Highly conducting core–shell phase change materials for thermal regulation

Applied Thermal Engineering 66 (2014) 131e139

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Highly conducting coreeshell phase change materials for thermal regulation Nuno Vitorino a, João C.C. Abrantes a, b, *, Jorge R. Frade a a b

Department of Materials and Ceramic Engineering, CICECO, University of Aveiro, 3810 Aveiro, Portugal UIDM, ESTG, Polytechnic Institute of Viana do Castelo, 4900 Viana do Castelo, Portugal

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Coreeshell composite model for highly enhanced transport properties.
Self organized graphiteeparaffin composites for fast latent heat charge and discharge.
Cellular composites by emulsification of paraffin in aqueous suspensions.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 9 September 2013 Accepted 2 February 2014 Available online 8 February 2014

A coreeshell model has been derived for microstructural design of PCM-based composites with optimized 3-dimensional organization of a conducting phase, and a novel method was developed to process self-assembled coreeshell composites for thermal regulation or heat storage. The method was based on emulsification of graphite suspensions in melted paraffin yielding a coreeshell microstructure based on self-organisation of graphite platelets with preferential orientation; this allows remarkable enhancement of thermal conductivity, which increases by at least one order of magnitude for 5 vol% graphite addition. The microstructure of the graphite shell remains stable upon repeated cycling above and below the melting temperature of the paraffin, and shape stabilization is also retained, even without external encapsulation. One confirm that the levels of thermal conductivity of these phase change materials is sufficient for latent heat discharge from relatively large spherical samples to surrounding air. Ó 2014 Elsevier Ltd. All rights reserved.

Keywords: Microstructural design Self-assembling Coreeshell Phase change materials Thermal conductivity

1. Introduction Phase change materials (PCM) are widely proposed for thermal management and heat or cold storage applications, based on the high latent heat. However, thermal conductivity is usually lower than 0.5 W m1 K1 [1] which sets kinetic limitations. In order to

* Corresponding author. UIDM, ESTG, Polytechnic Institute of Viana do Castelo, 4900 Viana do Castelo, Portugal. Tel.: þ351 258 819 700; fax: þ351 258 827 636. E-mail address: [email protected] (J.C.C. Abrantes). http://dx.doi.org/10.1016/j.applthermaleng.2014.02.001 1359-4311/Ó 2014 Elsevier Ltd. All rights reserved.

overcome these kinetic limitations a variety of strategies to increase the PCM thermal conductivity has been used [2e16]. Table 1 summarize some of these strategies, with emphasis on PCMbased composites with conducting metallic structures [4e6], PCM/carbon composites [8,9,17], and other less common composites [10,16,18]. Though most of these approaches rely on highly conducting phase, for the sake of simplicity, this yields limited gains in thermal conductivity [4,8,11,13,17], even on adding highly conducting materials, such as nanostructured carbons [8,12e15,17]. High volume fractions of the highly conducting phase increase thermal conductivity but affect latent heat storage [7].

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Table 1 Summary of strategies to improve the thermal conductivity PCM materials, where k is PCM thermal conductivity and l PCM latent heat. Strategies

PCM

Conductive phase

Preparation method

Conclusion

Ref.

PCM with conducting metallic structures

Paraffin

Micro aluminium particles (50 wt%) - Lesser rings - Longitudinal fins Porous nickel, 85% porosity Cooper nanowires, 58.9 wt% Multi-walled carbon nanotubes, 2 wt% Compressed expanded graphite (8e26 wt%) Expanded graphite, 10 wt% Expanded graphite, 20 wt% Graphite nanoplatelets, 7 wt% Graphene fillers, 4 wt%

Dispersion

Decrease of 60% in the charging time

[4]

Dispersion

Reduction of solidification time to 1/9 and 1/4

[5]

Paraffin

PCM/carbon composites

Erythritol (15 vol%) Tetradecanol Paraffin Paraffin Paraffin (n-docosane) Palmitic acid Paraffin wax Octadecanol

Other composites

Water/5% collagen solution Paraffin Paraffin Capric acid Polyethylene glycol

[6] [7] [8]

