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Energy 172 (2019) 580e591
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Energy
journal homepage: www.elsevier .com/locate/energy
Effects of thermal conductivity and density on phase changematerials-based thermal energy storage systems
Benli Peng a, b, Guanghan Huang b, Pengtao Wang b, Wenming Li b, Wei Chang b,Jiaxuan Ma b, Chen Li b, *
a Naval Architecture and Ocean Engineering College, Dalian Maritime University, Dalian, Liaoning, 116026, Chinab Department of Mechanical Engineering, University of South Carolina, Columbia, SC, 29208, USA
a r t i c l e i n f o
Article history:Received 6 September 2018Received in revised form19 December 2018Accepted 28 January 2019Available online 29 January 2019
Keywords:Phase change materialsCharging/discharging performanceThermal conductivity effectDensity and orientation effect
* Corresponding author. Department of MechanicaE-mail address: [email protected] (C. Li).
https://doi.org/10.1016/j.energy.2019.01.1470360-5442/© 2019 Elsevier Ltd. All rights reserved.
a b s t r a c t
This research systematically studies the impacts of thermal conductivity and density of phase changematerials (PCM) on the characteristics of PCM-based thermal energy storage systems (TES). We showthat the eutectic PCM, owing to its high thermal conductivity, has more stable temperature evolutionthan that of paraffin wax during both heat charging and discharging processes. The paraffin wax has anenhanced charging rate, when the heat is applied at the bottom, as a result of convection driven by theobvious temperature-dependent density of liquid paraffin wax. The convection and orientation effectsare significant in the charging process of paraffin wax, but insignificant for eutectic PCM, which arefurther confirmed by visualization and numerical studies. Specifically, a gap forms between the coveredplate wall and the solid paraffinwax after discharging process. This gap significantly inhibits the chargingprocess in a heat charging and discharging cycle. We also observed that the charging efficiency of theparaffin wax is substantially reduced by its high contact thermal resistance, which is 2e3 orders ofmagnitude higher than that of eutectic PCM. This shows that rapid thermal energy charging/dischargingrates, a highly desirable stable working temperature, and orientation-insensitivity of TES can be achievedusing PCM with a high thermal conductivity and a temperature-independent density.
© 2019 Elsevier Ltd. All rights reserved.
1. Introduction
Phase change materials (PCM) with a low melting point havebeen extensively employed in thermal energy storage systems(TES) [1e4], thermal management of electronics [3], building [5e7],heat recovery [8,9], heat pumps [10], electric vehicles [11], dieselengines [12], batteries [13e16] and spacecraft [17]. Optimizedcharging/discharging performances with stable temperature evo-lutions, small temperature differences, short charging/dischargingtime, and high charging/discharging efficiencies are highly desir-able for PCM in these applications. However, the PCM performancecan be greatly affected by thermal conductivity. PCM with a lowthermal conductivity, such as paraffinwax, hydrated salts, and fattyacids, have been widely employed in TES. Numerous techniqueshave been developed to improve their thermal conductivities, suchas embedding highly conductive nanomaterials [18e21], particles
l Engineering, University of South
[19] and fins [22e24]. The thermal conductivities of paraffin can beenhanced up to 48% and 60% by adding paraffin-nanomagnetitecomposites (PNMS) with weight concentrations at 10% and 20%[20], respectively, which accordingly increases the cost of theparaffin by 20e40%. However, the charging rate was still low evenafter integrating three additional fins on the hot wall [22]. The finconfigurations to enhance heat charging/discharging processesunder different conditions were also numerically analyzed [24].Similar observations have been reported using other filling mate-rials, including carbon nano tubes (CNT) [21] and carbon fibers[18,25]. The charging rate was fundamentally limited by the slightlyenhanced thermal conductivities and large interfacial thermalresistance between the PCM and filling materials.
The charging/discharging processes of PCM have been exten-sively investigated experimentally [10,22,24,26e30], theoretically[31] and numerically [32,33]. Wang et al. [29] experimentally
Carolina, Columbia, SC, 29208, USA.
Nomenclature
cp specific heat capacity (J$kg�1$K�1)h height (m)hsf latent heat of fusion (kJ$kg�1)k thermal conductivity (W$m�1$K�1)m mass (kg)p heating power (W)Q heat (J)q heat transfer rate (W)T temperature (�C)V volume (m3)
Greek Symbolsq time (s)r density (kg$m-3)ε charging efficiency
B. Peng et al. / Energy 172 (2019) 580e591 581
demonstrated that the charging rate of the capsule employing threePCM components was significantly enhanced compared toemploying single PCM component. However, the mechanism wasnot discussed in the study. Arefeh [32] numerically showed that theconduction heat transfer dominated at the beginning, then theconvection heat transfer started working and improved thecharging process when the phase change occurs. On the other hand,the experiment conducted by Kandasamy et al. [3] indicated thatthe orientation effect was not significant in practical applications.Yang et al. [31] analyzed the charging/discharging processes andprovided a theoretical guidance for applications of three PCM TESin a solar thermal power system. Ramalingam et al. [28] investi-gated the melting and solidification of paraffin wax in a concentrictube PCM TES. Naidu et al. [27] analyzed the charging and dis-charging process of paraffinwax and a small temperature vibrationwas found in the charging process. Again, the mechanism was notdiscussed. Moreover, the effect of thermal conductivity and densityof PCM on the charging/discharging rates and temperature evolu-tions are still unclear. The charging and discharging processes ofdifferent PCM need to be systematically investigated.
This research studies the effect of thermal conductivity anddensity of PCM on the charging/discharging processes of PCM-based TES, and provides a guide to select an appropriate PCM forpractical applications. A eutectic PCM and a paraffinwax, with highthermal conductivity ratio and similar volumetric energy density,were selected in this study [4,34]. An experimental system wasdesigned and built. The temperature evolutions measurement,visualization experiment and numerical simulation are performed.The temperature evolutions of two different PCM in charging/dis-charging under various thermal loads were characterized. Themechanism of the charging processes of eutectic PCM and paraffinwax were also analyzed through comparing contact thermal re-sistances. The convection and orientation effects during thecharging/discharging process of PCM were visualized. A short solidslice with small density of liquid paraffin wax was used as a tracerparticle to visualize and track the velocity of the liquid paraffinwaxduring the metling process. A numerical melting/solidificationmodel was established using the two dimensional (2D) enthalpy-porosity method [35e38] to verify the orientation effect (i.e., ef-fect of natural convection) in the charging process of paraffin wax.An experiment was conducted to minimize gravity impacts on PCMmelting by heating samples from the top surface. A cycling exper-iment including charging the PCM in the top heating condition,discharging the PCM and subsequently charging the PCM in the top
heating condition was also carried out to confirm the effect ofdesnity on parafifin wax performance.
