Thermal and heat transfer characteristics in a latent heat storage system using lauric acid

Thermal and heat transfer characteristics in a latentheat storage system using lauric acid

Ahmet Sarı a,*, Kamil Kaygusuz b

a Department of Chemistry, Gaziosmanpas�a University, 60100 Tokat, Turkeyb Department of Chemistry, Karadeniz Technical University, 61080 Trabzon, Turkey

Received 11 June 2001; accepted 2 November 2001

Abstract

The thermal and heat transfer characteristics of lauric acid during the melting and solidification pro-cesses were determined experimentally in a vertical double pipe energy storage system. In this study, threeimportant subjects were addressed. The first one is temperature distributions and temporal temperaturevariations in the radial and axial distances in the phase change material (PCM) during phase changeprocesses. The second one is the thermal characteristics of the lauric acid, which include total melting andtotal solidification times, the nature of heat transfer in melted and solidified PCM and the effect of Rey-nolds and Stefan numbers as inlet heat transfer fluid (HTF) conditions on the phase transition parameters.The final one is to calculate the heat transfer coefficient and the heat flow rate and also discuss the role ofReynolds and Stefan numbers on the heat transfer parameters. The experimental results proved that thePCMmelts and solidifies congruently, and the melting and solidification front moved from the outer wall ofthe HTF pipe (HTFP) to the inner wall of the PCM container in radial distances as the melting front movedfrom the top to the bottom of the PCM container in axial distances. However, it was difficult to establishthe solidification proceeding at the axial distances in the PCM. Though natural convection in the liquidphase played a dominant role during the melting process due to buoyancy effects, the solidification processwas controlled by conduction heat transfer, and it was slowed by the conduction thermal resistance throughthe solidified layer. The results also indicated that the average heat transfer coefficient and the heat flow ratewere affected by varying the Reynolds and Stefan numbers more during the melting process than during thesolidification process due to the natural convection effect during the melting process.� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Lauric acid; Melting; Solidification; Heat transfer coefficient; Heat flow rate

Energy Conversion and Management 43 (2002) 2493–2507www.elsevier.com/locate/enconman

*Corresponding author. Tel.: +90-356-2521582; fax: +90-356-2521585.

E-mail address: [email protected] (A. Sarı).

0196-8904/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

PII: S0196-8904(01)00187-X

mail to: [email protected]

1. Introduction

Thermal energy storage (TES) is becoming of increasing concern in recent times due to its beingthe key element to accomplish energy recovery and utilization of solar energy, industrial wasteheat and off peak electricity. It is basically classified as latent, sensible and chemical energystorage. Among these energy storage types, the most attractive form is latent heat storage in aphase change material (PCM) due to its having the advantages of high storage capacity in a smallvolume and charging/discharging heat from the system at a nearly constant temperature [1]. Thelatent heat thermal energy storage method for storing solar energy at low temperature has been

Nomenclature

L latent heat of phase change material (PCM) (kJ/kg)C specific heat of PCM (kJ/kg �C)M flow rate of heat transfer fluid (HTF) (kg/s)M mass amount of PCM (kg)T temperature (�C)Re Reynolds number, Re ¼ Mdo=lpdilSte Stefan number, Ste ¼ CðTw;i � TmÞ=Lq heat flow rate (W)ho heat transfer coefficient (kW/m2 �C)A surface area of HTF pipe (HTFP) (m2)t time (s)l length of HTFP (m)d diameter of HTFP (m)

Greek symbolsl viscosity (kg/m s)D difference or interval

Subscriptsw wateri inlet or inner of HTFPO outlet or outer of HTFPL logarithmicp pressurepcm phase change materiall liquid or lengths solid or solidificationm melting

2494 A. Sarı, K. Kaygusuz / Energy Conversion and Management 43 (2002) 2493–2507

drawing considerable attention in the prior few decades because of its having possible applica-bility in solar residential heating and cooling systems [2,3].

