# Methods to Characterize Effective Thermal Conductivity, Diffusivity and Thermal Response in Different Classes of Composite Phase Change Materials

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## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Tests to Measure the Thermal Storage Properties of C-PCMs

#### 2.2. Thermal Conductivity Measurements Methods

#### 2.3. Steady-State Methods: Axial Flow Methods

#### 2.3.1. Steady-State Conditions

#### 2.3.2. Axial Flow

#### 2.3.3. Heat Transport Mechanism

#### 2.3.4. Thermal Gradient Measurements

#### 2.4. Transient Methods: Hot Wire Method

#### 2.5. Transient Plane Heat Source (TPS) Method

_{3}/KCl eutectic [28]) and organic materials as active phases. In the latter case, paraffin [39,61,62], polyethylene glycol [26] n-octadecane [23] RT44HC [28]. As far as the passive phase is concerned, porous passive phases were often compressed expanded graphite, and the presence of thermal properties anisotropy has been considered in [29].

#### 2.6. Laser Flash Method

_{0.5}at which half of the temperature increase is reached, the sample thickness L and thermal diffusivity α is then derived [48]:

^{2}/t

_{0.5},

^{2}/s according to ASTM E1461 [46]), including high conductivity metals and thermal insulators, within which fall the thermal diffusivities of all C-PCM classes.

## 3. Experimental Setup for Thermal Response of coarse porous C-PCMs

^{2}K), sensitivity 560 (W/m

^{2})/mV. Their circular flat surface is 15.9 mm diameter and made of stainless steel. They further acted as K-type thermocouples (measurement point E).

