byconvection. When the solid melts or in the melt region, convection mechanism of the heattransfer drives the recirculation inside the melted the PCM, which is due to the buoyancy forces

rmax

rmax

Ø

Ø28

PCM container

PCMs

PCMI

Tir

z

Tr,z

Tr,z

Tr,z

14

14 14 14 14

Z5

Z4

Z3

Z2

Z1

2

3

4

5

1

0

Zm

ax

To

copper HTF pipe

inlet HTF (hot water)

Figure 2. Temperature measurements points inside the PCM.



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TableI.

Theplacementofthethermocouples.

1r m

ax

r min¼

r 0r 1

r 2r 3

r 4r 5

ZmaxZ1

Z2

Z3

Z4

Z5

08

47,3

47,3

47,3

47,3

47,3

47,3

47,3

Tr,z

T14,0,T28,0,T14,100,T28,100,T14,200,T28,200,T14,300,T28,300,

T14,400,T28,400,

T14,421,T28,421,

T42,0,T46,0

T42,100,T46,100

T42,200,T46,200

T42,300,T46,300

T42,400,T46,400

T42,421,T46,421

465

100200300400421

58

66,7

28

36,7

45,5

54,2

63

67T14,445,T28,445,

T14,200,T28,200,T14,300,T28,300,

T14,400,T28,400,

T42,445,T56,445,

Tr,z

T14,0,T28,0

T14,100,T28,100,

T36,100

T42,200

T42,300,T53,300

T42,400,T56,400,T62,445T65,445

465

100200300400445

10888,3

28

45,6

63,3

80,9

T14,200,T28,200,T14,300,T28,300,

T42,300,

Tr,z

T14,0,T28,0

T14,100,T28,100,

T42,100

T42,200,T61,200

T56,300,T70,300,

T77,300

325

100200300

15896,1

28

54,8

81,6

89,6

T14,100,T28,100,T14,200,T28,200,T14,230,T28,230,T42,230,

Tr,z

T14,0,T28,0

T42,100,T50,100

T42,200,T77,200

T56,230,T70,230,T84,230

254

100200230

208104

28

64,4

100,8

T14,200,T28,200,

T42,200,

T14,100,T28,100,

T42,100,

T56,100,T70,200,

T84,200,

Tr,z

T14,0,T28,0

T56,100,T61,100

T98,200

210

100200



DOI: 10.1002/er

30

40

50

60

70

80

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

Tem

per

ature

, T

(°C

)T

emper

ature

, T

(°C

)

20

30

40

50

60

70

80T14,100

T28,100

T36,100

z = 100 mm

Tem

per

ature

, T

(°C

)

T14,0

T28,0

z = 0 mm

20

30

40

50

60

70

80

90

Tem

per

ature

, T

(°C

)

20

30

40

50

60

70

80

90

Tem

per

ature

, T

(°C

)

20

30

40

50

60

70

80

90

Tem

per

ature

, T

(°C

)

20

30

40

50

60

70

80

90T14,200

T28,200

T42,200

z = 200 mm

T14,300

T28,300

T42,300

T53,300

z = 300 mm

T14,400

T28,400,T42,400,T56,400,T62,400

z = 400 mm

T14,445

T28,445,T42,445, T56,445, T65,445

z = 445 mm

(a)

Figure 3. Temporal variations of temperature during melting at some typical points for different values ofthe shell inclination angle: (a) f=08; (b) f=58; (c) f=108; (d) f=158; and (e) f=208.



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induced by the density gradients as a result of temperature differences. This recirculation insideenhances mixing and heat transfer within the molten PCM, which can be explained by the factthat the points near the upper part reach higher temperatures than the lower points. Note that

20

30

40

50

60

70

80T14,100

T28,100

T36,100

z = 100 mm

30

40

50

60

70

80

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

T14,0

T28,0

z = 0 mm

20

30

40

50

60

70

80

90T14,200

T28,200

T42,200

z = 200 mm

T14,300

T28,300

T42,300

T53,300

z = 300 mm

T14,400

T28,400,T42,400,T56,400,T62,400

z = 400 mm

T14,445

T28,445,T42,445, T56,445, T65,445

z = 445 mm

Tem

per

ature

, T

(°C

)T

emper

ature

, T

(°C

)

20

30

40

50

60

70

80

90

Tem

per

ature

, T

(°C

)

20

30

40

50

60

70

80

90

Tem

per

ature

, T

(°C

)

20

30

40

50

60

70

80

90

Tem

per

ature

, T

(°C

)T

emper

ature

, T

(°C

)

(b)

Figure 3. Continued.