2. Experiments
A schematic of the experimental system is shown in Fig. 1. Itconsists of a sample chamber, a test samples, a heating system, avoltage regulator, and a data acquisition system. The chamber(45.0mm� 38.0mm� 71.0mm) is made of polysulfone (McMas-ter, k¼ 0.26Wm�1 K�1). A hole with a diameter of 12.7mm anddepth of 61.0mm was drilled in the center of the block. A copperrod with a diameter of 12.7mm and length of 30.0mm wasmounted at the bottom section of the hole. A hole with a diameterof 6.35mm was drilled in the center of the copper rod to house acartridge heater.
A voltage regulator (ranging from 0.0 to 120.0 V) is used toadjust input heating power from 4.34 to 21.01W. Five T-typethermocouples (Omega, www.omega.com, USA) are installed in theholes along the sample chamber. The distance between twoneighboring holes is 6.0mm. The top of the sample chamber iscovered by a copper cap with a silicone gasket. The chamber isinsulated by mineral wools with thermal conductivity of~0.04Wm�1 K�1 (Thermafiber, Inc, www.thermafiber.com, USA,Thermafiber FRF). When a discharging process is carried out, thetop of the chamber is exposed to air. The stored heat is released toambient by natural convection. The PCM temperatures aremeasured by five T-type thermocouples with an uncertainty of±0.25 �C. The effective height of the cylindrical PCM sample is24.0mm which is the same as the highest position of the thermalcouple. The effective volume of PCM is 3.0387� 10�6m3. Theproperties of the eutectic PCM (Bi50Pb26.7Sn13.3Cd10) and paraffinwax are specified in Table 1. The volumetric energy density includesboth latent heat and sensible heat. The temperature difference incharactering the sensible heat is set from room temperature of~20 �C to a terminal temperature of ~80 �C. (The temperature dif-ference between ~ 20 �C to themelting point is used to calculate thesensible heat volumetric energy density in the solid state of PCM,and the temperature difference between melting point to ~80 �C isapplied to calculate the sensible heat volumetric energy density inthe liquid state of PCM.)
The charging processes of PCM and the performances weretested under seven thermal loads including 4.34W, 6.25W, 8.51W,11.11W, 14.06W, 17.36W and 21.01W. Moreover, the other twoworkloads (i.e., 5.45W for eutectic PCM and 7.5W for paraffinwax)were applied to verify the orientation effect in the charging process.The sample was heated up from the room temperature toapproximately 80 �C in the charging process. Then the insulationlayer at the top of the copper cap was removed for its dischargingprocess. Data was recorded in both charging and discharging pro-cesses. The effect of the buoyant force (induced the natural con-vection) on the charging and discharging processes wereinvestigated by heating PCM from the bottom and top (orientationeffect). The top heating can suppress the natural convection. Allexperiments were repeated twice under the same workingcondition.
A visualization study on the charging and discharging processesof the paraffin wax was conducted in a transparent glass cylinder,using a high-speed camera (Phantom v7.3) equipped with a macrolens (Sigma Ex-DG MACRO-105mm 1:2.8, depth offield:10e20mm). A short solid slice with nearly identical density ofliquid paraffinwax was used as a tracer particle to demonstrate theflow direction in the liquid PCM during the charging process. Theframe rate of the high-speed camera applied in the experiment is10 frames per second. The discharging process of eutectic PCM wasalso visualized in a metal cylinder for comparisons.
Copper Rod
Cap
Gasket
Sample
Heater Wires
Sample Chamber
Cartridge Heater
Therm
ocouples
(a)
h0=0mm
h1=6mm
h2=12mm
h3=18mm
h4=24mm
21
22
23
24
(b)
Fig. 1. (a) Schematic of the experimental system and (b) the thermocouples installation in the PCM sample.
B. Peng et al. / Energy 172 (2019) 580e591582
3. Data reduction
The total charging energy of a PCM consists of sensible heat Q1(for the solid state), the latent heat of fusion Q2, and the sensibleheat Q3 (for the liquid state) with correspondingly charging time q1,q2 and q3 in three stages. Therefore, three charging stages aredefined as following. Charging the solid PCM is the first stage,where temperature increases from the initial temperature ~20 �C tothe melting point. The melting process of PCM is the second stage
qeff ;av ¼ Qtotalqcharging
¼
ðTmelting
TinitialmPCM;scpPCM;sdT þmPCMhfusion þ
ðTterminal
Tmelting
mPCM;lcpPCM;ldT
qcharging(2)
and completed until the PCM completely melted. Charging theliquid PCM is the third stage, where the temperature increases fromthe completely melted PCM to the terminal temperature~80 �C. Thedischarging process is a reverse process to the charging process.
The total heat absorbed by the PCM during the charging process,equals to the mass of the PCM times the volumetric energy densityof the PCM, is written as [41,42],
Qtotal ¼ðTmelting
Tinitial
mPCM;scpPCM;sdT þmPCMhfusion
þðTterminal
Tmelting
mPCM;lcpPCM;ldT (1)
Table 1Major properties of the PCM used in this study in room temperature.
Properties Melting PointTmelt (�C)
Latent Heat hsf(kJ$kg�1)
Density r
(kg$m�3)Specific He(kJ$kg�1$K
Materials
Bi50Pb26.7Sn13.3Cd10 70 39.8 9580 0.184Paraffin Wax 69e73 200e220 [39] ~900 [40] 2.19e2.9 [
where mPCM is the mass of the PCM, and mPCM¼ rPCMVPCM, cpPCM isthe specific heat capacity of PCM, hfusion is the latent heat of fusion,Tmelting, Tinitial and Tterminal are themelting point, initial temperatureand terminal temperature of a PCM, respectively. The eutectic PCMand paraffin wax have a melting point ~70.0 �C, the initial tem-perature of ~20.0 �C and the terminal temperature of ~80.0 �C. Thesubscripts s and l represent the solid and liquid phases,respectively.
The average effective charging rate is calculated by,
where qcharging is the total charging time.
4. Results and discussions
4.1. Charging process
4.1.1. Temperature evolutionsThe comparisons of the temperature evolutions at different
heights during the charging processes of eutectic PCM(Bi50Pb26.7Sn13.3Cd10) and paraffin wax, with a heating power of8.51W from the bottom, are shown in Fig. 2.