Impregnation

k ¼ 10e66 W m1 K1 l ¼ 144e126 J g1 Improvement of 100% in thermal conductivity k ¼ 0.60 W m1 K1 Improvement of 200% in thermal conductivity k ¼ 0.99 W m1 K1 l ¼ 210 J g1. k ¼ 2.87 W m1 K1 in liquid phase k ¼ 1.52 W m1 K1 in solid phase 5.4 < k < 8.3 W m1 K1 Increase of 58% in thermal conductivity Increase of 64% in thermal conductivity Improvement of 100% in thermal conductivity

[9]

Dispersion Vacuum impregnation Dispersion Dispersion

Natural graphite, 15 wt% Porous silica, 25 wt% Expanded perlite, 10 wt% b-Aluminium nitride, 30 wt%

Emulsification Vacuum impregnation Vacuum impregnation

Modelling has been proposed as a strategy to design PCM-based materials with optimized thermal conductivity (e.g. Refs. [2,3]). Simple models can be adapted from the transport properties of composites with series or parallel distributions of the highly conducting phase (e.g. graphite) in a poorly conducting matrix. In these cases, the expected thermal conductivity of composites with parallel (kc,par), and series (kc,ser) organisations of highly conducting graphite and poorly conducting matrix can be described by:

kc;par ¼ f kg þ ð1  f Þkm

(1)


 kc;ser ¼ 1= f =kg þ ð1  f Þ=km

(2)

where f is the fraction of highly conducting graphite phase, kg and km are the thermal conductivities of conducting graphite and poorly conducting matrix. Note that thermal conductivity is

3

k ¼ 11.6 W m K , l ¼ 390 MJ m k ¼ 2.9 W m1 K1, l ¼ 87 J g1 Improvement of 30% in thermal conductivity

Dispersion

2. Models

1

Impregnation Dispersion Dispersion

Natural graphite, 30 wt%

The highest gains in thermal conductivity have been reported by preferential orientation of highly conducting phase, such as metallic fins [5], porous metallic matrixes [6], and also highly conducting carbons, such as graphene or carbon nanotubes [19]. High orientation of expanded graphite also yielded some of the highest results of thermal conductivity for graphite/PCM composites [9]. Note also that the applicability of graphite as highly conducting phase may even extend to metalegraphite composites, depending mainly on the ability to process composites with high orientation (e.g. Ref. [20]). The use of expensive materials such as carbon nanotubes of graphene and/or expensive processing costs is very likely to affect the prospects for commercial exploitation. Therefore, the present approach relies on the use of much cheaper graphite powders and a novel low cost processing method is proposed for these PCMe graphite composites. Processing is based on emulsification of melted paraffin in a graphite suspension, stabilized with addition of starch; this allows high flexibility for casting in any macroscopic shape, and shape stabilization is then easily attained by starch consolidation and drying at temperatures below the melting point of the dispersed paraffin droplets.

1

[17] [11] [12] [13] [14] [15] [16] [18] [10]

determined by the highly conducting phase with parallel arrangement, whereas series association is much closer to behaviour of the poorly conducting matrix. For random distribution of the conducting phase one may assume other classical models, such as McLachland model [21,22], proposed for electrical conduction. On extending this model to thermal conductivity:

8 1 h i9 1=t  1=t ih > > > = < fcr þð1  fcr Þðkc =km Þ1=t >  kg =km kg =km i ih  f ¼ 1þh 1=t > > > ðkc =km Þ1=t  1 fcr kg =km þ ð1 fcr Þðkc =km Þ1=t > ; : (3) where fcr represents a critical volume fraction to ensure percolation and t is a geometric fitting parameter with typical values close to 2. These predictions for random distributions are closer to series association than parallel behaviour, as shown below. Simpler models for electrical conductivity (e.g. the MaxwellGranet Eq. (4)) have also been proposed for the thermal conductivity of PCMegraphite composites [23], i.e.:

  kp þ 2km þ 2f kp  km kc   ¼ km kp þ 2km  2f kp  km

(4)

where kp is a fitting parameter corresponding to high value of thermal conductivity. Guidelines for optimization should thus be mainly based on the parallel model, as expected for arrays of parallel fins with 1dimensional arrangement (F1D) represented in Fig. 1. This is one of the classical concepts to enhance heat transfer in phase change materials, which can be based on arrays of metallic fins. The corresponding F2D and F3D models are best suited for heat dissipation in 2-dimensional or 3-dimensional configurations, as for spherical configurations. Similar concepts may be based on 1D, 2D or 3D arrays of tubes, honeycomb structures, plates, etc. A representative 3D arrangement of conducting plates (P3D) is, thus, shown in Fig. 1, including the corresponding equivalent circuit to obtain the relevant solution for conducting properties of such P3D composites. This model behaviour was used as an approximation for the main concept proposed in the present