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the density of the molten PCM is lower than that in the PCM in the solid phase. At largeroperating times, the region of the molten PCM extends to cover larger regions of the PCMcontainer. The PCM located near the lower/outer regions of the PCM tube remains solid, evenfor large operating times. This is because the amount of input energy at these conditions is notsufficient to achieve complete melting of the PCM. As can be seen from the figure, the storagegeometry with a 5o of the shell inclination angle suggested the lowest melting times. However, atthis point, we should remember the energy balance between the HTF and PCM at the tube wall,which is

Q

t¼ hADTlm

where Q and t represent the amount of heat stored by the PCM and the time, respectively, h isthe convective heat transfer coefficient of the HTF, A is the inner surface area of the HTF tubeand DTlm is the logarithmic mean temperature. From this energy balance, we see that

Melting time � 1=ðHeat transfer areaÞ

20

30

40

50

60

70

80

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

0 60 120 180

Time, t (min)

z = 0 mm

T14,0

T28,0

z =100 mm

T14,100

T28,100

T42,100

20

30

40

50

60

70

80

90T14,200

T28,200

T42,200,T61,200

z =200 mm

T14,300

T28,300,T42,300,T56,300

T70,300,T77,300

z =300 mm

Tem

per

ature

, T

(°C

)T

emper

ature

, T

(°C

)

20

30

40

50

60

70

80

90

Tem

per

ature

, T

(°C

)

20

30

40

50

60

70

80

Tem

per

ature

, T

(°C

)

(c)




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or in notational form

t�1

2pr0L

For a constant value of r0; the above correlation states that

t�1

Lð1Þ

As seen, the melting time is inversely proportional to the height of the PCM storage container.Here, it should be emphasized again, we keep the PCM mass and the radius of the HTF tubeconstant for each experiment using a different shell inclination angle. For the shell inclinationangles of 08 and 58, we use the same value of L, L¼ 465 mm: When we compare the meltingtimes for these two angles, we see that 08 requires higher times than 58 does. For example, fromthe T28,0�t variation for these two angles (see Figures 3(a) and (b)), we see that melting time is240min for 08, while it is 140min for 58. This indicates that the storage geometry with the shellinclination angle of 08 is superior to that of 58, suggesting about a 40% decrease in the total

20

30

40

50

60

70

80

0 60 120 180 240Time, t (min)

0 60 120 180 240Time, t (min)

0 60 120 180 240Time, t (min)

0 60 120 180 240Time, t (min)

T14,0

T28,0

z = 0 mm

10

20

30

40

50

60

70

80

T28,100, T42,100, T50,100

T14,100

z =100 mm

10

20

30

40

50

60

70

80

90T14,200

T28,200, T42, 200, T77,200

z = 200 mm

T14,230

T28,230,T42,230,T56,200,T70,230,T84,230

z = 230 mm

Tem

per

ature

, T

(°C

)T

emper

ature

, T

(°C

)

10

20

30

40

50

60

70

80

90

Tem

per

ature

, T

(°C

)T

emper

ature

, T

(°C

)

(d)




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melting time. Note such an enhancement is obtained without any extra costs (the same values ofthe total mass of the PCM, the storage volume, the convective heat transfer coefficient of theHTF, the inlet temperature and mass of the HTF). For the other values of the shell inclinationangle, the height of the geometry is different to that given for of 08 and 58. Since the height of thestorage geometry is different (see Table I), the melting times for 108, 158 and 208 cannot becompared with those for 08 and 58. However, assigning a proportionality constant for therelation given in Equation (1) using the values of 58, we can predict the melting times for theother shell inclination angles, 108, 158 and 208. As a result, we predict the melting times as 215,274 and 332min for 108, 158 and 208, respectively. For 108 and 158, these extrapolation valuesare consistent with those obtained (see Figures 3(c) and (d)). But for 208, the extrapolation valueunderestimates the measured value. From these results, we can conclude that lower meltingtimes or better performance are obtained in the range of 5–158 of the shell inclination angle thanthat either for 08 or for 208.