It clearly demonstrates that the temperature change rate of theeutectic PCM (Bi50Pb26.7Sn13.3Cd10) in all measured locations sharesa similar trend during the charging process and decreases sharplywhen the melting occurs. The temperature difference between two
at Capacity�1)
Thermal Conductivity kPCM(W$m�1$K�1)
Volumetric energy density(MJ$m�3)
18.0 487.0539] ~0.25 ~326.43
0 200 400 600 800 1000 1200 14000
10
20
30
40
50
60
70
80
90
Melting point
Tem
pera
ture
(o C)
Time (s)
Height=0mm Height=6mmHeight=12mm Height=18mm
Height=24mm
PCM: Paraffin wax; Heat power=8.51W (b)
0 110 220 330 440 550 660 770 880 990 110010
20
30
40
50
60
70
80
90
Melting pointT
empe
ratu
re(o C
)
Time (s)
Height=0mmHeight=6mmHeight=12mmHeight=18mmHeight=24mm
PCM:Bi50Pb26.7Sn13.3Cd10; Heater power=8.51W (a)
Bottom heating
Bottom heating
Fig. 2. Temperature evolutions during a charging process for different PCM (heating power¼ 8.51W (a) Bi50Pb26.7Sn13.3Cd10, melting point: ~70 �C, keutectic¼ 18Wm�1 K�1; (b)Paraffin wax, melting point: 69 �Ce73 �C, kwax¼ 0.25Wm�1 K�1, at the bottom heating condition).
B. Peng et al. / Energy 172 (2019) 580e591 583
neighboring positions is consistent and nearly identical in thecharging process of the eutectic PCM (Bi50Pb26.7Sn13.3Cd10), thetemperature distribution at the same charging time is stable and notemperature fluctuations were observed during the whole process.This indicates that conductive heat transfer dominates the wholecharging process of the eutectic PCM.
The heating process is non-uniform for the paraffin wax. Thetemperature at 0mm increases rapidly, but it presents differenttrends between 6mm and 24mm. Typically, the temperature at24mm remains at ~20 �C (i.e. the room temperature) after 400 s.However, the corresponding temperature for eutectic PCM is up to50 �C. The temperature at 6mm in eutectic PCM is up to 65 �Cwhenthe temperature of the heating surface reached its melting point(~70 �C), but the corresponding temperature in paraffinwax is only25 �C. This huge difference in temperature is induced by theextreme lower thermal conductivity of the paraffinwax and amuchlarger contact thermal resistance between the paraffinwax and theheating surface. Because a low thermal conductivity strongly im-pedes the heat transfer in the paraffinwax, which induces the hugetemperature difference between the two neighboring positions inthe paraffin wax. The high contact thermal resistance significantlyimpedes the heat transfer from the heating surface to the solidparaffin wax thus induces the huge temperature difference be-tween the heating surface and the paraffin wax. Moreover, thecontact thermal resistance is also dependent of the thermal con-ductivity of the PCM as discussed in the following section.
4.1.2. Effects of contact thermal resistanceThe contact thermal resistances between the PCM and the
heating surface beforemelting were analyzed. It can further explainthe huge difference of heat transfer performance between thesetwo PCM. The effective heat flux for the PCM in charging process iscalculated with an assumption of one dimensional heat conductionin the cylindrical [43], written as
q1 ¼ kPCM
P4i¼1
�T � Ti
��h� hi
�
P4i¼1
�h� hi
�2 (3)
where h is the installation height of the thermocouple, T is themeasured temperature, the average temperature T and averageheight h in Eq. (3) are calculated as,
T ¼
P4i¼1
Ti
4; h ¼
P4i¼1
hi
4(4)
The effective heat flux is obtained by the overall thermal resis-tance between the heating surface and PCM. The effective heat fluxthrough the PCM can be calculated as,
q1 ¼ Ts � T�Rc þ h
kPCM
� (5)
The contact thermal resistance, Rc, is calculated as,
Rc ¼ Ts � Tq1
� hkPCM
(6)
The contact thermal resistance and the effective heat flux be-tween the heating surface and the PCM about eutectic PCM andparaffin wax are compared in Fig. 3.
Fig. 3 illustrates that the effective heat flux in the highlyconductive eutectic PCM (from ~6 kWm�2 to ~20 kWm�2) is muchhigher than that of the paraffin wax (from ~28Wm�2 to~100Wm�2). The contact thermal resistance between the heatingsurface and the paraffinwax is 2e3 orders of magnitude larger thanthat of the eutectic PCM-heating surface interface.
4.1.3. Effects of natural convectionFor the paraffin wax, the temperature difference between the
two neighboring measurement positions, prior to its melting pointof 70 �C, is much larger than that of eutectic PCM, as shown in Fig. 2.It is consistent with a lower thermal conductivity and a highercontact thermal resistance of paraffin wax. The temperature in theparaffin wax increases more rapidly after the temperature exceedsits melting point. Temperature fluctuations up to 50 �C wereobserved during the charging process in the paraffin wax. Theselarge temperature fluctuations are different from the very smalltemperature variations experimentally observed by other re-searchers [27]. The temperature profile in paraffin wax is sub-stantially different from that of the eutectic PCM, which have notbeen reported in previous studies [44e46]. This is due to the sig-nificant density difference in solid and liquid phases [27] and thetemperature-dependent density of the liquid paraffinwax [47]. Thesolid paraffinwax with a relatively higher density descends toward
15 20 25 30 35 40 45 50 55 60 65 70 750.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Contact thermal resistance
Con
tact
ther
mal
resi
stan
ce10
4(m
2K
W-1
)
Surface temperature (oC)
Eutectic
0
2
4
6
8
10
12
14
16
18
20
Effective heat flux
Eff
ectiv
ehe
atfl
ux(k
Wm
-2)
(a)
15 20 25 30 35 40 45 50 55 60 65 70 750.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Contact thermal resistance
Con
tact
ther
ma l
resi
stan
ce(m
2K
W-1
)
Surface temperature (oC)
Paraffin wax(b)
0
14
28
42
56
70
84
98
Effective heat flux
Eff
ectiv
ehe
atfl
ux(W
m-2
)
Fig. 3. Contact thermal resistance between PCM and copper rod and the effective heat flux in PCM. (a) eutectic PCM, (b) paraffin wax.
t=t0+8s t=t0+9s t=t0+10s t=t0+11s t=t0+12s
t=t0+2s t=t0+4s t=t0+6s t=t0+7st=t0
Bubble
Fig. 4. The bubble as highlighted by blue color and the natural convection during the charging process of the paraffin wax. A piece of solid slice was moving in clockwise directiondue to the natural convection as highlighted by red color.
