Improving the Sierpinski carpet model arithmetic to accurately predict the thermal conductivity of fatty acid/carbon composite phase-change materials
•The GTC solution modifies the expression of the general solution of the dimensionless thermal conductivity.•The new formula called the FSC solution can narrow the gap between the predicted value and the experimental results.•The optimal fractal unit for frequency selection is proposed to reduce the...
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| Published in | Thermal science and engineering progress Vol. 40; p. 101743 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.05.2023
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2451-9049 2451-9049 |
| DOI | 10.1016/j.tsep.2023.101743 |
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| Abstract | •The GTC solution modifies the expression of the general solution of the dimensionless thermal conductivity.•The new formula called the FSC solution can narrow the gap between the predicted value and the experimental results.•The optimal fractal unit for frequency selection is proposed to reduce the dependence of predicted value on fractal unit.
The effective thermal conductivity is an important physical parameter of composite phase-change materials (PCMs). In this study, a new analytic expression of the dimensionless thermal conductivity is proposed to predict the dimensionless thermal conductivity of fatty acid–carbon materials composite PCMs based on the Sierpinski carpet model and the thermal resistance network model of a fractal geometry combined with the principle of the weighted average. The new analytical expression can be used to overcome the issue of the predicted values deviating considerably from the experimental results when the fractal series n is too small. At the same time, an accurate solution for the dimensionless ratio (t+) of the width of the carbon materials to the side length of the Sierpinski carpet is presented. Compared with the general solution algorithm proposed by Song, the commonly used quadratic parallel (QP) prediction model, and the Maxwell–Eucken model, this algorithm is more reliable. The proposed prediction model can be used to predict the effective thermal conductivity of fatty acid–carbon materials. |
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| AbstractList | •The GTC solution modifies the expression of the general solution of the dimensionless thermal conductivity.•The new formula called the FSC solution can narrow the gap between the predicted value and the experimental results.•The optimal fractal unit for frequency selection is proposed to reduce the dependence of predicted value on fractal unit.
The effective thermal conductivity is an important physical parameter of composite phase-change materials (PCMs). In this study, a new analytic expression of the dimensionless thermal conductivity is proposed to predict the dimensionless thermal conductivity of fatty acid–carbon materials composite PCMs based on the Sierpinski carpet model and the thermal resistance network model of a fractal geometry combined with the principle of the weighted average. The new analytical expression can be used to overcome the issue of