## 4. Validation and Preliminary Tests

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Pielichowska, K.; Pielichowski, K. Phase change materials for thermal energy storage. Prog. Mater. Sci.
**2014**, 67–123. [Google Scholar] [CrossRef] - Su, W.; Darkwa, J.; Kokogiannakis, G. Review of solid-liquid phase change materials and their encapsulation technologies. Renew. Sustain. Energy Rev.
**2015**, 373–391. [Google Scholar] [CrossRef] - Zhang, P.; Xiao, X.; Ma, Z.W. A review of the composite phase change materials: Fabrication, characterization, mathematical modeling and application to performance enhancement. Appl. Energy
**2016**, 165, 472–510. [Google Scholar] [CrossRef] - Şahan, N.; Paksoy, H. Novel shapeable phase change material (PCM) composites for thermal energy storage (TES) applications. Sol. Energy Mater. Sol. Cells
**2018**, 174, 380–387. [Google Scholar] [CrossRef] - Sugo, H.; Kisi, E.; Cuskelly, D. Miscibility gap alloys with inverse microstructures and high thermal conductivity for high energy density thermal storage applications. Appl. Therm. Eng.
**2013**, 51, 1345–1350. [Google Scholar] [CrossRef] - Singh, S.P.; Barman, B.K.D.; Kumar, P. Cu-Bi alloys with high volume fraction of Bi: A material potentially suitable for thermal surge protection and energy storage. Mater. Sci. Eng. A
**2016**, 677, 140–152. [Google Scholar] [CrossRef] - Gariboldi, E.; Perrin, M. Metallic Composites as Form-Stable Phase Change Alloys. Mater. Sci. Forum
**2018**, 941, 1966–1971. [Google Scholar] [CrossRef] - Tong, X.; Li, N.; Zeng, M.; Wang, Q. Organic phase change materials confined in carbon-based materials for thermal properties enhancement: Recent advancement and challenges. Renew. Sustain. Energy Rev.
**2019**, 108, 398–422. [Google Scholar] [CrossRef] - Umair, M.M.; Zhang, Y.; Iqbal, K.; Zhang, S.; Tang, B. Novel strategies and supporting materials applied to shape-stabilize organic phase change materials for thermal energy storage—A review. Appl. Energy
**2019**, 235, 846–873. [Google Scholar] [CrossRef] - Qureshi, Z.A.; Ali, H.M.; Khushnood, S. Recent advances on thermal conductivity enhancement of phase change materials for energy storage system: A review. Int. J. Heat Mass Transf.
**2018**, 127, 838–856. [Google Scholar] [CrossRef] - Trigui, A.; Karkri, M.; Boudaya, C.; Candau, Y.; Ibos, L. Development and characterization of composite phase change material: Thermal conductivity and latent heat thermal energy storage. Compos. Part B Eng.
**2013**, 49, 22–35. [Google Scholar] [CrossRef] - Pakrouh, R.; Hosseini, M.J.; Ranjbar, A.A. A parametric investigation of a PCM-based pin fin heat sink. Mech. Sci.
**2015**, 6, 65–73. [Google Scholar] [CrossRef] [Green Version] - Pradeep, P.; Assistant, C.; Karthick, P.; Assistant, S.; Suthan, C. Review on the Design of Pcm Based Thermal Energy Storage Systems. Imp. J. Interdiscip. Res.
**2016**, 2, 203. [Google Scholar] - Sharma, A.; Sciacovelli, A.; Verda, V.; Maute, K.; Pizzolato, A. Design of effective fins for fast PCM melting and solidification in shell-and-tube latent heat thermal energy storage through topology optimization. Appl. Energy
**2017**, 208, 210–227. [Google Scholar] [CrossRef] - Paek, J.W.; Kang, B.H.; Kim, S.Y.; Hyun, J.M. Effective thermal conductivity and permeability of aluminum foam materials. Int. J. Thermophys.
**2000**, 453–464. [Google Scholar] [CrossRef] - Chen, C.R.; Buddhi, D.; Sharma, A.; Tyagi, V.V.; Chen, C.R.; Buddhi, D. Review on thermal energy storage with phase change material and applications. Renew. Sustain. Energy Rev.
**2009**, 13, 318–345. [Google Scholar] [CrossRef] - Zalba, B.; Marín, J.M.; Cabeza, L.F.; Mehling, H. Review on thermal energy storage with phase change: materials, heat transfer analysis and applications. Appl. Therm. Eng.
**2003**, 23, 251–283. [Google Scholar] [CrossRef] - Wei, G.; Wang, G.; Xu, C.; Ju, X.; Xing, L.; Du, X.; Yang, Y. Selection principles and thermophysical properties of high temperature phase change materials for thermal energy storage: A review. Renew. Sustain. Energy Rev.
**2018**, 81, 1771–1786. [Google Scholar] [CrossRef] - Barreneche, C.; Pisello, A.L.; Fernández, A.I.; Cabeza, L.F. Experimental Methods for the Characterization of Materials for Latent Thermal Energy Storage. In Green Energy and Technology; Frazzica, A., Cabeza, L.F., Eds.; Recent Adv. Mater. Syst. Therm. Energy Storage; Springer International Publishing: Cham, Switzerland, 2019; pp. 89–101. [Google Scholar] [CrossRef]
- Günther, E.; Hiebler, S.; Mehling, H. Determination of the heat storage capacity of PCM and PCM-objects as a function of temperature. In Proceedings of the 10th International Conference Thermal Energy Storage, Ecostock, Pomona, NJ, USA, 31 May–2 June 2006; pp. 1–7. Available online: https://www.researchgate.net/publication/228839104_Determination_of_the_heat_storage_capacity_of_PCM_and_PCM-objects_as_a_function_of_temperature (accessed on 26 June 2019).