B. Peng et al. / Energy 172 (2019) 580e591584
the liquid paraffin wax, and the temperature-dependent density ofthe liquid paraffin wax induces strong natural convection (clock-wise direction flowmarked by the solid slice in Fig. 4) and enhancesheat transfer as indicated by large temperature fluctuations. Thisstrong natural convection during the paraffin wax melting processis clearly observed in the visualization study, as shown in Fig. 4. Thevisualization is conducted in a glass cylinder and using a high-speed camera (10 frames per second). The natural convection isnot found in the charging process of the eutectic PCM, and the glasscylinder is broken during the charging process of the eutectic PCM.It is due to its high density and high stress to the glass cylinder,herein, no visualization results about the charging process ofeutectic PCM were recorded. Moreover, some small air bubbles arealso observed in the liquid paraffinwax, highlighted by a blue circleshown in Fig. 4. These bubbles may come from the air trappedbetween the glass cylinder and the solid paraffin wax and/or in thesolid paraffin wax during the filling process.
The liquid paraffin wax at high temperature is driven by thebuoyant force, which may heat or even melt the solid paraffin wax,leading to a temperature spike [48]. Then the liquid paraffin wax iscooled down by the melting of solid paraffin, resulting in a sharptemperature drop as highlighted in Fig. 2 (b). The natural
convection effect in the charging process of paraffin wax is clearlyrepresented by the flow field in numerical simulation, as shown inFig. 5 (a) (at the bottom heating condition) and Fig. 5 (b) (at the topheating condition). The similar phenomena have been numericallypredicted with a melting/solidification model using the enthalpy-porosity method [35e38]. The effective heating power applied inthe numerical simulation is 1.0W. However, the flow fields in thecharging process of eutectic PCM is not shown here because there isno velocity field in the liquid eutectic PCM during the chargingprocess. Moreover, the temperature contours during the chargingprocesses of eutectic PCM and paraffin wax in different heatingconditions (i.e. the bottom heating condition and the top heatingcondition) are predicted, which clearly verify the non-existance ofnatural convection in the liquid eutectic PCM during the chargingprocess.
When the paraffinwax is heated from the bottom, a vortex flowis developed in the melted liquid paraffinwax (q> 200 s), as shownin Fig. 5 (a). But such a vortex flow is not observed in the liquidparaffin wax when heating the sample from the top, as shown inFig. 5 (b). This clearly verifies that the heating orientation ofparaffin wax can significantly affect its charging performance. Themelting height of the paraffinwax under bottom heating condition
=100s =200s =400s =1000s
(a) Bottom heating
(b) Top heating, 50× magnification
=1000s=400s=200s=100s
Fig. 5. Flow field in charging process of paraffin wax at different heating styles ((a) bottom heating, (b) top heating with 50�magnification), the effective heating power is 1.0W.
B. Peng et al. / Energy 172 (2019) 580e591 585
is about 20mm, which is much higher than that under top heating(about 13mmat the charging time q¼ 1000 s). However, naturalconvection is not observed on eutectic PCM, because its densities insolid and liquid phases are nearly identical. Although the thermalconductivity ratio between the eutectic PCM and paraffinwax is 72,the total charging time of paraffinwax is only 33%e86% longer thanthat of eutectic PCM when the heat load ranges from 4.34W to21.01W. This is because the intense and strong natural convectionsignificantly enhances the charging rate and obviously shortens thetotal charging time of paraffin wax.
The absence of nature convection in the charging process ofliquid eutectic PCM can be further verified from the numericalpredicted temperature contours. The temperature contours duringthe charging processes of eutectic PCM and paraffinwax at differentheating conditions (bottom heating condition and top heatingcondition) are respectively shown in Fig. 6 and Fig. 7.
When heated from the bottom, the temperature contour issmooth and flat before melting occurs in the bulk paraffin wax,except for the positions that are very near the heating surface(q¼ 100 s), as shown in Fig. 6(a). However, after melting occurs inthe paraffin wax with a distance from the heating surface, thenatural convection, induced by the temperature-dependent densityof paraffinwax significantly disturbs the temperature contours. Thetemperature contour distorts (q¼ 400 s), which agrees well withthe present of vortex flow as shown in Fig. 5 (a). The natural con-vection becomes more intense and complicated along with morecharging time (q¼ 1000 s), resulting in more irregular temperaturecontour. It is also obviously found in the flow field (three vortexes)shown in Fig. 5 (a). However, for the top heating, the temperaturecontours remain smooth and flat during the charging process of
paraffin wax, as shown in Fig. 6 (b). It indicates that there is nonatural convection in the paraffin wax, and conductive heattransfer dominates the charging process. Moreover, the naturalconvection causes the temperature of heating surface much lowerunder the bottom heating than that under the top heating. Thisverifies the significant benefits of the natural convection to thecharging process at the bottom heating.
Different from the temperature contours in the charging processof paraffin wax shown in Fig. 6, the temperature contours ofeutectic PCM are smooth and flat with heating from the bottom andthe top cases in the whole charging process as illustrated in Fig. 7.The same temperature contour clearly illustrates no natural con-vection occurring in the charging process of eutectic PCM.Conductive heat transfer dominates the charging process.
4.1.4. Effects of orientationThe experimental and simulation results of orientation effects
on the temperature evolutions during the charging processes ofthese two PCM are shown in Figs. 8 and 9, respectively. Other tworandom heating powers (5.45W for eutectic PCM and 7.5W forparaffin wax) are applied in the experiment to verify the orienta-tion effects. The almost overlapped temperature evolution curvesunder bottom heating and top heating clearly demonstrate that thetemperature evolutions are independent of the orientation for theeutectic PCM samples both in experimental and numerical study(shown in Fig. 8 (a) and Fig. 9 (a) respectively). It indicates thatconductive heat transfer dominates the melting process of theeutectic PCM. which can be further verified by the temperaturecontour shown in Fig. 7.
Unlike eutectic PCM, the temperature evolutions during the
(a) Bottom heating
-0.006 -0.003 0.000 0.003 0.0060.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)
x (m)
20.00
31.81
43.63
55.44
67.25
79.06
90.88
102.7
114.5
=100s
-0.006 -0.003 0.000 0.003 0.0060.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)x (m)
20.00
36.44
52.88
69.31
85.75
102.2
118.6
135.1
151.5
=400s
-0.006 -0.003 0.000 0.003 0.0060.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)
x (m)
37.00
52.88
68.75
84.63
100.5
116.4
132.3
148.1
164.0
=1000s
(b) Top heating
-0.006 -0.003 0.000 0.003 0.0060.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)
x (m)
29.00
70.50
112.0
153.5
195.0
236.5
278.0
319.5
361.0=1000s-0.006 -0.003 0.000 0.003 0.006
0.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)
x (m)
20.00
45.25
70.50
95.75
121.0
146.3
171.5
196.8
222.0=400s-0.006 -0.003 0.000 0.003 0.006
0.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)
x (m)
20.00
31.81
43.63
55.44
67.25
79.06
90.88
102.7
114.5=100s
Fig. 6. The temperature evolution in charging process of paraffin wax at different heating styles ((a) bottom heating, (b) top heating), the effective heating power is 1.0W.