In a latent heat energy storage system, one of the main elements is the PCM and its se-lection criteria. To find better PCMs for actual heating and cooling applications, many studieshave been performed on the PCMs. Most of the investigations were focused on salt hydrates,paraffin, non-paraffin organic acids, clathrates and eutectic organic and inorganic compounds[4]. In these material groups, the thermal characteristics and heat transfer behavior of manyPCMs have been investigated in early years by several authors [5,6]. However, in the finaldecade, the studies concerning this subject have been sustained. Choi and Kim investigatedheat transfer in a circular finned and unfinned heat exchanger system with magnesium chlo-ride hexahydrate and concluded that finned heat transfer surfaces can be utilized to enhancethe heat transfer from the PCM to the heat transfer tube [7]. Cho and Choi determined thethermal characteristics of a paraffin in a spherical capsule [8]. They observed that the averageheat transfer coefficient and heat transfer rate were affected by varying the experimental pa-rameters during the melting than during the solidification due to the natural convection effectduring the melting process. Banaszek et al. analyzed a new idea on the use of a vertical spiralheat exchanger employing paraffin wax (PPW-20) [9]. They also examined the influence of itsgeometry and air flow conditions on the unit performance. Morcos performed a thermalanalysis of a shell and tube heat exchanger concept, which has a dimpled tube with circularmild steel fins, for a latent heat storage system in solar heating applications [10]. Thermalanalysis of the proposed modular finned heat exchanger concept shows that the system per-formance is strongly influenced by the heat flux into the module. El-Dessouky et al. performeda study focused on the convection effect on heat transfer in a vertical aligned phase changeenergy storage system where the HTF flow direction is reversed [11]. They observed that thePCM heat transfer coefficient is higher for the case of PCM heating from the bottom to thetop of the system.

On the other hand, a limited number of investigations can be found in the literature on fattyacids as PCMs. Hasan performed parametric studies for palmitic and stearic acid in a simple tube-in-tube heat exchanger system [12,13]. He found that the PCMs were appropriate compounds forsolar domestic water heating. The present authors investigated the usability of some fatty acids,such as stearic, palmitic and myristic acid, as PCMs in a latent heat energy storage system [14,15].The authors reported that the investigated PCMs could be considered to be good storage mate-rials for solar space and greenhouse heating.

In the light of the above literature studies on the usability of fatty acids for energy stor-age, it can be clearly explained that they generally have desirable thermophysical, thermody-namic and kinetic characteristics for low temperature latent heat energy storage applications.Moreover, before using a PCM for an actual energy storage application, establishment of thethermal performance criteria and heat transfer characteristics of the PCM is an importantnecessity. Also required is the configuration of the heat exchanger system including thePCM container and heat transfer fluid pipe (HTFP). Therefore, in this study, lauric acid, whichis a fatty acid of industrial grade, was selected as a PCM due to its having the desiredenergy storage properties. In order to determine the thermal performance of lauric acid in a ver-tical double pipe latent heat energy storage system, the thermal and heat transfer characteristics

A. Sarı, K. Kaygusuz / Energy Conversion and Management 43 (2002) 2493–2507 2495

of the PCM during the melting and solidification processes were determined experimen-tally.

2. Experimental apparatus and procedure

2.1. Experimental apparatus

A schematic diagram of the present experimental apparatus is shown in Fig. 1. A detaileddiagram of the heat exchanger system is also shown in Fig. 2. The heat exchanger system consistsof a PCM container and a HTFP, which is introduced into the PCM container. The PCM wasfilled in the annular space between the PCM container and the HTFP. The heat exchanger systemwas constructed from iron, and its dimensions are shown in Fig. 2. In order to measure thetemperature distributions in the PCM, eight temperature probes were embedded at axial distancesalong the PCM container lengths of 60, 160, 260 and 360 mm from the bottom to top and radial

Fig. 1. Schematic diagram of the present experimental apparatus: (1) test section (PCM container), (2–3) constant

temperature bath, (4) flow control valve, (5) flow meter, (6) heat transfer fluid pipe (HTFP), (7) temperature probe, (8)

circulation pump, (9) data acquisition system, (10) PC Data logger.