- Zhao, W. Characterization of Encapsulated Phase Change Materials for Thermal Energy Storage. Ph.D. Thesis, Lehigh University, Bethlehem, PA, USA, 2012. [Google Scholar]
- Xie, J.; Li, Y.; Wang, W.; Pan, S.; Cui, N.; Liu, J. Comments on thermal physical properties testing methods of phase change materials. Adv. Mech. Eng.
**2013**, 2013, 695762. [Google Scholar] [CrossRef] - Solé, A.; Miró, L.; Barreneche, C.; Martorell, I.; Cabeza, L.F. Review of the T-history method to determine thermophysical properties of phase change materials (PCM). Renew. Sustain. Energy Rev.
**2013**, 26, 425–436. [Google Scholar] [CrossRef] - Pincemin, S.; Olives, R.; Py, X.; Christ, M. Highly conductive composites made of phase change materials and graphite for thermal storage. Sol. Energy Mater. Sol. Cells
**2008**, 603–613. [Google Scholar] [CrossRef] - Sari, A.; Karaipekli, A. Thermal conductivity and latent heat thermal energy storage characteristics of paraffin/expanded graphite composite as phase change material. Appl. Therm. Eng.
**2007**, 27, 1271–1277. [Google Scholar] [CrossRef] - Wang, W.; Yang, X.; Fang, Y.; Ding, J.; Yan, J. Preparation and thermal properties of polyethylene glycol/expanded graphite blends for energy storage. Appl. Energy
**2009**, 86, 1479–1483. [Google Scholar] [CrossRef] - Zhang, Z.; Shi, G.; Wang, S.; Fang, X.; Liu, X. Thermal energy storage cement mortar containing n-octadecane/expanded graphite composite phase change material. Renew. Energy
**2013**, 50, 670–675. [Google Scholar] [CrossRef] - Huang, Z.; Gao, X.; Xu, T.; Fang, Y.; Zhang, Z. Thermal property measurement and heat storage analysis of LiNO3/KCl–Expanded graphite composite phase change material. Appl. Energy
**2014**, 115, 265–271. [Google Scholar] [CrossRef] - Ling, Z.; Chen, J.; Xu, T.; Fang, X.; Gao, X.; Zhang, Z. Thermal conductivity of an organic phase change material/expanded graphite composite across the phase change temperature range and a novel thermal conductivity model. Energy Convers. Manag.
**2015**, 102, 202–208. [Google Scholar] [CrossRef] [Green Version] - Mills, A.; Farid, M.; Selman, J.R.; Al-Hallaj, S. Thermal conductivity enhancement of phase change materials using a graphite matrix. Appl. Therm. Eng.
**2006**, 26, 1652–1661. [Google Scholar] [CrossRef] - Zamiri, A.; Yavari, F.; Fard, H.R.; Pashayi, K.; Rafiee, M.A.; Yu, Z.; Ozisik, R.; Borca-Tasciuc, T.; Koratkar, N. Enhanced Thermal Conductivity in a Nanostructured Phase Change Composite due to Low Concentration Graphene Additives. J. Phys. Chem. C
**2011**, 115, 8753–8758. [Google Scholar] [CrossRef] - Chen, Y.J.; Nguyen, D.D.; Shen, M.Y.; Yip, M.C.; Tai, N.H. Thermal characterizations of the graphite nanosheets reinforced paraffin phase-change composites. Compos. Part A Appl. Sci. Manuf.
**2013**, 44, 40–46. [Google Scholar] [CrossRef] - Zhong, Y.; Zhou, M.; Huang, F.; Lin, T.; Wan, D. Effect of graphene aerogel on thermal behavior of phase change materials for thermal management. Sol. Energy Mater. Sol. Cells
**2013**, 113, 195–200. [Google Scholar] [CrossRef] - Li, H.; Jiang, M.; Li, Q.; Li, D.; Chen, Z.; Hu, W.; Huang, J.; Xu, X.; Dong, L.; Xie, H.; et al. Aqueous preparation of polyethylene glycol/sulfonated graphene phase change composite with enhanced thermal performance. Energy Convers. Manag.
**2013**, 75, 482–487. [Google Scholar] [CrossRef] - İnce, Ş.; Seki, Y.; Ezan, M.A.; Turgut, A.; Erek, A. Thermal properties of myristic acid/graphite nanoplates composite phase change materials. Renew. Energy
**2015**, 75, 243–248. [Google Scholar] [CrossRef] - Wang, J.; Xie, H.; Xin, Z. Thermal properties of paraffin based composites containing multi-walled carbon nanotubes. Thermochim. Acta
**2009**, 488, 39–42. [Google Scholar] [CrossRef] - Choi, D.H.; Lee, J.; Hong, H.; Kang, Y.T. Thermal conductivity and heat transfer performance enhancement of phase change materials (PCM) containing carbon additives for heat storage application thermique et de la Ame performance de transfert de chaleur de mate changement de phas. Int. J. Refrig.