With an increase in Tg, the solidification will require smaller times at any point considered.The higher the inlet temperature is, the higher the heat transfer rates are as a result of increasing

20

30

40

50

60

70

80

0 60 120 180 240 300 360 420 480

Time, t (min)

0 60 120 180 240 300 360 420 480

Time, t (min)

Time, t (min)

Tem

pera

ture

, T (

˚C)

Tem

pera

ture

, T (

˚C)

20

30

40

50

60

70

80

Tem

pera

ture

, T (

˚C)

T14,0

T28,0

0 60 120 180 240 300 360 420 480

T 14,100

T28,100,T42,100,T56,100,T64,100

z = 100 mm

20

30

40

50

60

70

T14,200,T28,200,T42,200,T56,200, T70,200,T84,200,T98,200

z = 200 mm

(e)




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temperature differences between the inner wall of the storage container and the bulk of theflowing HTF, water. The effect of the inlet temperature of the water on the time variation of thetemperature of the PCM at some representative points for the inclination angle of 108 isillustrated in Figure 4 at ’m ¼ 8 kg min�1: At each point, increasing inlet temperatures of theHTF lead to smaller melting times and gives more enthalpy flow from the HTF into the PCM.As observed, an increase in the HTF inlet temperature results in higher temperature gradientnear the HTF tube. This gradient diminishes by the increasing melting time.

Figure 5 shows the effect of the mass flow rate of the HTF on the temporal variation oftemperature for the inclination angle of 108 at Tg¼ 858C: As seen from the figure, the influenceof the mass flow rate of the HTF on the melting time at that point is negligible. The fact thathigher mass flow rates require higher pumping powers will result in choosing the lower valuesfor an energy-efficient thermal energy storage process.

4. CONCLUSIONS

In this experimental study, a novel modification on a tube-in-shell-type storage geometry hasbeen proposed in which the outer surface of the shell is inclined. Temporal behaviour of thePCM, paraffin, undergoing a non-isothermal solid–liquid phase change during its melting orcharging by the HTF, hot water, has been determined for different values of the inlettemperature and the mass flow rate of the HTF. The new geometry has been shown to respondwell with the melting characteristics of the PCM and to enhance heat transfer inside the PCM

20

30

40

50

60

70

0 60 120 180 240 300 360 420 480 540 600Time, t(min)

0 60 120 180 240 300 360 420 480 540 600Time, t(min)

Tem

pera

ture

,T (

˚C)

Tem

pera

ture

,T (

˚C)

Tem

pera

ture

,T (

˚C)

Ti = 85˚C, 80˚C, 75˚C, 70˚C

Ti = 85˚C, 80˚C, 75˚C, 70˚C

T28,0T42, 100

Ti = 85˚C, 80˚C, 75˚C, 70˚C

T70, 300

20

30

40

50

60

70

80

20

30

40

50

60

70

80

0 60 120 180 240 300 360 420Time, t (min)

Figure 4. Effect of the inlet temperature of HTF on the temporal variations of temperaturefor f ¼ 108 and ’m ¼ 8 kgmin�1:



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for a specific range of the shell inclination angle. From these results, it has been concluded thatlower melting times or better performance could be obtained in the range of 5–158 of the shellinclination angle than that either for 08 or for 208.

ACKNOWLEDGEMENTS

The authors greatly acknowledge the financial support of this work by the Karadeniz Technical UniversityResearch Fund under Grant No. 2001.112.3.2 and 2002.111.002.4.

REFERENCES

Abhat A. 1983. Low temperature latent heat thermal energy storage: heat storage materials. Solar Energy 30:313–332.Banu D, Feldman D, Hawes D. 1998. Evaluation of thermal storage as latent heat in phase change material wallboard

by differential scanning calorimeter and large scale thermal testing. Thermochica Acta 317:39–45.Cho K, Choi SH. 2000. Thermal characteristics of paraffin in a spherical capsule during freezing and melting processes.

International Journal of Heat and Mass Transfer 43:3183–3196.Dincer I, Rosen MA. 2002. Thermal Energy Storage, Systems and Applications. Wiley: New York.Enibe SO. 2002. Performance of a natural circulation solar air heating system with phase change material energy storage.

Renewable Energy 27:69–86.

10

20

30

40

50

60

70

80

0 60 120 180 240 300

Time, t(min) Time, t(min)

Tem

per

ature

, T

(°C

)

Tem

per

ature

, T

(°C

)

8 kg/min, 6 kg/min, 4 kg/min



T50,100 T77,200

T84,230

20

30

40

50

60

70

80

Tem

per

ature

, T

(°C

)

20

30

40

50

60

70

80

0 60 120 180 240

Time, t(min)

0 60 120 180 240

Figure 5. Effect of the inlet mass flow rate of HTF on the temporal variations of temperaturefor f ¼ 108 and Tg¼ 858C:



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an experimental optimization study on a tube-in-shell latent heat storage

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