Fig. 2. Detailed diagram of the test section and temperature probes locations.


distances in the PCM of 10, 20 and 30 mm from the inner wall of the PCM container toward theHTFP outer wall. The probe located at the 360 mm axial position was only used to record thetemperatures of the air gap above the PCM. Two temperature probes were soldered on the HTFPwall over two axial locations (160, 260 mm) to measure the temperatures of the HTFP outersurface. Two temperature probes were also placed at the initial and end locations of the HTFPto measure the inlet and outlet temperatures of the heat transfer fluid (HTF, water).

All temperature probes, which are LM 335 H, were calibrated according to the Fluka model 80PK Type K immersion probe temperature sensor. Calibration was performed from the referencetemperature curves for both cooling and heating and has an accuracy of �1%. During the ex-perimental runs, all probes functioned in that condition. Electrical signals from the probes weretransmitted to the PCADC 16 interface card module contained in the CPU, and then, this formwas automatically processed by the computer in accordance with the program designed for theexperiments. A selected inlet HTF temperature for the experimental runs was maintained bymeans of two constant temperature baths (hot and cold). The HTF flow rate was measured by acalibrated flowmeter with a measuring accuracy of �0.01 kg/min. The outside surface of the PCMcontainer was well insulated by a glasswool of 30 mm thickness in order to prevent heat lossesto the surroundings.

2.2. Heat storage material

In the present study, lauric acid, which has 95% purity, was used as a latent heat energy storagematerial. Lauric acid is chemically stable, non-poisonous and non-corrosive over a large storageperiod. It has also no subcooling during solidification and a small volume change during the phasechange process. Table 1 depicts the thermophysical properties of lauric acid such as phasetransition temperature range (�C), latent heat storage capacity (kJ/kg) and specific heats (kJ/kg �C), which were determined by a differential scanning calorimeter (DSC) technique.

2.3. Experimental procedure

Before the experimental runs, the PCM container was filled with 2 kg lauric acid, and a few runswere made in order to calibrate the system and allow for melting of the solid PCM pieces. Amelting run starts at room temperature, where the PCM is in a solid state. Throghout this period

Table 1

Thermophysical properties of lauric acid

Chemical formula C11H23COOH

Melting temperature range (�C) 41–43

Latent heat (kJ/kg) 211.6

Specific heat (kJ/kg �C)at 25 �C 1.76

at 65 �C 2.27

Density (kg/dm3) [2]

Solid 1.007

Liquid 0.862

Thermal conductivity (W/m �C) [2] 1.6


hot HTF was passed into the HTFP at a constant flow rate and a constant temperature over themelting range. When all the probe temperatures were above the melting temperature range,the melting process was finished. Temperature data were collected at intervals of 2 min. When themelting process was completed, the solidification period was initiated by passing cold HTF intothe HTFP at a constant flow rate and a constant temperature below the solidification range.Temperature values of the PCM were measured and recorded at the same time intervals as in themelting period. The melting and solidification processes of the PCM were repeated at differentinlet HTF temperatures and flow rates in the laminar range. The key HTF parameters for ex-amining the results were the Reynolds and Stefan numbers. The Reynolds numbers were 15.56(1.5 kg/min), 31.12 (3 kg/min) and 46.68 (4.5 kg/min), and the Stefan numbers were 0.283 (62 �C),0.340 (64 �C) and 0.396 (66 �C) for the melting processes. For the solidification processes, theReynolds numbers were 10.37 (1.0 kg/min), 15.56 (1.5 kg/min) and 20.74 (2.0 kg/min), as theStefan numbers were 0.0567 (36 �C), 0.0756 (34 �C) and 0.0945 (32 �C).