N. Vitorino et al. / Applied Thermal Engineering 66 (2014) 131e139

133

heat

flux

F1D

F2D

F3D

Rms

Rgs

Rgp

L

δ

P3D Fig. 1. Schematic representations of representative models for composites including a coreeshell model for conducting plates with 3-D distribution (P3D) and an alternative models for conducting fins with F1D, F2D and F3D arrangements. Rms, Rgs and Rgp represent respectively the thermal resistance of series matrix, series graphite and parallel graphite.

work, i.e., the development of self-organized coreeshell microstructures. Equivalent circuits are often used to analyse heat conduction in complex systems, and can be used to derive a relatively simple analytical solution for the dependence of thermal conductivity of P3D-type composites on the conductivity ratio of individual components, and on fraction of conducting phase. The equivalent circuit proposed for the P3D model (Fig. 1) comprises the flux along aligned conducting graphite (Rgp ¼ (L/kg)/(2Ld)), and a secondary flux across the . -coreeshellecoreeshell- . series association (Qser). The corresponding resistance for the . -coreeshellecoree shell- . series path (Eq. (5)) is:


  2 Rser ¼ Rms þ Rgs ¼ ðL=km Þ þ d=kg ðL  dÞ

(5)

 2 kc z

d L

"

 2 # d kg þ 1  km L

(9)

where

  f ¼ 3

d L

 2 2

d

(10)

L

Solutions for these proposed models are shown in Fig. 2, to emphasize the great advantage of designed organization of the conducting phase, in order to enhance thermal conductivity at the lowest conducting fraction. All these solutions were calculated on assuming 2 orders of magnitude between the conducting phase and the poorly conducting matrix (i.e. kg:km ¼ 100:1), which should be a reasonable approximation for a paraffin matrix with

and on combining fluxes Qgp and Qser:

L2 kc

25



     1  DT kg DT d L 2 z2ðLdÞ þ þ ðL  dÞ DT L km kg L

(6)

Eq. (6) then yields the dependence of thermal conductivity of the composite on shellecore thickness ratio (d/L):

  2 "     # 1  4 dL þ dL d d 2     kc ¼ kg 2 þ km kg L L 1 d þ d L

L

(7)

km

In addition, relatively simple geometrical considerations also yield the dependence of volume fraction of conduction phase on shellecore thickness ratio, as follows:

  f ¼ 3

d L

 2 3

d L

 3 þ

d L

A similar model for 3-D arrays of conducting fins yields:

(8)

P

P3D

20 F3D

kc /km



15 10

R

5 0

S 0

0.1

0.2

0.3

0.4

f Fig. 2. Predictions for the relative thermal conductivity of composites computed for kg:km ¼ 100 on assuming parallel (P), series (S) or random orientation (R), and the models for tridimensional arrangement of conducting plates (P3D) or fibers/tubes (F3D). Experimental data were also taken from relevant literature: - Zhong [9], A Fang [24], * Fukai [23], D, Karaipekli [25e27], , Sari [11,17,28e30], B Kim [12], x Cui [31], : Wang [18].