B. Peng et al. / Energy 172 (2019) 580e591586
charging process of the paraffin wax are highly dependent on theorientation as displayed in Fig. 8 (b), but such significant differencein the charging times has not been observedwhen the heating fromhorizontal, vertical, or slanted orientations were reported by Kan-dasamy et al. [3]. When heating from the bottom, natural convec-tion plays a significant role during themelting process and shortensthe total charging time. When heating from the top, it takes muchlonger to heat the whole paraffin wax sample after minimizing theeffect of natural convection. The numerical results show that thenatural convection can significantly shorten the charging time ofparaffin wax, as shown in Fig. 9 (b). It further validates that naturalconvection can significant enhance charging process [49,50] andshortern charging time. Therefore, the benefits of the orientationeffect in the charging process of paraffin wax needs to be consid-ered in practical applications.
4.1.5. Charging time and effective charging rate (under bottomheating)
The PCM charging time of each stage at various heating powersis shown in Fig. 10 for the eutectic PCM and the paraffin wax,respectively. It indicates the charging time on the second stage (i.e.the melting process) takes the longest time for two PCM because ofthe phase change. The first and third stages take a very short timedue to the absent of phase change, where only sensible heattransfer plays a role. The charging time for each stage reduces withincreasing heating power. The charging time on the second stage ofparaffinwax is ~2 times longer than that of the eutectic PCM. This is
also primarily a collective effect of its lower thermal conductivityand stronger natural convection.
Fig. 11 shows the total charging time and the correspondingaverage effective charging rate of eutectic PCM and paraffin waxfrom ~20 �C to ~80 �C at various heating powers. Consistently, thetotal charging time of the paraffin wax is much longer than that ofthe eutectic PCM. Although the thermal conductivity of the paraffinwax is ~1/72 of eutectic PCM, the charging rate of paraffin wax isenhanced by the strong natural convection during the chargingprocess, which greatly shortens its total charging time. The totalcharging time of the paraffin wax is only 1.33 to 1.86 times longerthan those of the eutectic PCM for heating power in a range of4.34e21.01W. This is much less than the thermal conductivity ra-tio. The average effective charging rate of the two PCM increaseswith the heating power increases. However, the charging rate of theeutectic PCM increases at much larger rate than that of the paraffinwax due to its much higher thermal conductivity. This study il-lustrates that the PCMwith higher thermal conductivity can enablemore rapid charging processes.
4.1.6. Charging efficiencyThe integration performance of TES is characterized by the
charging efficiency, which is defined as,
εcharging ¼ qeff ; avpheater
� 100% (7)
where εcharging is the charging efficiency, and pheater is the heating
(a) Bottom heating-0.006 -0.003 0.000 0.003 0.006
0.000
0.005
0.010
0.015
0.020
0.025
0.030y
(m)
x (m)
32.78
33.61
34.44
35.26
36.09
36.92
37.74
38.57
39.40
=100s
-0.006 -0.003 0.000 0.003 0.0060.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)x (m)
69.58
69.71
69.85
69.99
70.13
70.26
70.40
70.54
70.67
=400s
-0.006 -0.003 0.000 0.003 0.0060.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)
x (m)
69.98
70.51
71.03
71.56
72.08
72.61
73.13
73.66
74.18
=800s
(b) Top heating-0.006 -0.003 0.000 0.003 0.006
0.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)
x (m)
32.78
33.61
34.44
35.26
36.09
36.92
37.74
38.57
39.40=100s-0.006 -0.003 0.000 0.003 0.006
0.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)
x (m)
69.58
69.71
69.85
69.99
70.13
70.26
70.40
70.54
70.67=400s-0.006 -0.003 0.000 0.003 0.006
0.000
0.005
0.010
0.015
0.020
0.025
0.030
y(m
)
x (m)
69.98
70.51
71.03
71.56
72.08
72.61
73.13
73.66
74.18=800s
Fig. 7. The temperature evolution in charging process of eutectic PCM at different heating styles ((a) bottom heating, (b) top heating), the effective heating power is 1.0W.
0 200 400 600 800 1000 1200 1400 1600 18000
10
20
30
40
50
60
70
80
90
100
110
120
Tem
pera
ture
(o C)
Time (s)
Bottom heating, h=0mm Bottom heating, h=6mmBottom heating, h=18mm Top heating, h=0mmTop heating, h=6mm Top heating, h=18mm
Cycle experiment: Top heating, h=0mmTop heating, h=6mm Top heating, h=18mm
Paraffin wax, heat power=7.5W
(b)
0 200 400 600 800 1000 1200 1400 160010
20
30
40
50
60
70
80
90Eutectic PCM
Tem
pera
ture
(o C)
Time (s)
Top heating, h=0mmTop heating, h=6mmTop heating, h=18mmBottom heating, h=0mmBottom heating, h=6mmBottom heating, h=18mm
Heat power=5.45W (a)
Fig. 8. The temperature evolution of various PCM under different heating style: bottom heating and top heating ((a) eutectic PCM, (b) paraffin wax).
B. Peng et al. / Energy 172 (2019) 580e591 587
power.The charging efficiencies of eutectic PCM and paraffin wax at
various heating powers are compared in Fig. 12. The charging effi-ciency of the eutectic PCM is improved with an increase in heatingpower. The charging efficiency is improved by 13.14%e25.3% whenthe heating power increased from 4.34 to 21.01W, respectively.However, the charging efficiency of the paraffin wax is nearly
constant, especially when the heating power exceeds 8.41W. Thissaturated charging efficiency of the paraffinwax could be restrictedby its lower thermal conductivity compared to eutectic PCM. Thisrestriction is more obvious under high thermal loads. It demon-strates that although the natural convection can strongly enhancethe charging process of paraffin wax, the benefit is not infinite,according to the curves shown in Fig. 12. Therefore, the value of
0 110 220 330 440 550 660 770 880 990 11000
8
16
24
32
40
48
56
64
72
80
88
96
Effective heat power: 1.0 W
Tem
pera
ture
(o C)
Time (s)
Bottom heating, h=0mmBottom heating, h=6mmBottom heating, h=18mmTop heating, h=0mmTop heating, h=6mmTop heating, h=18mm
Numerical Results: Eutectic PCM (a)
0 200 400 600 800 1000 1200 1400 16000
8
16
24
32
40
48
56
64
72
80
88
96
Effective heat power: 1.0 W
Numerical Results: Paraffin wax
Tem
pera
ture
(o C)
Time (s)
Bottom heating, h=0mmTop heating, h=0mmBottom heating, h=6mmTop heating, h=6mmBottom heating, h=18mmTop heating, h=18mm
(b)
Fig. 9. Simulation results about the temperature evolution comparison in the charging process of the two PCM at bottom and top heating styles ((a) eutectic PCM, (b)paraffin wax).