3. Results and discussion

In the present study, the thermal characteristics for the PCM during the phase change processesinclude temperature distributions, temporal temperature values in the radial and axial distancesand total phase transition times for varying Reynolds and Stefan numbers. It also includes the heattransfer phenomena throughout the melting and solidification processes of the PCM. In order toestablish the thermal characteristics of the PCM, several experiments were performed for the PCMat various inlet HTF temperatures and flow rates, where only some temperature data, which exhibitobviously the melting and solidification behaviors, were considered. In addition, the temporaltemperature values were used to calculate the heat transfer characteristics, which were the averageheat transfer coefficients and the heat flow rates for the phase change processes of the PCM.

3.1. Melting process

Typical temperature histories in the radial and axial distances of the PCM during the melt-ing process are shown in Figs. 3 and 4, respectively, when the Reynolds number was 31.12 (for

Fig. 3. Temperature variations in radial direction of the PCM during the melting process (Axial distance: 160 mm;

Tw;i ¼ 62 �C).


3 kg/min) and the Stefan number was 0.283 (for 62 C). Figs. 3 and 4 show that the temperatureincrease was linear at the initial stage of the melting process, and then it became non-linear inshape with nearly zero slope where the non-linear temperature interval corresponded to the PCMmelting temperature range which is 41–43 �C. As also seen in Table 1, this temperature range isequal to the value obtained by the DSC analysis technique. On the other hand, temporal tem-perature values for the same HTF parameters were also plotted versus the radial and the axialdistances, as shown in Fig. 5a and b, where it can be clearly observed that the temperature curvesbecome closer to each other when the PCM temperature reached the melting range. The totalmelting time was established as approximately 180 min by examining the curves in Figs. 3–5a and5b. These figures also depict that the melting front moves from the outer wall of the HTFP to theinner wall of the PCM container in the radial direction as it proceeds to the bottom along the axiallength in the PCM.

By examination of the temperature distributions in the radial and axial directions of the PCM,the nature of the melting process could be explained as follows: Sensible heat was transferred fromthe HTFP wall to the PCM solid by pure conduction with respect to the temperature gradient

Fig. 4. Temperature variations in axial direction of the PCM during the melting process (Radial distance: 20 mm;

Tw;i ¼ 62 �C).

Fig. 5. Temporal temperature variations of the PCM during the melting process (a) in radial direction, (b) in axial

direction (Ste ¼ 0:283; 62 �C; Re ¼ 31:12; 3 kg/min).


between the HTFP wall and the PCM solid. The absorbing operation of the sensible heat wasrapidly realized at the initial stage of the melting process due to the large temperature gradient.Therefore, a thin liquid layer formed between the HTFP wall and the softened solid PCM. Thesolid–liquid interface line expanded along the radial and axial locations with increasing time.After some time, the melting front was governed by natural convection heat transfer in the meltedPCM. The natural convection in the PCM depends on the temperature difference and the distancebetween the HTFP wall and the solid–liquid interface. The increase of the distance between theHTFP wall and the interface, resulting from the increased amount of melted PCM, expedites thenatural convection that reduces the influence of heat conduction. On the other hand, it should notbe forgetten that the convection heat transfer mechanism was enhanced by the buoyancy effectswith increasing distance between the HTFP wall and the solid–liquid interface. For example,during the first 60 min, though the temperature values of the T1 position were higher than those ofthe T3 and T7 positions, after a large time period, especially as the PCM melts, the temperaturevalues of the T3 and T7 positions were higher than that of the T1 position (as seen in Fig. 5b). Thereason for that is that the liquid PCM rapidly migrates from the bottom to the top of the con-tainer, since the liquid PCM has the lower density and viscosity, and the solid PCM at the topdescends to the bottom. Thus, this phenomenon, known as buoyancy effects, increased the con-vection heat transfer in the melted PCM. Similar results were reported for different PCMs andheat exchanger systems by several authors [7,11–15].

