www.elsevier.com/locate/enconman

Energy Conversion and Management 46 (2005) 971–984

Experimental study of the characteristics ofsolidification of stearic acid in an annulus and its thermal

conductivity enhancement

Zhongliang Liu *, Xuan Sun, Chongfang Ma

The Key Laboratory of Enhanced Heat Transfer and Energy Conservation of the Education Ministry,

The Beijing Municipal Key Laboratory of Heat Transfer and Energy Conversion, College of Environmental

and Energy Engineering, Beijing University of Technology, Beijing 100022, PR China

Received 12 February 2004; accepted 25 May 2004

Available online 5 August 2004

Abstract

The thermal and heat transfer characteristics of stearic acid during the solidification processes were

investigated experimentally in a vertical annulus energy storage system. The temperature distribution

and temperature variations with time at different radial positions during the freezing processes wereobtained. The thermal characteristics of the stearic acid, including movement of the solid–liquid interface

in the radial direction, and the effects of Reynolds number on the heat transfer parameters were studied.

The heat flux was estimated by using a simple approximate model. A new copper fin was designed and fixed

to the electrical heating rod to enhance the thermal conductivity of the stearic acid. The results show that

the new fin can enhance both the conduction and the natural convection heat transfer of the PCM, and the

enhancement factor during solidification is estimated to be as high as 250%. The effect of the fin width on

the enhancement was also examined experimentally, and it is found that the fine fin usually produce more

effective enhancement.� 2004 Elsevier Ltd. All rights reserved.

Keywords: Solidification; Latent heat thermal storage; Enhancement; Fins; Experimental; Reynolds number

0196-8904/$ - see front matter � 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.enconman.2004.05.011

* Corresponding author. Fax: +86 10 67391983.

E-mail address: liuzhl@bjut.edu.cn (Z. Liu).

Nomenclature

A cross-sectional area of annulus (m2)de hydraulic diameter of annulus (m)Rsa thermal resistance of stearic acid (�C/W)Rtube thermal resistance of wall of PCM stainless steel tube (�C/W)Rwater waterside thermal resistance (�C/W)T1 temperature measured by TC1 (�C)tsa average temperature of stearic acid in radial direction (�C)Tsurface arithmetic average of T7, T8 and T9 (�C)twater average temperature of cooling water (�C)u average velocity of cooling water inside annulus (m/s)

Greeksmf kinematic viscosity of cooling water (m2/s)v wetted perimeter (m)k thermal conductivity of stainless steel tube (W/m �C)d thickness of PCM tube (m)

972 Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984

1. Introduction

Energy storage plays a critical role in enhancing the applicability, performance and reliabilityof a wide range of energy systems because the discrepancy between energy supply anddemand can be eliminated by a proper energy storage system [1]. Thermal energy storageprovides an energy reservoir to offset this discrepancy and to combat energy needs fluctuations.Of various thermal energy storage methods, latent thermal energy storage employing phasechange material (PCM) is one of the most attractive forms for its advantages of high energy stor-age density and charging/discharging heat at a nearly constant temperature. So, the use of thelatent heat of a PCM as a thermal energy storage medium has gained considerable attentionrecently.

As one may expect, finding a high performance PCM is the key issue for realistic application oflatent heat thermal storage technology. Therefore, a great variety of PCMs have been investigatedconstantly by many researchers, including salt hydrates, paraffin waxes and non-paraffin organiccompounds [2–6]. Some fatty acids were also tried as PCMs for thermal energy storage by Hasanand Sayigh [7] and Sari and Kaygusuz [8–10]. They observed that palmitic, lauric and myristicacids are suitable materials for energy storage in solar heating and cooling applications. They alsoobserved that the melting and solidification times are not affected by the flow rate of the heattransfer fluid within their tested flow rate range.

Various methods for thermal conductivity enhancement of PCMs have been investigated bymany researchers. Some of the most common methods are attaching fins to heat transfer walls,dispersing metal particles or rings or carbon fibers of high conductivity into PCMs [1,11–14].

Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984 973

Velraj et al. [11] conducted a comparative experimental study on the enhancement methodsof using fins, adding lessing rings into PCM and bubble agitation and concluded from theirexperimental results that fixing fins to the heat transfer surface and incorporating lessing ringsinto PCMs are highly suitable for enhancing the solidification processes, and bubble agitationcan be used for promoting the melting processes. Fukai et al. [12,15] added carbon fibersto PCMs in the form of the random type and the brush type. They showed that the brush typeis more effective than the random type. Eftekhar et al. [14] investigated experimentally a differentheat transfer enhancement method for melting of paraffin by constructing a model that consistsof vertically arranged fins between two isothermal planes, which not only provides additionalconduction paths but also promotes natural convection within the molten PCM. Their photo-graphs of the molten zone indicate that a buoyant flow induced in the neighborhood of thevertical fin causes more rapid melting of the solid wax. Though there are still many experimen-tal studies that reported significant enhancement in the thermal conductivity by dispersing highconductivity materials into PCMs, this method is less practical compared with inserting finsinto PCMs since the substances dispersed in PCMs usually sink to the bottom or float tothe top of the container due to their different densities from the PCMs after a long termoperation.

In this paper, the influences of Reynolds number and inlet temperature of the cooling water onthe solidification processes are investigated experimentally. A new fin is designed and is used toenhance the heat transfer of the solidification process. The effects of the fin widths on the enhance-ment were studied and are reported.

2. Experimental system and procedure

The experimental set up is shown in Fig. 1. It mainly consists of a heat exchanger, a high tem-perature bath, a low temperature bath, two circulation pumps, a data acquisition/switch unit,T-type thermocouples, HP data logger, a Pentium III PC and the piping system. The heat ex-changer consists of two concentric cylindrical stainless steel pipes. The external cylindrical tubeis 600 mm long with an inner diameter of 91 mm, while the internal PCM tube is 550 mmlong with an inner diameter of 46 mm and a wall thickness of 2.5 mm. The PCM tube, togetherwith the electrical heating rod is placed concentrically into the external tube, which forms anannular space for the cooling water. The electrical heating rod is placed into the PCM tubeconcentrically to provide an annulus for storing the stearic acid. The electrical heating rod isof a diameter of 19.9 mm and runs through the whole PCM tube with a heating length of 550mm. The whole heat exchanger is well insulated by applying a porous polythene insulator of athickness of 150 mm. Four thermocouples are distributed evenly along the radial direction atthe same section of 255 mm from the bottom end of the tube. The radial locations of the ther-mocouples from the rod axes are 10, 14.33, 18.66 and 23 mm, respectively. In order to obtain theouter wall temperature of the PCM tube, 3 thermal couples (T7, T8 and T9) are soldered to thewall. The inlet and outlet temperatures of the cooling water are measured by thermal couples T5and T6, respectively. All thermocouples were calibrated before use and it was observed that eachthermocouple has an extremely high sensitivity between �50 and 150 �C and has an accuracy of0.2 �C.

Fig. 1. Schematic diagram of the apparatus: (1) HP data logger; (2) high temperature bath; (3, 8, 9, and 10) ball valves;

(4) heat exchanger; (5) low temperature bath; (6) PIII PC; (7) flow-meter; (11 and 12) mixing chambers; (13) external

tube; (14) electrical heating rod; (15) PCM tube; (16) thermocouples carrier for T1, T2, T3 and T4; T5 and T6 thermal

couples for inlet outlet temperatures; T7, T8 and T9 thermocouples for wall temperature of the PCM tube.

974 Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984

Stearic acid is filled in the annulus formed by the PCM tube and the electrical heating rod. Thestearic acid used is of analytical purity. The DSC analysis is conducted, and the result shows thatthe solid–liquid transition temperature of this stearic acid is 67.7 �C and its latent heat is 224.3kJ/kg.