N. Vitorino et al. / Applied Thermal Engineering 66 (2014) 131e139

km < 0.5 W m1 K1 and poorly oriented graphite with kg in the range 10e50 W m1 K1. The solutions for random distribution [21] were calculated on assuming typical values for the percolation limit (fcr ¼ 0.3) and geometric factor t ¼ 2. In addition, one superimposed representative results from the literature for PCM-based materials with graphite or other carbon inclusions. Examples of highly enhanced thermal conductivity are those reported for paraffine graphite composites obtained by impregnation of compressed expanded graphite [9], and for composites with carbon fibres [24]. One must also take into account that thermal conductivity of graphiteePCM composites might be very dependent on preferential orientation of the highly anisotropic graphite phase. The main purpose of the present work was, thus, to develop a novel method to achieve both 3-dimensional organization of the highly conducting phase, and preferential orientation of graphite particles, to take advantage of their anisotropy. 3. Experimental 3.1. Preparation of cellular paraffin/graphite composites The proposed P3D model behaviour was taken as a guideline for development of paraffinegraphite composites with coreeshell microstructures to attempt maximization of thermal conductivity at the lowest contents of conducting phase. These composites with different graphite contents were prepared by emulsification of melted paraffin in graphite aqueous suspension, with starch consolidation and subsequent drying, as proposed recently [15]. The precursor reactants were commercial graphite powder (Merck 1.04206.2500), paraffin wax (Merck 1.07337.2500) with 0.89 g cm3, and starch (Riedel-de Haen 33615). The approximate melting point of the paraffin wax was confirmed by differential scanning calorimetry (DSC), which shows an exothermic peak with a maximum at about 58  C. 5 wt% of commercial starch was dissolved in water and heated at 90  C, for 5 min. Graphite was then added to this aqueous medium and stirred at 20,000 rpm during 5 min, using a high speed disperser (IKA T e 25 Ultraturax). The resulting suspension was then added to previously melted paraffin at about 90  C, and this mixture was stirred at 15,000 rpm for 10 min, to form an emulsion. This was cooled to room temperature, to solidify the paraffin droplets, and dried for 3 days at 50  C, i.e. below the melting point of paraffin, to prevent coalescence. Subsequent contraction by water evaporation and starch consolidation yielded a cellular graphite skeleton filled with solidified paraffin droplets, as revealed by scanning electron microstructures. Note that this novel processing method yields direct dispersion of the paraffin droplets in the cellular network of graphite, with a great flexibility for microstructural design and to adjust the graphite to paraffin ratio. This avoids limitations of other methods proposed in the literature, including complex processing of graphite porous matrixes and subsequent impregnation (e.g. Ref. [23]), and functionalization or intercalation of graphite [25]. 3.2. Characterization FT-IR spectroscopy (Bruker Tensor 27 FT-IR) was used to analyse interactions between paraffin wax and graphite precursors in the paraffinegraphite composites, based on characteristic absorption bands. The microstructural characterization of composites was performed using Scanning electron microscopy (SEM e Hitachi SU1510), combined with image analyses (ImageJ software). Fracture surfaces of selected samples were treated at 180  C, for 2 h, to reveal the graphite skeleton, by volatilization of paraffin from exposed cavities. A C-Therm thermal conductivity analyser (TCI)

was used for thermal conductivity measurements, based on the modified transient plane source technique. The approximate range of melting temperatures and latent heat were evaluated by differential scanning calorimetry, DSC, (Perkin Elmer (Norwalk, CT) DSC-7, using sapphire as a reference material). These measurements were performed on heating from 30  C to 90  C, at 5  C min1, and latent heat was evaluated by integration of the endothermic peak. Assessment of latent heat discharge was accomplished by temperature measurements in the centre and in the external surface of paraffinegraphite composites with spherical geometry. The selected PCMegraphite composite with z6.2 vol% was prepared as indicated above (Chapter 3.1) and cast into a spherical polymeric capsule at about 80  C, then cooled to solidify the isolated paraffin droplets and to induce starch consolidation of the continuous aqueous phase. This yielded self-supported composite samples, which retained spherical shape on removing the external capsule, and were slowly dried below the melting temperature of the paraffin, The final diameter decreased slightly to D z 4 cm, after this drying step. A K type thermocouple was placed at the centre of the composite, during casting in the spherical capsule. The temperature in the external surface was measured with an infrared camera (FLIR i7). Note that a similar procedure can be used for other macroscopic configurations such as cylindrical symmetry [27], or plate configuration. In addition, recently developed numerical codes [28,29] were used to analyse the relative role of heat conductions and surface heat exchange under the actual conditions of latent heat discharge. 4. Results and discussion 4.1. Structural and microstructural characterization Fig. 3 show the FT-IR spectra of pure graphite, pure paraffin and 2G and 15G composites. These FT-IR spectra of graphiteeparaffin composites retain the main absorption peaks of paraffin at about 2915, 2850, 1460 and 730 cm1, related to vibrations of eCH2 and e CH3 groups [30]. However, the intensities of the peaks at about 1460 and 730 cm1 decrease in the graphiteeparaffin composites (relative to the main bands at about 2915 and 2850 cm1), mainly for the highest graphite content, suggesting interactions of graphite particles with the paraffin phase. Nevertheless, this does not induce significant shift in wave number of the relevant functional groups, also indicating that paraffinegraphite interactions are rather weak.