**2014**, 42, 112–120. [Google Scholar] [CrossRef] - Liang, W.; Zhang, G.; Sun, H.; Chen, P.; Zhu, Z.; Li, A. Graphene-nickel/n-carboxylic acids composites as form-stable phase change materials for thermal energy storage. Sol. Energy Mater. Sol. Cells
**2015**, 132, 425–430. [Google Scholar] [CrossRef] - Xiao, X.; Zhang, P.; Li, M. Preparation and thermal characterization of paraffin/metal foam composite phase change material. Appl. Energy
**2013**, 112, 1357–1366. [Google Scholar] [CrossRef] - Zhang, Y.; Jiang, Y. A simple method, the -history method, of determining the heat of fusion, specific heat and thermal conductivity of phase-change materials. Meas. Sci. Technol.
**1999**, 10, 201–205. [Google Scholar] [CrossRef] - Cavrot, J.-P.; Lassue, S.; Younsi, Z.; Joulin, A.; Rousse, D.R.; Zalewski, L. Experimental and numerical investigation of a phase change material: Thermal-energy storage and release. Appl. Energy
**2011**, 88, 2454–2462. [Google Scholar] [CrossRef] - ASTM E1225-13, Standard Test Method Thermal Conductivity of Solids Using the Guarded-Comparative-Longitudinal Heat Flow Technique; ASTM International: West Conshohocken, PA, USA, 2013.
- Franco, A. An apparatus for the routine measurement of thermal conductivity of materials for building application based on a transient hot-wire method. Appl. Therm. Eng.
**2007**, 27, 2495–2504. [Google Scholar] [CrossRef] - ASTM. C1113, Standard Test Method for Thermal Conductivity of Refractories by Hot Wire (Platinum Resistance Thermometer Technique) 1; ASTM: West Conshohocken, PA, USA, 2015; Volume 9, pp. 1–6. [Google Scholar] [CrossRef]
- Shinzato, K.; Baba, T. A laser flash apparatus for thermal diffusivity and specific heat capacity measurements. J. Therm. Anal. Calorim.
**2001**, 64, 413–422. [Google Scholar] [CrossRef] - ASTM. E1461-13, Standard Test Method Thermal Diffusivity by Flash Method; ASTM International: West Conshohocken, PA, USA, 2013. [Google Scholar]
- He, Y. Rapid thermal conductivity measurement with a hot disk sensor. Thermochim. Acta
**2005**, 436, 122–129. [Google Scholar] [CrossRef] - Zhao, D.; Qian, X.; Gu, X.; Jajja, S.A.; Yang, R. Measurement Techniques for Thermal Conductivity and Interfacial Thermal Conductance of Bulk and Thin Film Materials. J. Electron. Packag.
**2016**, 138, 040802. [Google Scholar] [CrossRef] [Green Version] - Py, X.; Olives, R.; Mauran, S. Paraffin/porous-graphite-matrix composite as a high and constant power thermal storage material. Int. J. Heat Mass Transf.
**2001**, 44, 2727–2737. [Google Scholar] [CrossRef] - Tasnim, S.H.; Hossain, R.; Mahmud, S.; Dutta, A. Convection effect on the melting process of nano-PCM inside porous enclosure. Int. J. Heat Mass Transf.
**2015**, 85, 206–220. [Google Scholar] [CrossRef] - Hong, S.T.; Herling, D.R. Effects of surface area density of aluminum foams on thermal conductivity of aluminum foam-phase change material composites. Adv. Eng. Mater.
**2007**, 9, 554–557. [Google Scholar] [CrossRef] - Feng, S.; Zhang, Y.; Shi, M.; Wen, T.; Lu, T.J. Unidirectional freezing of phase change materials saturated in open-cell metal foams. Appl. Therm. Eng.
**2015**, 88, 315–321. [Google Scholar] [CrossRef] - Sadeghi, E.; Hsieh, S.; Bahrami, M. Thermal conductivity and contact resistance of metal foams. J. Phys. D Appl. Phys.
**2011**, 44, 125406. [Google Scholar] [CrossRef] - Alshaer, W.G.; Rady, M.A.; Nada, S.A.; del Barrio, E.P.; Sommier, A. An experimental investigation of using carbon foam–PCM–MWCNTs composite materials for thermal management of electronic devices under pulsed power modes. Heat Mass Transf.
**2017**, 53, 569–579. [Google Scholar] [CrossRef] - Coquard, R.; Baillis, D.; Quenard, D. Experimental and theoretical study of the hot-ring method applied to low-density thermal insulators. Int. J. Therm. Sci.
**2008**, 324–338. [Google Scholar] [CrossRef] - Xiao, X.; Zhang, P.; Li, M. Thermal characterization of nitrates and nitrates/expanded graphite mixture phase change materials for solar energy storage. Energy Convers. Manag.
**2013**, 73, 86–94. [Google Scholar] [CrossRef] - Haillot, D.; Nepveu, F.; Goetz, V.; Py, X.; Benabdelkarim, M. High performance storage composite for the enhancement of solar domestic hot water systems. Part 2: Numerical system analysis. Sol. Energy
**2012**, 64–77. [Google Scholar] [CrossRef] - Tong, X.C. Characterization Methodologies of Thermal Management Materials. In Advanced Materials for Thermal Management of Electronic Packaging; Springer: New York, NY, USA, 2011; pp. 59–129. [Google Scholar]
- ASTM. Standard test method for thermal conductivity of plastics by means of a transient line-source technique. In 2001 Annual Book ASTM Standard; ASTM: West Conshohocken, PA, USA, 2001; Volume 8, pp. 699–703. [Google Scholar]