The melting process was initiated by circulating hot water from the high temperature bath at aconstant flow rate of 1.6 kg/min. The inlet temperature of the circulating water is maintained at 80�C and is higher than the melting temperature of the stearic acid. After the melting process wascompleted and a uniform temperature distribution across the stearic acid was reached, the hotwater circulation was stopped and the solidification process was triggered directly by circulatingthe low temperature water (35–45 �C) from the low temperature bath at different flow rates (1.6–3.3 kg/min). The temperatures were recorded every 20 s.

Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984 975

3. Results and discussions

3.1. Solidification curves

The temperature variation with time of the stearic acid at different radial positions is shown inFig. 2. At the very beginning period of the solidification, the temperature of the stearic aciddropped very rapidly. During this period, the temperature of the stearic acid is high, and the stea-ric acid is in the liquid state. Thus, natural convection controls the heat transfer process within thestearic acid. With the large initial temperature difference and the smaller thermal resistance, theheat transfer rate between the cooling water and the stearic acid is large. Since the PCM is basi-cally in the liquid state, the heat dissipated from the PCM is mainly its sensible heat. The largetemperature difference, the strong natural convection and the sensible heat release explain therapid temperature drop during this period. When T1 reaches the solidification point, the solidifi-cation process starts and proceeds into the phase change controlled period. Now the stearic acidnear the inner wall of the PCM tube begins to freeze and discharge its latent heat. The solid stearicacid has a small thermal conductivity, and thus, this frozen layer of PCM acts as a thermal insu-lator and has a large thermal resistance. As one may expect, discharging the latent heat of thestearic acid and the weakened heat transfer process will certainly slow the temperature droppingprocess. However, as the solidification approaches the late period of solidification, the amount oflatent heat released is becoming smaller and smaller, and the heat dissipation from the PCM isagain mainly the sensible heat of the solid stearic acid. Therefore, though the temperature differ-ence between the cooling water and the PCM is becoming smaller, the temperature decreases morequickly compared with the phase change controlled period.

The temperature distribution in the radial direction at different times is shown in Fig. 3. It canbe seen from this figure that the gradient of the temperature profile at 2 min is much smaller thanthat of the temperature profiles at 20 and 35 min. This is due to the unsteady state heat transferbehavior of the solidification process. At 2 min, the process is at its very initial period, and thus,

0 20 40 60 80 100 120Time(min)

40

50

60

70

80

Tem

pera

ture

(°C

)

Water flow rate: 3.3kg/minInlet water temperature 45°C

TC1TC3TC2TC4

Fig. 2. Temperature variation with time of stearic acid at different radial positions.

10 14 18 22

Radial distance(mm)

35

45

55

65

75

Tem

per

atu

re(˚

C)

Water flow rate:1.7kg/min

2min20min35min60min80min

Inlet water temperature: 35˚C

Fig. 3. Temperature profile during solidification of stearic acid.

976 Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984

the initial condition of the uniform temperature distribution controls the process. However, astime elapses, the influence of this initial condition becomes weaker and weaker. At the same time,as more and more of the stearic acid is turned into the solid state, the effects of the natural con-vection are also suppressed, and thus, the equivalent thermal conductivity of the PCM becomessmaller. Hence, as the solidification process proceeds, the temperature distribution across thePCM along the radial direction becomes steeper. This is the reason why the temperature distribu-tion is more even at 2 min compared with those at longer times. However, it should also be notedthat the slope of the temperature profile at 80 min is smaller than that at 20, 35 and 60 min. This isbecause, at 80 min, the solidification is nearly completed and is approaching the uniform temper-ature of the end of the unsteady process, while at 20, 35 and 60 min, the solidification process is inprogress and the thermal conduction plays a more and more important role as more and more ofthe stearic acid is cooled to the solid state. Because of the low conductivity of the stearic acid, theslope of the temperature profile in the radial direction during this period is, thus, becoming largerand larger as time proceeds.