4 6 8 10 12 14 16 18 20 220
160
320
480
640
800
960
1120
1280
1440
1600(a)
Cha
rgin
gtim
e(s
)
Heater power (W)
First stage,
Second stage,
Third stage,
PCM: Bi50Pb26.7Sn13.3Cd10
4 6 8 10 12 14 16 18 20 220
400
800
1200
1600
2000
2400
2800
3200
3600C
harg
ing
ti me
(s)
Heat power (W)
First stage,
Second stage,
Third stage,
PCM: Paraffin wax (b)
Fig. 10. The charging time of each stage and the total charging time at various heating powers ((a) Eutectic, melting point ~70 �C, keutectic¼ 18Wm�1 K�1; (b) Paraffin wax, meltingpoint: 69 �Ce73 �C, kwaxz0.25Wm�1 K�1).
4 6 8 10 12 14 16 18 20 220.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
Ave
rage
effe
ctiv
ech
argi
ngra
te( W
)
Heat power (W)
Paraffin waxBi50Pb26.7Sn13.3Cd10
Average effective charging rate (b)
4 6 8 10 12 14 16 18 20 220
400
800
1200
1600
2000
2400
2800
3200
3600
Cha
rgin
gtim
e(s
)
Heater power (W)
Bi50Pb26.7Sn13.3Cd10
Paraffin wax
Heating from about 20oC to 80oC (a)
Fig. 11. (a) The total charging time and (b) the corresponding average effective charging rate of different PCM.
B. Peng et al. / Energy 172 (2019) 580e591588
4 6 8 10 12 14 16 18 20 220
3
6
9
12
15
18
21
24
27
30
Cha
rgin
gef
fici
ency
(%)
Heat power (W)
Paraffin waxBi50Pb26.7Sn13.3Cd10
Charging efficiency
Fig. 12. The charging efficiency of different PCM with different thermal conductivitiesat various heating powers.
B. Peng et al. / Energy 172 (2019) 580e591 589
heating power needs to be considered in the charging process ofparaffin wax to economically and optimally operate the TES.Meanwhile, the heating power supplied to the charging process ofeutectic PCM can be a little higher to charge the eutectic PCMmorerapidly and operate the system more economically.
4.2. Discharging process
4.2.1. Temperature evolutionsFig. 13 shows the temperature evolution in the discharging
processes of the eutectic PCM and the paraffin wax. It clearlydemonstrates that the eutectic PCM maintains a constant meltingpoint temperature for more than 800 s in the discharging process.The temperatures at all measured locations are nearly identicalowing to its high thermal conductivity. Heat absorbed in theeutectic PCM is quickly transferred to the cooling surface, resultingin a nearly constant temperature until the solidification process iscompleted. Moreover, during the discharging process, the tem-perature near the cooling surface decreases below the meltingpoint first, then the temperature of locations with a distance from
Te m
pera
ture
(o C)
0 250 500 750 1000 1250 1500 1750 2000 225042
49
56
63
70
77
84
91
98
Melting point
Tem
pera
ture
(o C)
Time (s)
Height=6mmHeight=12mmHeight=18mmHeight=24mm
PCM: Bi50Pb26.7Sn13.3Cd10 (a)
Solidification process
Fig. 13. Temperature evolution during discharging process applying different PCM ((a) Bi50Ppoint: 69 �Ce73 �C, kwax¼ 0.25Wm�1 K�1).
the cooling surface reduces in a short period of time. However, thetemperature keeps dropping rapidly during the entire dischargingprocess of the paraffin wax except near the melting point (a slowdecrease rate of the temperature is maintained near the meltingpoint, actually a little higher than melting point shown in Fig. 13(b)). However, a constant temperature cannot be maintained inthe solidification process of the paraffin wax. This is because of thelow thermal conductivity of paraffin wax. The heat stored inparaffin wax with a distance from the cooling surface cannot beeffectively transferred to the cooling surface. As a result, the tem-perature drops more rapidly near the cooling surface as indicatedby the temperature at 24mm. Moreover, the volume of paraffinwax shrinks and a hole is formed at the center of the solid paraffinwax during the discharging process, which induces the tempera-ture near the cooling surface to keep dropping rapidly. The tem-perature of paraffin wax with a distance from the cooling surfacedrops slowly. The time that the temperature keeps a slow decreaserate becomes longer when the distance becomes longer from thecooling surface, implying that the low thermal conductivity ofparaffinwax strongly impedes the heat transfer. The detailed studyabout the volume shrinking and the formation of the hole duringthe discharging process of paraffinwax by visualization experimentis described in the following section. The same experiment abouteutectic PCM is also conducted for comparison.
4.2.2. Visualization studyA visualization study on the discharging processes of the
eutectic PCM and paraffin wax were respectively conducted in ametal cylinder and a glass cylinder. The comparison results areshown in Fig. 14.
The results demonstrate there is no obvious change in the vol-ume during the discharging process of the eutectic PCM. However,for the paraffinwax, the volume shrinks and eventually leads to theformation of a hole. This hole is caused by a ~10% volume reductionduring the discharging process (about 3.0 cm3 reduces when thetotal volume of the liquid paraffin wax is about 30.0 cm3 for theinitial temperature of paraffinwax 80 �C). The volume of the hole isabout 1.3 cm3 shown in Fig. 14 (b). This hole well supports thetemperature evolution shown in Fig. 8 (b). The charging time withheating from the top in the cycling experiment is longer than that atthe top heating in the first experiment marked by an ellipse. Theorientation effects are also confirmed by this formed hole. How-ever, the hole is not formed between the solid paraffinwax and the
0 500 1000 1500 2000 2500 3000 3500 4000 450035
42
49
56
63
70
77
84
91
98
Melting point
Time (s)
Height=6mmHeight=12mmHeight=18mmHeight=24mm
PCM: Paraffin wax (b)
b26.7Sn13.3Cd10, melting point: ~70 �C, keutectic¼ 18Wm�1 K�1, (b) Paraffin wax, melting
t=t0
Liquid
t=t0+300s
Solid
Liquid
t=t0+410s
Solid
Hole
t=t0+360s
Solid
Hole
t=t0+590s
Solid
Hole
(b)
Solid
(a)
t=t0+290st=t0
Liquid
t=t0+70s
Liquid
t=t0+150s
Liquid
t=t0+220s
Solid
Fig. 14. Discharging processes of paraffin wax and eutectic PCM ((a) eutectic PCM, (b) paraffin wax).