- Peñas, J.R.V.; de Zárate, J.M.O.; Khayet, M. Measurement of the thermal conductivity of nanofluids by the multicurrent hot-wire method. J. Appl. Phys.
**2008**, 104, 044314. [Google Scholar] [CrossRef] [Green Version] - Goli, P.; Legedza, S.; Dhar, A.; Salgado, R.; Renteria, J.; Balandin, A.A. Graphene-enhanced hybrid phase change materials for thermal management of Li-ion batteries. J. Power Sources
**2014**, 248, 37–43. [Google Scholar] [CrossRef] [Green Version] - Li, Z.; Sun, W.G.; Wang, G.; Wu, Z.G. Experimental and numerical study on the effective thermal conductivity of paraffin/expanded graphite composite. Sol. Energy Mater. Sol. Cells
**2014**, 128, 447–455. [Google Scholar] [CrossRef] - Cezairliyan, A.; Baba, T.; Taylor, R. A high-temperature laser-pulse thermal diffusivity apparatus. Int. J. Thermophys.
**1994**, 15, 317–341. [Google Scholar] [CrossRef] - Wróbel, G.; Rdzawski, Z.; Muzia, G.; Pawlak, S. Determination of thermal diffusivity of carbon/epoxy composites with different fiber content using transient thermography. J. Achiev. Mater. Manuf. Eng.
**2009**, 37, 518–525. [Google Scholar] - Elgafy, A.; Lafdi, K. Effect of carbon nanofiber additives on thermal behavior of phase change materials. Carbon
**2005**, 43, 3067–3074. [Google Scholar] [CrossRef] - Oya, T.; Nomura, T.; Okinaka, N.; Akiyama, T. Phase change composite based on porous nickel and erythritol. Appl. Therm. Eng.
**2012**, 40, 373–377. [Google Scholar] [CrossRef] - McMasters, R.L.; Dinwiddie, R.B. Anisotropic thermal diffusivity measurement using the flash method. J. Thermophys. Heat Transf.
**2014**, 28, 518–523. [Google Scholar] [CrossRef] - Pietrak, K.; Winiewski, T.S. A review of models for effective thermal conductivity of composite materials. J. Power Technol.
**2015**, 95, 14–24. [Google Scholar] [CrossRef] - Floury, J.; Carson, J.; Pham, Q.T. Modelling Thermal Conductivity in Heterogeneous Media with the Finite Element Method. Food Bioprocess Technol.
**2008**, 1, 161–170. [Google Scholar] [CrossRef] - Li, Z.; Gariboldi, E. Reliable estimation of effective thermal properties of a 2-phase material by its optimized modelling in view of Lattice Monte-Carlo simulation. Comput. Mater. Sci.
**2019**, 169, 109125. [Google Scholar] [CrossRef] - Xu, W.; Zhang, H.; Yang, Z.; Zhang, J. The effective thermal conductivity of three-dimensional reticulated foam materials. J. Porous Mater.
**2009**, 16, 65–71. [Google Scholar] [CrossRef] - Dul’nev, G.N. Heat transfer through solid disperse systems. J. Eng. Phys.
**1965**, 9, 275–279. [Google Scholar] [CrossRef] - Di Giorgio, P.; Iasiello, M.; Viglione, A.; Mameli, M.; Filippeschi, S.; di Marco, P.; Andreozzi, A.; Bianco, N. Numerical Analysis of a Paraffin/Metal Foam Composite for Thermal Storage. In Journal of Physics: Conference Series; IOP Publishing: London, UK, 2017; p. 12032. [Google Scholar]
- Lafdi, K.; Mesalhy, O.; Shaikh, S. Experimental study on the influence of foam porosity and pore size. J. Appl. Phys.
**2007**, 102, 1–6. [Google Scholar] [CrossRef] - Tian, Y.; Zhao, C.Y. A numerical investigation of heat transfer in phase change materials (PCMs) embedded in porous metals. Energy
**2011**, 36, 5539–5546. [Google Scholar] [CrossRef] [Green Version] - Pomianowski, M.; Heiselberg, P.; Jensen, R.L.; Cheng, R.; Zhang, Y. A new experimental method to determine specific heat capacity of inhomogeneous concrete material with incorporated microencapsulated-PCM. Cem. Concr. Res.
**2014**, 55, 22–34. [Google Scholar] [CrossRef] - Nield, D.A.; Bejan, A. Internal Natural Convection: Heating from Below BT-Convection in Porous Media. In Convection in Porous Media; Nield, D.A., Bejan, A., Eds.; Springer International Publishing: Cham, Switzerland, 2017; pp. 241–361. [Google Scholar]
- Bhattacharya, A.; Calmidi, V.V.; Mahajan, R.L. Thermophysical properties of high porosity metal foams. Int. J. Heat Mass Transf.
**2002**, 45, 1017–1031. [Google Scholar] [CrossRef]