3.2. The effects of the inlet water temperature

Fig. 4 depicts the location of the solid–liquid interface versus time with different inlet water tem-peratures. As the inlet water temperature is decreased from 45 to 35 �C, the time for completion ofthe solidification (time calculated from the onset to the completion of solidification) is greatlyshortened from 48 to 14 min. This can be explained by the following equation:

Q ¼ tsa � twaterRsa þ Rtube þ Rwater

ð1Þ

where tsa is the average temperature of the stearic acid, twater is the average temperature of thecooling water, Rsa is the thermal resistance of the stearic acid, Rtube is the thermal resistance of

10 14 18 22Radial distance(mm)

0

20

40

60

Tim

e(m

in)

Water flow rate: 3.3kg/minInlet water temperature:

40˚C35˚C40˚C

Fig. 4. Comparison of movement of the solid–liquid interfaces with different cooling water inlet temperatures.

Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984 977

the wall of the PCM tube and Rwater is the waterside thermal resistance that is mainly determinedby the flow rate of the cooling water. As the inlet temperature of the cooling water falls, the tem-perature difference between the stearic acid and the cooling water is linearly increased, but thechange of the cooling water temperature, as one may expect, will not significantly change the val-ues of Rsa, Rtube and Rwater. Therefore, the heat flow Q increases as the inlet temperature of thecooling water decreases. Since the total heat removal needed for solidification of the given amountof the stearic acid is a constant, the time for the completion of the solidification is, therefore,shortened because of this increased heat removal rate.

Fig. 5 compares the temperature profiles during solidification of the stearic acid with differentcooling water inlet temperatures. It is noted that the influence of the inlet temperature of the cool-ing water is becoming more significant as time elapses. With the same flow rate of cooling water,the average temperature in the radial direction is generally lower for the inlet water temperature of40 �C than for 45 �C. Also, as one can see from the figure, the gradient of the temperature profileis very small, and the temperature difference between the two inlet temperature cases is nearlyequal to the difference of the inlet temperatures at 90 min, which indicates a very small heat trans-fer rate between the cooling water and the PCM and that the whole system is approaching itssteady state.

3.3. The effects of Reynolds number

The Reynolds number of the cooling water in our solidification experiments is defined by thefollowing equation:

Ref ¼ude

mfð2Þ

10 14 18 22Radial distance (mm)

20

30

40

50

60

70

Tem

per

atu

re (˚C

)

Water flow rate:.3kg/min45°C, 3 min40°C, 3 min45°C, 30 min

40°C, 30 min45°C, 90 min40°C, 90 min

Fig. 5. Comparison of temperature profile during solidification of stearic acid with different cooling water inlet

temperatures.

978 Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984

de ¼4Av

ð3Þ

where Ref is the Reynolds number, u is the average velocity of the cooling water (m/s), de is thehydraulic diameter of the annulus (m), mf is the kinematic viscosity of the cooling water (m2/s), A isthe cross-sectional area of the annulus (m2) and v is the wetted perimeter of the annulus (m). Thevalue of the Reynolds number is changed by changing the flow rate of the cooling water, and thetested range of the Reynolds number is 200–500. The flow of cooling water is, therefore, laminarfor all the experiments reported in this paper. Figs. 6 and 7 present the comparisons of the tem-perature variation with time of the location TC2 with different cooling water Reynolds numbers.From these figures, we can see that the temperature variation of the PCM is insensitive to theReynolds number. There are two main reasons for this. The first is that the range of the Reynoldsnumber is not large enough to cause significant change in the convection heat transfer coefficientof the cooling water. The second is the fact that though the convection heat transfer coefficient onthe external wall of the PCM tube is not very large, its thermal resistance is still very small com-pared with the thermal resistance of the PCM due to the low thermal conductivity of the stearicacid, that is to say, the thermal resistance of the cooling water convection heat transfer is not dom-inant over the whole heat transfer process. The differences of the temperature variations betweenthe different Reynolds numbers, therefore, result from the fact that the average cooling water tem-perature with a larger Reynolds number is lower than that with a smaller Reynolds number, whilethe temperature of the PCM is maintained the same.