The effect of Reynolds and Stefan numbers on the total melting time is given in Fig. 6a and b. Itcan be deduced from these figures that the total melting time was reduced approximately by 32%at T2, 27% at T3 and 24% at T7 positions as the Reynolds number was increased by three times(as seen in Fig. 6a). This means that the driving force resulting from the increased Reynoldsnumber and, thus, the increased temperature gradient decreased the total melting time. These

Fig. 6. (a) Effect of Reynolds number on the total melting time in radial and axial directions of the PCM (Tw;i ¼ 62 �C;Ste ¼ 0:283), (b) effect of Stefan number (Re ¼ 31:12; 3 kg/min).


values also indicate that the increasing driving force by the Reynolds number was more effective inthe outer radial and the lower axial positions in the PCM. It can be seen in Fig. 6b that the totalmelting time was reduced approximately by 23% at T2, 20% at T3, and 19% at T7 positions,respectively, when the Stefan number was increased from 0.283 (at 62 �C) to 0.396 (at 66 �C).These results show that the total melting time was shortened by 21%, on average, with an increaseof 4 �C of the inlet HTF temperature.

3.2. Solidification process

Typical temperature variations during the solidification process in the radial and axial direc-tions of the PCM are shown in Figs. 7 and 8 when the Reynolds and Stefan numbers were 15.56(for 1.5 kg/min) and 0.0756 (for 34 �C), respectively. As seen in these figures, the PCM solidified inthe temperature range of 43–41 �C, which corresponds to the melting temperature range. Thus, itcan be said that the PCM has an isothermal phase transition temperature range and no subcoolingproperty. The PCM temperature dropped fast at the beginning of the solidification process, and

Fig. 7. Temperature variations in radial direction of the PCM during the solidification process (Axial distance: 160 mm;

Tw;i ¼ 34 �C).

Fig. 8. Temperature variations in axial direction of the PCM during the solidification process (Radial distance: 20 mm;

Tw;i ¼ 34 �C).


then, it was nearly constant with increasing time. Fig. 9a and b show the temporal temperaturesfor the solidification process in the axial and radial directions, where the zone between the curvesbecomes narrow as the PCM releases the latent heat at the solidification temperature range.

Examination of the curves for the solidification process along the radial direction, as seen inFigs. 7 and 9a, shows that the solidification process started at the innermost position (T4) andthen proceeded toward the outermost position (T2) of the PCM container. However, the solidi-fication front along the longitudinal distances in the PCM was not as clear as along the radialdistances. Namely, it firstly located at the lowest axial distance (T1 position as given in Fig. 9b)since the cool HTF flows from the bottom to the top. Similar behavior was reported by El-Dessouky et al. in a study on paraffin wax [11]. At the second stage, the solidification processstarted at the top section of the PCM (T7 position as given in Fig. 9b) and then finished in themiddle section of the PCM (T3 position as given in Fig. 9b).

By examination of the solidification curves, it may be thought that the solidification processtaking place at the lowest axial location in the PCM is governed by only the conduction heattransfer mechanism. However, at the highest axial location, it is controlled mostly by conductionand, in addition, convection heat transfer between the liquid PCM and air gap above the PCM.This additional convection was due to the fact that the temperature of the air gap was lower thanthat of the top layer (as given in Fig. 8).

Fig. 10a and b show the effect of the Reynolds and Stefan numbers on the total solidificationtime in the radial and axial directions. It can be seen clearly in Fig. 10a that the total solidificationtime was reduced approximately by 21% at T2, 24% at T3 and 15% at T7 positions when theReynolds number was increased by two times. Moreover, the total solidification time was reducedapproximately by 20% at T2, 23% at T3 and 17% at T7 positions when the Stefan number wasincreased from 0.0567 (36 �C) to 0.0945 (32 �C), or with an increase of 4 �C in driving force (asseen in Fig. 10b). It can be concluded from these results that the solidification rate in the T2 andT3 positions was more affected by increasing the Reynolds and Stefan numbers than in the T7position. The reason for that is that there was already available an additional convection at the T7

Fig. 9. Temporal temperature variations of the PCM during the solidification process (a) in radial direction, (b) in axial

direction (Ste ¼ 0:0756; 34 �C; Re ¼ 15:56; 1.5 kg/min).