Graphite Absorvance (a.u.)

134

15G 2G

Paraffin

4000 3500 3000 2500 2000 1500 1000 Wave number / cm-1

500

Fig. 3. FTIR spectrum of pure graphite, paraffin and graphiteeparaffin composites with 2 wt% (2G) and 15 wt% graphite (15G).

N. Vitorino et al. / Applied Thermal Engineering 66 (2014) 131e139

400

→2

300

1,5

200

1

100

0,5

0

100 / Cell Size / μm-1

2,5

Cell Size / μm

SEM images of composites with different graphite contents, Fig. 4, also suggest that interaction between paraffin and graphite plays a very important role on the microstructures of corresponding composites obtained by emulsification of liquid paraffin in aqueous suspension of graphite, and subsequent drying. The fraction of graphite is clearly the determining factor on the average size of paraffin droplets, with decrease in droplet size by about one order of magnitude on increasing the graphite contents from z0.82 vol% to z9.18 vol%. One can also assume that graphite facilitates the emulsification step by preferential location at the interface between liquid paraffin and the aqueous medium, promoting emulsification. Compatibility of graphite platelets with liquid paraffin may be promoted by prevailing hydrophobic character of the basal plane of graphite platelets, whereas addition of starch promotes compatibility with the aqueous medium. This is confirmed by close relation between interfacial area (per unit volume) and graphite content (Fig. 5). Note that reciprocal diameter is a measure of the area:volume ratio (¼1.5 d1) of spherical droplets. Preferential location at the interface between paraffin and the aqueous medium during the emulsification step was found after drying the aqueous medium and subsequent volatilization of the paraffin phase, to reveal the self-organized cellular graphite, Fig. 6. The highest magnification shows reasonable evidence of graphite platelets with preferential orientation along the cellular wall. Further evidence of preferential self-alignment of graphite platelets at the interface is also shown in Fig. 7. This sample was prepared by dropping the graphite suspension on melted paraffin, then allowing separation of the denser aqueous suspension at the bottom and the lighter liquid paraffin layer at the top. Upon solidification one easily removed the paraffin layer with attached graphite platelets, to show orientation of these platelets. In

135

0 0

2

4 6 8 Graphite vol.%

10

Fig. 5. Cell size vs graphite content. Error bars represent confidence intervals for 95% confidence degree.

addition, the low angle XRD pattern also shows evidence of preferential (002) orientation, whereas other reflections are difficult to distinguish from background noise. This is consistent with preferential orientation in the self-organized graphite shell formed upon emulsification. Note also that the paraffinegraphite interface shows sharper paraffin XRD reflections relative to the as received paraffin. 4.2. Thermal behaviour The thermal conductivity of the paraffin phase (z0.42 W m1 K1) is low for thermal regulation or fast charge/ discharge response in heat storage applications such as solar heat

Fig. 4. Composites microstructures with different graphite contents.

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N. Vitorino et al. / Applied Thermal Engineering 66 (2014) 131e139

Fig. 6. SEM microstructures of cellular graphite exposed after surface vaporization of the paraffin phase.

storage for hot water or domestic heating. Thus, the actual paraffinegraphite composites with coreeshell microstructures are a very promising low cost approach to overcome this limitation by increasing the thermal conductivity by at least one order of magnitude for 10 wt% graphite (z4.3 vol%), as shown in Fig. 8; this is attained without significant effect on melting temperatures or excessive penalties for latent heat, as shown in Fig. 9. Drop in latent heat was z9% for composites with z4.3 vol% graphite. Note also that the enhancement in thermal conductivity is attained with a low cost carbon polymorph (graphite), and processing of the actual coreeshell microstructures is also facile and rather inexpensive, compared to other methods reported in the relevant literature. The high thermal conductivity of these composites can be ascribed to self-assembling of the graphite particles, with the additional contribution of preferential crystallographic orientation, as shown by SEM microstructures, Figs. 4, 5 and 7. Both effects are, probably, promoted by interactions of graphite particles with both phases in the emulsified water-liquid paraffin system, as discussed above. This is also consistent with trends predicted by the coree shell P3D model, as shown in Fig. 10. Best fitting for the actual experimental results is obtained with kg:km z 400 and, on combining with the conductivity of paraffin (km z 0.42 W m1 K1) this yieldskg z 160 W m1 K1; this high value of thermal conductivity is unlikely for graphite with random orientation, and is also consistent with significant preferential orientation of graphite platelets. Note that the thermal conductivities of carbon foams may show differences by several orders of magnitude, depending mainly on crystallinity and preferential orientations. Glassy carbon foams show poor conductivity and were initially proposed for thermal insulation [31], whereas high crystallinity and preferential orientation yield the highest thermal conductivity [32] suitable for thermal management [33]. However, processing of those materials require very demanding conditions with temperatures up to 2800  C, which is ill-suited to meet low cost requirements for intensive heat storage applications.