**Figure 1.**Representative length-scale of C-PCM materials related to the arrangement of the passive phases. Length scale of some tens of micrometer (

**a**), of tenths of millimeter (

**b**) and of some millimeter (

**c**). Foam images in (b) and (c) adapted from [15], reprinted by permission from Springer Nature.

**Figure 3.**Axial flow methods: (

**a**) A scheme of a comparative cut bar, (

**b**) an example of the symmetric experimental setup (adapted after [11] with permission from Elsevier).

**Figure 4.**Schematic apparatus for hot wire tests (adapted from [56] with permission of Elsevier).

**Figure 5.**Schematic view of transient plane heat source method (adapted after [61] with permission form Elsevier).

**Figure 6.**Scheme of the laser flash (LF) method applied to a C-PCM sample (adapted from [32] with permission of Elsevier).

**Figure 7.**(

**a**) Simplified representation of the “experimental set-up n. 4”: (

**1**) Sample, (

**2**) heat flux sensor, (

**3**) Al cylinder, (

**4**) base insulator, (

**5**) Al plaque, (

**6**) weight pans,

**(7**) lateral insulator, (

**8**) heat flux sensor’s cable, (

**9**) K-type thermocouples at point E, (

**10**) electrical hot-plate, (

**11**) N-type thermocouples at points A–D, (

**12**) mustimeter, (

**13**) PC for data acquisition. (

**b**) Picture of the experimental setup.

**Figure 8.**(

**a**) Correlation between the thermal contact resistance (Ra) and the ratio between total heat entered at the bottom surface of the sample (Qtot) and that derived from probe heat flux (QA). (

**b**) Comparison between experimental (solid lines) and modeled (dashed lines) temperatures at points A–D at different depth of the specimen, all laying in the active phase.

**Figure 9.**Experimental (

**a**) and modeled (

**b**) heating rate vs. temperature at points A–D, in the active phase of coarse porous C-PCM. FE model considered the porous material as a cubic rod-side lattice.

**Figure 10.**FE modeled temperature increase in two points laying at the same distance from the sample bottom in the active phase (solid line) and passive phase (dashed line), when sample bottom has a controlled temperature increase (black solid line). Each colour refers to a model considering a specific cell: 1: Rod-side, 2: Body centered cubic, 3: Primitive cubic, 4: Face centered cubic.