position. When discussing the above mentioned heat transfer behaviors, another important factormust be considered, that is, the solid conduction thermal resistance, which plays an important roleon the solidification rate. The conduction thermal resistance in the solidified PCM, Rst is given byEq. (1) at steady state [5]:

Rst ¼ rw lnðr=rwÞ=2ks ð1Þ

where r is the radius of the solid–liquid interface, rw is the radius of the HTFP and ks is the thermalconductivity of the solid PCM. It can be deduced from this equation that the solidification processis fast at the beginning of the period due to the solid–liquid interface with low radius but continuesat a lower rate with increasing the interface radius. In the similar way, it is expected that in theradial direction, the solidification rate is lower at the outermost location than the innermost lo-cation due to the increasing ratio of r/rw and, thus, increasing Rst with time. The obtained resultsduring the solidification process wholly confirm the above mentioned idea and also agreed withthe results reported by some researchers [5,7,11–15].

When comparing the time for charging only the latent heat during the melting process with thetime for discharging the same amount of latent heat during the solidification process, it can beseen that the charging time was much smaller than the discharging time. For example, under thesame experimental conditions, the charging time was 70 min, and the discharging time was 90 min.The cause of this delay in time for the solidification process was mainly due to the above men-tioned conduction thermal resistance in the solidified PCM. However, it should not be forgottenthat the charging time would be shortened by natural convection in melted PCM during themelting process.

Fig. 10. (a) Effect of Reynolds number on the total solidification time in radial and axial directions of the PCM

(Ste ¼ 0756; 34 �C), (b) effect of Stefan number on the solidification time (Re ¼ 15:56; 1.5 kg/min).


3.3. Average heat transfer coefficient

In this study, the local heat transfer coefficient could not be estimated more accurately for thepresent heat exchanger system since the temperature difference between the outer surface of theHTFP and the PCM was not the same along the axial heights of the HTFP. Thus, the averageheat transfer coefficient, instead of the local heat transfer coefficient, was calculated for themelting and solidification processes by the following equation [16]:

Avho ¼ ðq=ADTLÞ ð2Þwhere the surface area of the HTFP, A, and the sensible heat transfer rate, q were calculated asfollows:

A ¼ pdol ð3Þ

q ¼ MCp;wðTw;i � Tw;oÞ ðfor melting processÞ ð4Þ

q ¼ MCp;wðTw;o � Tw;iÞ ðfor solidification processÞ ð5ÞThe logarithmic mean temperature difference, DTL was calculated for the present system as fol-lows:

DTL ¼ ðT9� T8Þ � ðT5� T4ÞlnðT9� T8Þ=ðT5� T4Þ ðfor melting processÞ ð6Þ

DTL ¼ ðT8� T9Þ � ðT4� T5ÞlnðT8� T9Þ=ðT4� T5Þ ðfor solidification processÞ ð7Þ

Figs. 11a and 12a show the effect of Reynolds number on the average heat transfer coefficient forthe melting and solidification processes, respectively. The average heat transfer coefficient for themelting process was increased approximately by 62% and by 43% approximately for the solidi-

Fig. 11. (a) Effect of Reynolds number on the average heat transfer coefficient for the PCM during the melting process,

(b) effect of Stefan number on the average heat transfer coefficient for the PCM.


fication process when the Reynolds number was increased by two times. These results proved thatthe average heat transfer coefficients were affected by increasing the Reynolds number moreduring the melting process than during the solidification process. Moreover, the average heattransfer coefficient for the melting process was increased approximately by 71% and increased by45% approximately for the solidification process in the case of 4 �C temperature change at theinlet HTF (as shown in Figs. 11b and 12b). These results indicated that the average heat transfercoefficients were affected by the Stefan number more during the melting process than during thesolidification process. The reason is that the magnitude of the natural convection occurring in themelted PCM can be significantly changed by the Stefan number during the melting process.