B. Peng et al. / Energy 172 (2019) 580e591590
heating surface with heating from the bottom.
4.2.3. Discharging time and rateThe total discharging time of PCM is defined as that the elapsed
time for cooling down from the temperature of PCM (~95 �C) to thetemperature of the bottom PCM (~50 �C) by natural convection heattransfer between the copper cap and the air. The average dis-charging rate is defined as the ratio of the total heat absorbed by thePCM (similarly calculated by equation (1)) to the total dischargingtime, which is written as.
qeff ;av;dis ¼Qtotal;dis
qdischarging¼
ðTmelting
T50mPCM;scpPCM;sdT þmPCMhfusion þ
ðT95Tmelting
mPCM;lcpPCM;ldT
qdischarging(8)
The total discharging time and the corresponding average dis-charging rates of both PCM are shown in Fig. 15. The total dis-charging time of the paraffin wax is ~4000 s, which is two timeslonger than that of the eutectic PCM ~2000 s. The average dis-charging rate of the paraffin is 0.22W, which is about below 1/3
2000
4000
0.7 0.22
Eutectic Parafin wax0
500
1000
1500
2000
2500
3000
3500
4000
4500
Dis
char
ging
time
(s)
Phase change materials
Discharging time
Discharging time andaverage discharging rate
from 95oC~50oC
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Average discharging rate
Ave
rage
dis c
harg
i ng
rate
(W)
Fig. 15. The discharging time and the average discharging rates of both PCM.
that of the eutectic PCM (about 0.7W). It indicates that the averagedischarging rates of PCM are highly related to their thermal con-ductivities. PCMwith higher thermal conductivities canmore easilytransfer the heat to the cooling surface at the same temperaturedifference thus can achieve much higher discharging rates.
5. Conclusions
The effects of the thermal conductivity and density of PCM oncharging/discharging performances of the highly conductiveeutectic PCM and non-conductive paraffin wax have been system-
atically investigated. The natural convection and orientation effectson the charging process of PCM were further studied and verifiedby visualization and numerical studies. High thermal conductivityPCM can achieve a more stable temperature evolution in thecharging process and maintain a stable temperature during thedischarging processes. The highly conductive PCM with almosttemperature-independent density are insensitive to orientations.For PCM with relatively low thermal conductivities and obvioustemperature-dependent densities, the obvious and strong naturalconvection can greatly enhance energy charging rates when heat isapplied from the bottom. The low thermally conductive PCM withsignificant temperature-dependent densities suffers from orienta-tion effect in both the charging and discharging processes.
Acknowledgements
The authors are grateful to the financial support of the ElectricPower Research Institute (EPRI 1-108059-01-05).
References
[1] Du K, Calautit J, Wang ZH, Wu YP, Liu H. A review of the applications of phasechange materials in cooling, heating and power generation in different tem-perature ranges. Appl Energy 2018;220:242e73.
[2] Jacobo P, Míguez Jos�e L, B�arbara C, L�opez, Gonz�alez Luis M, Lara Jos�e D.Experimental investigation of the thermal response of a thermal storage tankpartially filled with different PCMs (phase change materials) to a steep
B. Peng et al. / Energy 172 (2019) 580e591 591
demand. Energy 2015;91:202e14.[3] Kandasamy R, Wang XQ, Mujumdar AS. Application of phase change materials
in thermal management of electronics. Appl Therm Eng 2007;27:2822e32.[4] Sharma A, Tyagi VV, Chen CR, Buddhi D. Review on thermal energy storage
with phase change materials and applications. Renew Sustain Energy Rev2009;13(2):318e45.
[5] de Gracia A, Cabeza LF. Phase change materials and thermal energy storage forbuildings. Energy Build 2015;103:414e9.
[6] Khudhair AM, Farid MM. A review on energy conservation in building appli-cations with thermal storage by latent heat using phase change materials.Energy Convers Manag 2004;45(2):263e75.
[7] Waqas A, Ud Din Z. Phase change material (PCM) storage for free cooling ofbuildings-A review. Renew Sustain Energy Rev 2013;18:607e25.
[8] Jie J, Lee WL. Experimental investigations on using phase change material forperformance improvement of storage-enhanced heat recovery room air-conditioner. Energy 2015;93:1394e403.
[9] Zhang SL, Wu W, Wang SF. Integration highly concentrated photovoltaicmodule exhaust heat recovery system with adsorption air-conditioningmodule via phase change materials. Energy 2017;118:1187e97.
[10] Niu FX, Ni L, Yao Y, Yu YB, Li HR. Performance and thermal charging/dis-charging features of a phase change material assisted heat pump system inheating mode. Appl Therm Eng 2013;58(1e2):536e41.
[11] Malik M, Dincer I, Rosen MA. Review on use of phase change materials inbattery thermal management for electric and hybrid electric vehicles. Int JEnergy Res 2016;40(8):1011e31.
[12] Sangki P, Seungchul W, Jungwook S, Kihyung L. Experimental study on heatstorage system using phase-change material in a diesel engine. Energy2017;119:1108e18.
[13] Fereshteh S, Aziz B, Mohammadmehdi A, Gholamreza K. Thermal manage-ment analysis of a Li-ion battery cell using phase change material loaded withcarbon fibers. Energy 2016;96:355e71.
[14] Ling ZY, Wang FX, Fang XM, Gao XN, Zhang ZG. A hybrid thermal manage-ment system for lithium ion batteries combining phase change materials withforced-air cooling. Appl Energy 2015;148:403e9.
[15] Pradyumna G, Stanislav L, Aditya D, Ruben S, Jacqueline R, Alexander AB.Graphene-enhanced hybrid phase cange material for thermal management ofLi-Ion batteries. J Power Sources 2014;248:37e43.
[16] Wu WX, Yang XQ, Zhang GQ, Ke XF, Wang ZY, Situ WF, Li XX, Zhang JY. Anexperimental study of thermal management system using copper mesh-enhanced composite phase change materials for power battery pack. Energy2016;113:909e16.