**Table 1.**Phases, experimental parameters and literature sources for axial flow methods on composite phase change materials (C-PCMs). In the table ND stands for ‘not defined’. TCR: Thermal Contact Resistance.

Composite PCMs | Testing T [°C] | k Range [W/mK] | Sample Size [mm ^{3}] | Insulation | Flux Meter Dimension [mm ^{3}] | Peculiar Aspects | Reference |
---|---|---|---|---|---|---|---|

CENG/paraffin CENG/hexadecane | ND | 3–70 | 25 × 25 × 25 | PS foam | 25 × 25 × 65 (Aluminum) | Tested 2 commercial paraffin waxes | Py et al. [49] |

Graphite matrix/paraffin | 8/45 | 4–60 | 70 × 70 × 10 | Unknown | 70 × 70 × 17.55 (Stainless steel) | DSC analyses performed in different sample regions | Mills et al. [30] |

Al foam/ paraffin | 16/76 | 10–25 | 89 × 38 × 13 | Silicon rubber | 89 × 38 × 102 (Copper) 89 × 38 × 1.6 (Copper) | Determination of keff through the rule of mixture reveals to be erroneous. | Hong et al. [51] |

NG/Unknown PCM ENG/Unknown PCM EGP/Unknown PCM | 25/217 | 1–9 | $\mathit{\pi}$(12.5)^{2} × 25 | ND | ND | Graphite fins dispersion was optimized through mathematical simulations. | Pincemin et al. [24] |

Al foam | ND | 3–7 | $\mathit{\pi}$(12.5)^{2} × 18 | ND | $\mathit{\pi}$(12.5)^{2} × 45 (Iron) | The effect of TCR was evaluated. | Sadeghi et al. [53] |

Graphene nanosheets/1-octadecano | ND | 0.3–0.9 | $\mathit{\pi}$(6.35)^{2} × 6.35 | Teflon | $\mathit{\pi}$(6.35)^{2} × ND (Indium) | The effect of TCR was evaluated. | Yavari et al. [31] |

Metal foam/Unknown PCM | +12/−7 | 1.95–3.92 | 30 × 40 × 50 | Cotton (lateral) PMMA (top) | 30 × 40 × 4 (Copper) | Tested different contact conditions; images taken to monitor cooling | Feng et al. [52] |

Multi Walled Carbon NanoTubes/RT65 paraffin | 10–40 °C | 0.195–0.24 | $\mathit{\pi}$(50)^{2} × 39 | ND | ND | The effect of up to 1% MWCNT tested | Alshaer1 et al. [54] |

Composite PCMs | Testing T [°C] | k Range [W/mK] | Sample Geometry [mm^{3}] | Wire Insulation | Wire Sizes [mm] | Peculiar Features | Reference |
---|---|---|---|---|---|---|---|

EG/paraffin | 10/70 | 0.4–0.8 | 32 × 22 × 105 | ND | d = 0.18 l = 105 (Platinum) | The EG wt.% optimum was around 10. | Sari et al. [25] |

MWCNT/ Paraffin | 15/65 | 4–60 | ND | Alumina | d = 0.07 l = ND (Platinum) | The mechanism of k enhancement caused by MWNT addition needs further investigation. | Wang et al. [36] |

CENG/paraffin; CENG/ stearic acid; CENG/ pentaglycerin | 25 | 5–60 (radial); 2–9 (axial) | 25 × 25 × 25 | ND | ND | The radial and axial thermal conductivity were distinguished due to anisotropy. | Haillot et al. [57] |

EG/NaNO_{3};EG/KNO _{3};EG/ NaNO _{3}-KNO_{3} | ND | 0.15–0.30 | ND | ND | d = 0.03 l = 116 (Platinum) | Quadratic parallel model was successfully used to predict the k_{eff}. | Xiao et al. [56] |

MWCNT/stearic acid/PVP; EG/stearic acid/PVP; Graphene/stearic acid/PVP | ND | 0.17–0.21 | ND | Teflon | d = 0.05 l = 190 (Platinum) | The study also presented an experimental apparatus to evaluate the PCM performance during cooling. | Choi et al. [37] |