3.4. Heat flow rate

In the present study, heat flow rates were calculated by using the amounts of charging sensibleand latent heats to the PCM during the melting process and by using the amounts of dischargingsensible and latent heats from the PCM during the solidification process in following equations:

q ¼ mpcm½Cp;sðTw;i � TpcmÞ þ L�=Dtm ðfor melting processÞ ð8Þ

q ¼ mpcm½Cp;lðTpcm � Tw;iÞ þ L�=Dts ðfor solidification processÞ ð9Þ

where up to the PCMmelting or solidification temperature, Tpcm was taken as an average of all theprobe temperature values in the radial and axial directions in the PCM. However, in calculatingthe charging or discharging latent heat, an assumption was made: the mass amounts of the meltedor solidified PCM were equal to one another in the subsequent melting or solidification timeintervals. The reason this assumption may be accepted is that the PCM melted and solidifiedcongruently throughout the experimental runs.

The effect of the Stefan number on the heat transfer rates during the melting and solidificationprocesses is shown in Fig. 13a and b, respectively. As a first observation with respect to these

Fig. 12. (a) Effect of Reynolds number on the average heat transfer coefficient during the solidification process

(Ste ¼ 0:0756; 34 �C), (b) effect of Stefan number on the average heat transfer coefficient (Re ¼ 10:37; 1 kg/min).


figures, it may be noted that the heat flow rates just decreased and then were constant with in-creasing time. The zero slope sections of the curves correspond to the charging flow rates of thelatent heat or discharging flow rates. Meanwhile, the heat flow rate at the beginning of the meltingprocess was approximately 1300 W when the driving force was 24 �C (Ste ¼ 0.396), it was ap-proximately 1190 when the driving force was 20 �C (Ste ¼ 0:283). Though the heat flow rate forthe beginning of the solidification process was established at about 680 W when the drivingforce was 10 �C (Ste ¼ 0:0945), it was established at about 570 W when driving force was 6 �C(Ste ¼ 0:0567).

As a quantitative result obtained from these figures, it can be also noted that the average heatflow rate for the melting process increased by 25% approximately in the case of an increase of 4 �Cin the driving force, and the average heat flow rate increased by 17% approximately for the so-lidification process in the case of a decrease of 4 �C for the inlet HTF temperature, or an increaseof 4 �C in the driving force.

4. Conclusions

The following conclusions are made in the light of the results obtained for the present latentheat energy storage system during the melting and solidification processes of lauric acid:

1. Lauric acid melts and solidifies in an isothermal temperature range which corresponds to 41–43�C. Thus, it has no subcooling during the solidification.

2. The melting and solidification front moved from the outer wall of the HTFP to the inner wallof the PCM container in the radial direction as the melting front moved from the top to thebottom in the axial direction in the PCM. However, it was difficult to establish the solidificationmoving along the axial PCM lengths.

Fig. 13. (a) Effect of Stefan number on the heat transfer rate for the PCM during the melting process (Ste ¼ 0:283;62 �C; Ste ¼ 0:396; 66 �C), (b) effect of Stefan number (Ste ¼ 0:0567; 36 �C; 0.0945; 32 �C) on the heat transfer rate for

the PCM during the solidification process.


3. The melting front was mostly governed by convection heat transfer in the melted PCM due tobouyoncy effects, whereas the solidification front was controlled by conduction heat transferand slowed by the solid conduction thermal resistance due to the increase of the solid–liquidinterface radius.

4. The effect of Reynolds and Stefan numbers on the total melting and solidification times wasalmost same.

5. The average heat transfer coefficients were affected by the Reynolds and Stefan numbers moreduring the melting process than during the solidification process.

6. The average heat flow rates during the melting and solidification processes increased by 25%and 17%, respectively, in the case of changing by 4 �C the inlet HTF temperature.

7. As a result, it was found that lauric acid as a PCM, which has 95% purity, an isothermal phasetransition temperature range (41–43 �C) and desirable thermal and heat transfer characteristics,is a suitable thermal energy storage material in space and greenhouse heating applications.

Acknowledgements

The authors would like to thank Gaziosmanpas�a University Research Fund for its financialsupport of this work.

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Thermal and heat transfer characteristics in a latent heat storage system using lauric acid

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