In order to prove the above theory, the heat flux across the PCM wall during solidification ofthe stearic acid was estimated by the following equation:

qsurface ¼kðT 1 � T surfaceÞ

dð4Þ

0 20 40

Time (min)

60 80 10035

45

55

65

75

85

Tem

per

atu

re (˚C

) Re=342Re=228

Inlet water temperature: 35˚C

Fig. 6. Comparison of temperature of TC2 with different cooling water Reynolds numbers during solidification of

stearic acid.

0 20 40 60 80 100Time (min)

35

45

55

65

75

85

Tem

pera

ture

(°C

)

Inlet water temperature: 35°CRe=228Re=456

Fig. 7. Comparison of temperature of TC2 with different cooling water Reynolds numbers during solidification of

stearic acid.

Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984 979

where k is the thermal conductivity of the stainless steel wall of the PCM tube, T1�Tsurface is thetemperature difference between the internal wall surface and the external wall surface of the PCMtube and d is the wall thickness of the PCM tube. The results are given in Fig. 8. Though Eq. (4) isnot strictly correct, it does give a rough trend of the heat flux dissipated from the PCM to the

0 25 50 75 100

Time (min)

0

1

2

3

Hea

t flu

x(kw

/m2 )

Inlet water temperature: 35°CRe=228Re=342Re=456

Fig. 8. Heat flux versus time during solidification of stearic acid with different cooling water Reynolds numbers.

980 Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984

cooling water during the solidification process. We can again conclude that the Reynolds numberof the cooling water has only a very weak influence on the solidification process within the testedrange.

3.4. The effects of fins

In order to enhance the solidification process of the stearic acid, a new fin is designed and at-tached to the electrical heating rod. The fin, made of copper, has the shape of a spiral twisted tapeand spans the whole annular gap, which can effectively enhance both the conduction and naturalconvection heat transfer of the PCM. A series of experiments were conducted with and withoutfins. The main results are outlined in Figs. 9–11.

Fig. 9 depicts the comparison of the temperature profiles at various solidification stages withand without fins. It can be observed clearly that the temperature distribution of the stearic acidwith fins (0.5 cm in width) at 2, 20 and 60 min are significantly more even than that without fins,which means that the fin has produced an important enhancement of the solidification process.Using the data as depicted in Fig. 9, one can calculate the temperature differences across thePCM with and without fins, and it is obvious that the temperature difference across the PCMis greatly reduced by attaching fins to the electrical heating rod. At 2 min, the temperature differ-ence is reduced from 8.3 to 3.3 �C, at 20 min, the difference is reduced from 12.3 to 6.3 �C andfinally at 60 min, it is reduced from 3.3 to 2.5 �C. If we assume that the equivalent thermal con-ductivity of the PCM is in inverse proportion to this temperature difference, which is a goodapproximation even for unsteady heat conduction, then we can estimate the thermal conductivityenhancement of the fins from these data: at 2, 20 and 60 min, the equivalent thermal conductivityis increased by 150%, 95% and 33%, respectively. These results prove that inserting these new finsinto the PCM is a very effective method for enhancing the solidification process. It should also be

10 14 18 22

Radial distance (mm)

35

45

55

65

75

Tem

pera

ture

(°C

) 2min, without fins2min, with fins20min, without fins20min, with fins60min, without fins60min, with fins

Fig. 9. Comparison of temperature profiles during solidification of stearic acid with and without fins (water flow rate:

3.3 kg/min; inlet temperature: 35 �C; fin width: 5 mm).

10 14 18 2235

42

49

56

63

70

3min, fin width:0.253min, fin width:0.530min, fin width: 0.2530min, fin width:0.565min, fin width: 0.2565min, fin width:0.5

Radial distance (mm)

Tem

pera

ture

(°C

)

Fig. 10. Comparison of temperature profiles during solidification of stearic acid with fins of different widths (water flow

rate: 3.0 kg/min; inlet water temperature: 35 �C).

Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984 981

noted that the thermal conductivity enhancement of the PCM by the fins is more significant in theinitial period than in the later period. This fact proves that the new fin can enhance not only theheat conduction effects of the PCM but also the natural convection effects. The liquid portion ofthe stearic acid is becoming smaller and smaller as the solidification process proceeds, and as aresult, the effects of the natural convection effects are restrained.

10 14 18 22Radial distance(mm)

2

6

10

14

18

Tim

e(m

in)

Water flow rate: 3.3kg/min

Without finsInlet water temperature: 35°C

Fin width: 0.25cmFin width: 0.5cm

Fig. 11. Interface location during solidification of stearic acid with fins of different width.

982 Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984

In order to investigate the effects of the fin geometry on the heat transfer enhancement, fins ofdifferent width were manufactured and applied. It should be noted that the total amount of cop-per inserted into the annulus as fins is the same though the fins are of different width. Fig. 10 givesa comparison of the temperature profiles of the stearic acid with a 2.5 mm width fin and that witha 5 mm width fin. It can be concluded from this figure that the temperature profile of the stearicacid with a 5 mm width fin is slightly steeper than that with a 2.5 mm width fin, which demon-strates that fine fins are more effective than large fins in enhancing the solidification process ifan equal amount of the fin material is used. This is mainly because the effective fin surface areaof the fine fin is a little greater than that of the large fin, and the fine fins cut the whole PCM annu-lus into more and smaller PCM chambers. As one understands, dividing a vertical narrow gapinto many shorter segments is one of the effective methods for enhancing natural convection heattransfer. It is worthwhile noting that the slopes of the curves are getting smaller as time elapses,and the effects of the fin width are a little more apparent in the initial period than in the later per-iod. This again proves that our fin can enhance both the conduction and the natural convectioneffects because, as the cooling proceeds, more and more stearic acid is solidified, and the naturalconvection effects become less and less important.

Fig. 11 presents the movement of the solidification interface of the stearic acid without finsand with fins of different widths. As we can observe from the figure, the time for the onsetof solidification and the time for the completion of the whole solidification process both de-crease greatly when a 5 mm width fin is inserted into the annulus. This is because the finscan enhance the equivalent thermal conductivity of the stearic acid very effectively, and the heatreleased from the stearic acid can be more easily transferred to the cooling water. Thus, the tem-perature of the outermost stearic acid falls more rapidly to the freezing point. From this figure,we can see that the width of the fins also has an apparent influence on the solidification onsettime and the completion time.

Z. Liu et al. / Energy Conversion and Management 46 (2005) 971–984 983

4. Conclusions

Based on the experimental results and the discussions above, the following conclusions may bedrawn:

(a) The rate of heat transfer and consequently the time for completing solidification are directlyrelated to the inlet temperature of the cooling water.(b) The Reynolds number of the cooling water has only a very weak influence on the solidificationprocess of the stearic acid within the range tested.(c) If the discharging process of a latent heat storage system is realized by forced convection ofliquids, as is used in this paper, the main thermal resistance of such a system is the thermal resist-ance of the PCM.(d) Stearic acid is a good PCM for energy storage for domestic solar water heating. It has a suit-able melting/solidification point of 67–70 �C and a relatively high latent heat of 224.3 kJ/kg. Inaddition, it has no significant supercooling.(e) A novel spiral twisted fin designed to enhance the thermal conductivity of the PCM is testedand is found to be very effective. The experiments prove that the enhancement factor for the solid-ification process can be as high as 250% and reducing the fin width can usually lead to even moreeffective enhancement of the PCM thermal conductivity though more precise experiments areneeded to verify the exact effects.

Acknowledgements

This work is supported by Key Project No. G2000026306 of The National FundamentalResearch and Development Program, The Ministry of Science and Technology of The People�sRepublic of China, National Key Technologies R & D Program Project 2003BA808A19-7,Chinese National Natural Science Foundation Project No. 50276001, Beijing Natural ScienceFoundation Project No. 3032007 and the Key Lab Project KP05040102 of Beijing Universityof Technology.

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