Graphite nanoplates/ myristic acid | ND | 0.15–0.21 | ND | ND | d = 0.04 l = 19 (Nickel) | DSC analysis were performed to evaluate thermal reliability after 100 thermal cycles. | Ince et al. [35] |

**Table 3.**Phases, experimental parameters and literature sources for transient plane heat source tests on C-PCMs.

Composite PCMs | Testing T [°C] | Thermal Conductivity [W/mK] | Sample Dimension [mm^{3}] | Commercial Device | Reference |
---|---|---|---|---|---|

EG/polyethylene glycol | 25 | 0.3–1.4 | ND | TPS2500, Hot Disk Inc., Göteborg, Sweden | Wang et al. [26] |

Cement mortar-EG/n-octadecane | 25 | 1.8–2.2 | 100 × 100 × 10 | TPS2500, Hot Disk Inc., Sweden | Zhang et al. [27] |

Nickel foam/ paraffin Copper foam/ Paraffin | ND | 0.3–4.9 | 100 × 100 × 10 | TPS2500, Hot Disk Inc., Sweden | Xiao et al. [39] |

EG/LiNO_{3}-KCl | 25 | 4–16 | ND | TPS2500, Hot Disk Inc., Sweden | Huang et al. [28] |

EG/paraffin | ND | 0.7–14.0 | $\mathit{\pi}$(30)^{2} × 30 | TPS2500, Hot Disk Inc., Sweden | Li et al. [62] |

LPE graphene/paraffin | 7/42 | 0.1–85.0 | ND | TPS2500, Hot Disk Inc., Sweden | Goli et al. [61] |

EG/RT44HC | 30/60 | 4–16 | $\mathit{\pi}$(20)^{2} × 10 | TPS2500, Hot Disk Inc., Sweden | Ling et al. [29] |

Composite PCMs | Testing T [°C] | Thermal Conductivity [W/mK] | Sample Dimension [mm^{3}] | Commercial Device | Reference |
---|---|---|---|---|---|

Carbon nanofibers/paraffin | 25 | 0.25–3.00 | $\pi $(9)^{2} × 3.3 | ND | Elgafy et al. [65] |

Porous nichel/erythriol | 25 | 0.861–14.2 | $\pi $(5)^{2} × 2 | TC-7000, Rigaku, Tokyo, Japan | Oya et al. [66] |

Graphite nanosheets/ paraffin | ND | 0.33–4.47 | ND | LFA-447 Nanoflash, NETZSCH, Selb, Germany | Chen et al. [32] |

Graphene aerogel/ octadecanoic acid | 25 | 0.184–2.635 | $\pi $(6)^{2} × 2 | LFA-447 Nanoflash, NETZSCH, Germany | Zhong et al. [33] |

Sulfonated graphene/ polyethylene glycol | 37 | 0.263–1.042 | $\pi $(5)^{2} × 2 | TC-7000H, Sinku-Riko Inc., kanagawa, Japan | Li et al. [34] |

Polydimethylsiloxane-graphene-nickel foam/paraffin | 25 | 0.092–1.626 | ND | LFA-447 Nanoflash, NETZSCH, Germany | Liang et al. [38] |

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**MDPI and ACS Style**

Gariboldi, E.; Colombo, L.P.M.; Fagiani, D.; Li, Z.
Methods to Characterize Effective Thermal Conductivity, Diffusivity and Thermal Response in Different Classes of Composite Phase Change Materials. *Materials* **2019**, *12*, 2552.
https://doi.org/10.3390/ma12162552

**AMA Style**

Gariboldi E, Colombo LPM, Fagiani D, Li Z.
Methods to Characterize Effective Thermal Conductivity, Diffusivity and Thermal Response in Different Classes of Composite Phase Change Materials. *Materials*. 2019; 12(16):2552.
https://doi.org/10.3390/ma12162552

**Chicago/Turabian Style**

Gariboldi, Elisabetta, Luigi P. M. Colombo, Davide Fagiani, and Ziwei Li.
2019. "Methods to Characterize Effective Thermal Conductivity, Diffusivity and Thermal Response in Different Classes of Composite Phase Change Materials" *Materials* 12, no. 16: 2552.
https://doi.org/10.3390/ma12162552