[17] Swanson TD, Birur GC. NASA thermal control technologies for roboticspacescraft. Appl Therm Eng 2003;23:1055e65.
[18] Jun FK, Yuichi H, Yoshi M, Osamu M. Improvement of thermal characteristicsof latent heat thermal energy storage units using carbon-fiber brushes: ex-periments and modeling. Int J Heat Mass Tran 2003;46:4513e25.
[19] Kalaiselvam S, Parameshwaran R, Harikrishnan S. Analytical and experimentalinvestigations of nanoparticles embedded phase change materials for coolingapplication in modern buildings. Renew Energy 2012;39:375e87.
[20] Sahan N, Fois M, Paksoy H. Improving thermal conductivity phase changematerials-A study of paraffin nanomagnetite composites. Sol Energy Mater SolCell 2015;137:61e7.
[21] Wang JF, Xie HQ, Xin Z, Li Y, Chen LF. Enhancing thermal conductivity ofpalmitic acid based phase change materials with carbon nanotubes as fillers.Sol Energy 2010;84(2):339e44.
[22] Kamkari B, Shokouhmand H. Experimental investigation of phase changematerial melting in rectangular enclosures with horizontal partial fins. Int JHeat Mass Tran 2014;78:839e51.
[23] Khan Z, Khan ZA. Experimental investigations of charging/melting cycles ofparaffin in a novel shell and tube with longitudinal fins based heat storagedesign solution for domestic and industrial applications. Appl Energy2017;206:1158e68.
[24] Mahmood MJ, Fariborz H, Saeid S, Abduljalil AA-A. Heat transfer enhancementof phase change materials by fins under simultaneous charging and dis-charging. Energy Convers Manag 2017;152:136e56.
[25] Nomura T, Tabuchi K, Zhu C, Sheng N, Wang S, Akiyama T. High thermalconductivity phase change composite with percolating carbon fiber network.
Appl Energy 2015;154:678e85.[26] Mehla N, Yadav A. Thermal analysis on charging and discharging behaviour of
a phase change material-based evacuated tube solar air collector. Indoor BuiltEnviron 2016:1e17.
[27] Naidu PVK, Nair AM. Analysis of paraffin wax as a phase change material. Int JCurrent Eng Tech 2018;8(1):52e5.
[28] Ramalingam S, Marimuthu C. Melting and solidification of paraffin wax in aconcentric PCM storage for solar thermal collector. Int J Chem Sci 2016;14(4):2634e40.
[29] Wang JF, Ouyang YX, Chen GM. Experimental study on charging processes of acylindrical heat storage capsule employing multiple-phase-change materials.Int J Energy Res 2001;25(5):439e47.
[30] Wang ZY, Tao P, Liu Y, Xu H, Ye QX, Hu H, Song CY, Chen ZP, Shang W, Deng T.Rapid charging of thermal energy storage materials through plasmonicheating. Sci Rep 2014;4:6246.
[31] Xu Y, He YL, Li YQ, Song HJ. Exergy analysis and optimization of charging-discharging processes of latent heat thermal energy storage system withthree phase change materials. Sol Energy 2016;123:206e16.
[32] Arefeh H. CFD modeling of heat charging process in a direct contact containerfor mobilized thermal energy storage. Sweden: Malardalen University; 2011.
[33] Wang WL, Li HL, Guo SP, He SQ, Ding J, Yan JY, Yang JP. Numerical simulationstudy on discharging process of the direct-contact phase change energystorage system. Appl Energy 2015;150:61e8.
[34] Ge HS, Li HY, Mei SF, Liu J. Low melting point liquid metal as a new class ofphase change material: an emerging frontier in energy area. Renew SustainEnergy Rev 2013;21:331e46.
[35] Beata NZ. The enthalpy-porosity method applied to the modelling of the iceslurry melting process during tube flow. Process Eng 2016;157:114e21.
[36] Swaminathan CR, Voller VR. A general enthalpy method for modeling solid-ification processes. Metal Trans B 1992;23(5):651e64.
[37] Voller VR, Prakash C. A fixed-grid numerical modeling methodology forconvection-diffusion mushy region phase-change problems. Int J Heat MassTran 1987;30:1709e20.
[38] oller VR, Swaminathan CR. Generalized source-based method for solidificationphase change. Numer Heat Tran B 1991;19:175e89.
[39] Specific heat capacity. Diracdelta.co.UK science and engineering encyclopedia.Warwick, England: Dirac Delta Consultants Ltd; 2013.
[40] Kaye GWC, Laby TH. Mechanical properties of materials. Kaye and laby tablesof physical and chemical constants. National Physical Laboratory; 2013.
[41] Lane GA. Phase change materials for thermal energy storage, Technology, vol.2. Boca Raton, USA: CRC Press; 1985.
[42] Pielichowska K, Pielichowski K. Phase change materials for thermal energystorage. Prog Mater Sci 2014;65:67e123.
[43] Peng BL, Ma XH, Lan Z, Xu W, Wen RF. Experimental investigation on steamcondensation heat transfer enhancement with vertically patternedhydrophobic-hydrophilic hybrid surfaces. Int J Heat Mass Tran 2015;83(27):27e38.
[44] Akgun M, Aydm O, Kaygusuz K. Experimental study on melting/solidificationcharacteristics of a paraffin as PCM. Energy Convers Manag 2007;48:669e78.
[45] Kaygusuz K, Sari A. Thermal energy storage system using a technical gradeparaffin wax as latent heat energy storage material. Energy Sources 2005;27:1535e46.
[46] Stella PJ, Udayakumar M, Suresh S. Heat transfer characteristics in latent heatstorage system using paraffin wax. J Mech Sci Technol 2012;26(3):959e65.
[47] Viscosity of paraffin wax-viscosity table and viscosity chart. :https://wiki.anton-paar.com/en/paraffin-wax/..
[48] Wang PT, Sun HW, Wong PY, Fukuda H, Ando T. Modeling of droplet-basedprocessing for the production of high-performance particulate materials us-ing the level set method. Numer Heat Tran Part A: Appl 2012;61(6):401e16.
[49] Fornarelli F, Ceglie V, Fortunato B, Camporeale SM, Torresi M, Oresta P,Miliozzi A. Numerical simulation of a complete charging-discharging phase ofa shell and tube thermal energy storage with phase change material. EnergyProc 2017;126:501e8.
[50] Syeda HT, Rakib H, Shohel M, Animesh D. Convection effect on the meltingprocess of nano-PCM inside porous enclosure. Int J Heat Mass Tran 2015;85:206e20.