The macroscopic shape and the coreeshell microstructure remains stable upon repeated cycling above and below the melting temperature of the paraffin, without disruption of the graphite shells or leakage of melted paraffin; this yields shape stabilization for bulk composite samples, without requiring external encapsulation, which is a further advantage in terms of prospective commercial exploitation. Shape stabilization of the actual coreeshell composites allowed experimental tests of heat discharge for PCM-based heat storage, without requiring external encapsulation. The experimental procedure was based on spherical samples, and thermal response was evaluated after previous melting of the paraffin phase as described in the experimental chapter. Temperature of surrounding air remained at z20  C throughout the experiment whereas an infrared sensor was used to measure the temperature at the surface, and a K-type thermocouple measured the temperature at the centre The time dependence of temperature at the surface (Fig. 11) shows that this remains much closer to the temperature at the centre than to surrounding air temperature (z20  C), indicating that heat discharge is controlled mainly by interfacial heat transfer limitations. Fig. 11 also shows the infrared images used to estimate the composite surface temperature during the latent heat discharge. Deviations from the plateau of temperature at the centre suggest a transition from latent heat discharge to discharge of sensible heat. Complete latent heat discharge is, thus, expected after about 12.5 min, as indicated by a circle in Fig. 11. This is also close to conditions when temperature differences between the centre and surface reach a maximum. This time scale of latent heat discharge was, thus, used to estimate the relative roles of heat conduction and heat transfer from the external surface to surrounding air, based on numerical codes developed for latent heat discharge with spherical symmetry [29]. The main relevant parameters are the Stefan number cpDT/l, which represents the sensible heat cpDT to latent heat ratio (l) ratio and Biot number hD/k, which represents a ratio

N. Vitorino et al. / Applied Thermal Engineering 66 (2014) 131e139

137

16 λ=202.1 J g-1

Heat flow (mW)

14

λ=189.5 J g-1

12 10

λ=161.0 J g-1

8 6 4 2

0 45

50

55 60 Temperature / ºC

65

70

Fig. 9. DSC curves without graphite (A), composites with 4.3 vol% (:) and 9.2 vol% (C) of graphite.

Fig. 7. SEM microstructure showing preferential orientation of graphite platelets after solidification of paraffin in contact with aqueous suspension, and corresponding XRD (marked as graph. & par.). Separate XRD patterns of precursors (graphite and paraffin) are shown for comparison.

between equivalent resistances to heat transport imposed by insufficient thermal conductivity (k) or insufficient heat transfer coefficient from the external surface to surrounding air (h), D, being the diameter of the sphere. These parameters determine the corresponding dimensionless time scale s ¼ ta/D2, where a ¼ k/(rcp)

denotes thermal diffusivity, which varies with thermal conductivity, density (r), and specific heat (cp). On combining relevant conditions (DT z 58.6e20  C) and properties of the actual paraffin/ graphite composites (cp z 2.23  103 J kg1 K1; k z 6.5 W m1 K1, r z 9.85  102 kg m3) one obtained (cpDT/ l z 0.434) and a z 2.96  106 m2 s1. These values were, thus, used to estimate the value of Biot number (hD/k z 0.272) which yields the estimated time scale. Fig. 12 shows the corresponding numerical predictions for time dependence of surface temperature and for the fraction of discharged latent heat. Though numerical predictions for time dependence of surface temperature (Fig. 12) are within the range of measured results (Fig. 11), numerical predictions suggest faster decrease on approaching complete discharge of latent heat. In addition, the value of Biot number that matches the estimated time scale (hD/ k z 0.272) yields a value of heat transfer coefficient (h z 44 W m1 K1) which is higher than expected for air under conditions of natural convection or laminar flow [34]. This suggests that the ideal conditions assumed by the model behaviour [29] still differ significantly from the real conditions of latent heat discharge. Note that the model assumes that a clear interface separates the outer macroscopic layer of graphite cells filled with solid paraffin from the inner core consisting of graphite cells filled with melted paraffin. It is also assumed that this interface remains at melting

10

0.9 →

4

0.8

→

2

0

0.7 0

2

4

6

Graphite vol.%

8

10

Fig. 8. Improvement of thermal conductivity with the graphite content, (:), and relative latent heat of composites (-) and theoretical relative latent heat (dashed line).

kc / W m-1 K-1

8 6

1000

8

λ Composite / λ Paraffin

Thermal Conductivity, / W m-1 K-1

1

400

200

6 4

100

2

50

0

0

0.05

f

0.1

0.15

Fig. 10. Thermal conductivity of paraffinegraphite composites vs volume fraction of graphite, at room temperature. The solid lines show fitting with the coreeshell P3D model, for kg:km ¼ 50, 100, 200, 400 and 1000, with a typical value for thermal conductivity of the matrix km ¼ 0.42 W m1 K1.

138

N. Vitorino et al. / Applied Thermal Engineering 66 (2014) 131e139

∆-Tcenter -Tsurface

Temperature / ºC

60 A

50

A

B

C

D

B C

40

D

30 20

0

10

20 30 (time / min)1/2

40

20 ºC

65 ºC

Fig. 11. Time dependence of temperature at the centre and at the surface during latent heat discharge from a spherical PCMegraphite composite (D z 4 cm) to air at T z 20  C. Infrared images of the composite surface during heat discharge.

temperature, with negligible undercooling, and that heat transfer determines the advance of this interface towards the centre of the spherical PCM/graphite composite. In real conditions, one may expect some degree of undercooling, causing drop in temperature at the centre before complete discharge of latent heat. In addition, heterogeneities in the highly conducting graphite network may favour a distribution of residual melted pockets in the solidified outer layer and onset of solid pocket in the melted core. Therefore, discharge time is probably longer than estimated above. Note also that the time dependence in Fig. 11 suggests other relevant changes such as convergence between temperatures at the centre and surface after about 25 min. If one considers this value for latent heat discharge time one obtains significantly lower values for the Biot number (hD/k z 0.124) and heat transfer coefficient (h z 20 W m1 K1), which are closer to the expected ranges.

based on emulsification of liquid paraffin in graphite aqueous suspensions with starch addition to stabilize graphite in aqueous suspension, and to yield subsequent consolidation. The method is easily reproducible and yields a low cost approach to enhance thermal conductivity. For 5 vol% graphite the thermal conductivity is enhanced by at least one order of magnitude, without undue excessive penalty for the heat storage ability. This enhancement of thermal conductivity relies on self-assembling of graphite platelets and their preferential crystallographic orientation upon emulsification of liquid paraffin in the aqueous graphite suspension, with addition of starch. Experimental tests of latent heat discharge to surrounding air at room temperature confirm that thermal conductivity is sufficient for fast latent heat discharge, provided that this is not affected by surface exchange limitations. Acknowledgements

5. Conclusions A coreeshell model (P3D) was proposed for optimized enhancement of thermal conductivity, based on 3-dimensional arrangement of conducting shells with a poorly conducting core of phase change material. This was used as a guideline for development of coreeshell composites with remarkable increase in thermal conductivity with relatively low volume fraction of conducting shells. These composites were produced by a facile method

This work was supported by FCT, Portugal, and European funding (programs COMPETE, QREN and FEDER) under Projects PTDC/CTM-ENE/2073/2012, PEst-C/CTM/LA0011/2013, Operação NORTE-07-0162-FEDER-000050 and PhD grant SFRH/BD/62598/ 2009. The SEM facility was funded by FEDER Funds through QREN e Aviso SAIECT-IEC/2/2010, Operação NORTE-07-0162-FEDER000050. Thermal Analysis Laboratory was funded by FEDER Funds through Programa Operacional Factores de Competitividade e COMPETE and by National Funds through FCT e Fundação para a Ciência e a Tecnologia under the project REEQ/515/CTM/2005. References

Fig. 12. Numerical predictions obtained for measured experimental conditions and on assuming that latent heat is fully discharged after 12.5 min or after 25 min. Thick lines show predictions for surface temperature and thin lines the corresponding predictions for fraction of discharged latent heat.

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