the predicted values deviating considerably from the experimental results when the fractal series n is too small. At the same time, an accurate solution for the dimensionless ratio (t+) of the width of the carbon materials to the side length of the Sierpinski carpet is presented. Compared with the general solution algorithm proposed by Song, the commonly used quadratic parallel (QP) prediction model, and the Maxwell–Eucken model, this algorithm is more reliable. The proposed prediction model can be used to predict the effective thermal conductivity of fatty acid–carbon materials. |
| ArticleNumber | 101743 |
| Author | Hao, Xubo Niu, Baolian Li, Yinglin Xu, Xianghe Guo, Haotian |
| Author_xml | – sequence: 1 givenname: Xianghe surname: Xu fullname: Xu, Xianghe – sequence: 2 givenname: Baolian surname: Niu fullname: Niu, Baolian email: niubaolian@163.com – sequence: 3 givenname: Xubo surname: Hao fullname: Hao, Xubo – sequence: 4 givenname: Haotian surname: Guo fullname: Guo, Haotian – sequence: 5 givenname: Yinglin surname: Li fullname: Li, Yinglin |
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| Cites_doi | 10.1016/j.ijrefrig.2020.07.025 10.1016/j.ceramint.2016.04.078 10.1016/j.jobe.2022.104894 10.1016/B978-0-12-815732-9.00074-7 10.1016/j.solmat.2017.12.036 10.1115/1.3099022 10.1016/j.ijheatmasstransfer.2015.08.103 10.1063/1.346274 10.1016/0165-1633(89)90054-3 10.1063/1.1728579 10.2514/2.6669 10.1016/j.applthermaleng.2022.118623 10.1016/j.rser.2022.112283 10.1016/S0016-7061(98)00102-5 10.1016/j.molliq.2022.120168 10.1016/j.energy.2018.12.162 10.1016/j.ijheatmasstransfer.2004.12.032 10.1016/j.icheatmasstransfer.2021.105534 10.1016/S0022-1694(96)03096-X 10.1016/j.renene.2006.11.011 10.1016/j.enconman.2013.04.007 10.1016/j.enbuild.2021.111443 10.1016/j.chaos.2008.01.005 10.1016/j.est.2020.101911 10.1115/1.2822515 10.1016/j.ijheatmasstransfer.2021.121782 10.1016/j.icheatmasstransfer.2007.03.008 10.1016/j.applthermaleng.2020.115340 10.1016/B978-0-12-817797-6.00005-1 10.1016/j.micromeso.2022.111722 10.1088/0022-3727/36/17/321 10.1063/1.1702301 10.1016/j.ijheatmasstransfer.2018.05.155 10.1016/j.matpr.2020.07.048 10.1016/j.jclepro.2020.120906 10.1088/1742-6596/1599/1/012008 10.1016/j.pss.2003.08.009 10.1016/j.applthermaleng.2015.04.049 10.1016/j.applthermaleng.2015.07.071 10.1016/j.jcis.2021.10.060 |
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| References | Sarı, Bicer, Al-Ahmed, Al-Sulaiman, Zahir, Mohamed (b0110) 2018; 179 Karaipekli, Sarı, Kaygusuz (b0115) 2007; 32 Yin, Zhang, Yang, Qiu (b0250) 2008; 37 Hashin, Shtrikman (b0145) 1962; 33 Naveenkumar, Nandha Gopan, Karthikeyan, Santhosh Kumar, Ravichandran (b0040) 2020; 33 NematpourKeshteli, Iasiello, Langella, Bianco (b0120) 2022; 212 Qin, Cai, Xu (b0210) 2021 Song, Zhang, Yuan, Yang, Cao (b0245) 2019; 170 Rozanna, Chuah, Salmiah (b0080) 2005; 1(4):495–513 Jung, Subban, McTigue, Martinez, Copping, Osorio (b0050) 2022; 160 Mahmoud M, Ramadan M, Pullen K, Abdelkareem MA, Wilberforce T, Olabi A-G, et al. Waste Heat Recovery Applications Incorporating Phase Change Materials. In: Encyclopedia of Smart Materials. Olabi A-G (editor). Oxford: Elsevier 2022; pp. 513-521. A A S, B K K (b0090) 2003; 28(6) Carson, Lovatt, Tanner, Cleland (b0160) 2005; 48 Shi, Fan (b0205) 2002; 1(1):4 Sonnenrein, Baumhögger, Elsner, Morbach, Neukötter, Paul (b0065) 2020; 119 Maxwell (b0150) 2014; 7(182) Dinesh, Bhattacharya (b0100) 2020; 28 Feng, Qin (b0105) 2022; 366 Senobar, Aramesh, Shabani (b0125) 2020; 32 Yao, X-L, Fan L-W, Xu X, Yu Z-T (b0170) 2016; 92 Su, Zhu, Tian, Wang, Zhang, Li (b0075) 2020; 174 Adler (b0180) 1996; 187 Chaichi, Bahramian (b0225) 2022; 333 Liu, Tian, Ouyang, Qian, Wang (b0035) 2022; 608 Wei G, Xing L, Du X, et al. Research status and selection of phase change thermal energy storage materials for CSP systems[J]. Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society of Electrical Engineering 2014；34(3):325-335. Xiao, Zhang, Li (b0260) 2013; 73 Yu, Cheng (b0200) 2012; 16 Mustafa, Alqaed, Sharifpur (b0060) 2022; 57 Thovert, Wary, Adler (b0175) 1990; 68 Poonia, Singh, Jain (b0045) 2022 Junaid, Rehman, Čekon, Čurpek, Farooq, Cui (b0010) 2021; 252 Tian, Huang, Fan, Weng, Ying, Yu (b0215) 2015; 90 Wang, Mujumdar, Yap (b0140) 2007; 34 Iasiello, Mameli, Filippeschi (b0095) 2020; 1599 Adler, Thovert (b0185) 1998; 51 Ghorbani, Mehrpooya, Ardehali (b0025) 2020; 259 Tian, Fang, Yu (b0255) 2016; 15 Kabir, Gemeda, Preller, Xu (b0055) 2021; 180 Pia (b0230) 2016; 42 Feldman, Shapiro, Banu (b0085) 1989; 18(3–4) Perrier, Bird, Rieu (b0195) 1999; 88 Li, Duan, Simon (b0015) 2021; 298(12):117203 Huang, Zhai, Gao, Xu, Fang, Zhang (b0240) 2015; 86 Landauer (b0155) 1952; 23 Salvatore, Springer (b0165) 2002; 55(4):B62 Gori, Corasaniti (b0190) 2004; 52 Wan, Wang, Udayraj. (b0070) 2018; 126 Sadati, Rahbar, Kargarsharifabad, KhalesiDoost (b0220) 2021; 127 Hsu C T, Cheng P, Wong K W. A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media[J]. 1995. Shouju LI, Liu Y, Sun W, Wang YJIJoMPC. ESTIMATION OF THERMAL CONDUCTIVITY OF POROUS MATERIAL WITH FEM AND FRACTAL GEOMETRY. 2009. Ma, Yu, Zhang (b0235) 2003; 36 Li, Li, Lin, Xie, Zhang, Chen (b0005) 2021; 22 Adler (10.1016/j.tsep.2023.101743_b0185) 1998; 51 Qin (10.1016/j.tsep.2023.101743_b0210) 2021 Liu (10.1016/j.tsep.2023.101743_b0035) 2022; 608 Jung (10.1016/j.tsep.2023.101743_b0050) 2022; 160 Ma (10.1016/j.tsep.2023.101743_b0235) 2003; 36 Thovert (10.1016/j.tsep.2023.101743_b0175) 1990; 68 Su (10.1016/j.tsep.2023.101743_b0075) 2020; 174 Sarı (10.1016/j.tsep.2023.101743_b0110) 2018; 179 A A S, B K K (10.1016/j.tsep.2023.101743_b0090) 2003; 28(6) 10.1016/j.tsep.2023.101743_b0020 Ghorbani (10.1016/j.tsep.2023.101743_b0025) 2020; 259 Maxwell (10.1016/j.tsep.2023.101743_b0150) 2014; 7(182) Gori (10.1016/j.tsep.2023.101743_b0190) 2004; 52 Xiao (10.1016/j.tsep.2023.101743_b0260) 2013; 73 Sonnenrein (10.1016/j.tsep.2023.101743_b0065) 2020; 119 Yin (10.1016/j.tsep.2023.101743_b0250) 2008; 37 Karaipekli (10.1016/j.tsep.2023.101743_b0115) 2007; 32 10.1016/j.tsep.2023.101743_b0030 NematpourKeshteli (10.1016/j.tsep.2023.101743_b0120) 2022; 212 Feng (10.1016/j.tsep.2023.101743_b0105) 2022; 366 Tian (10.1016/j.tsep.2023.101743_b0255) 2016; 15 Yu (10.1016/j.tsep.2023.101743_b0200) 2012; 16 Pia (10.1016/j.tsep.2023.101743_b0230) 2016; 42 Chaichi (10.1016/j.tsep.2023.101743_b0225) 2022; 333 Wang (10.1016/j.tsep.2023.101743_b0140) 2007; 34 Li (10.1016/j.tsep.2023.101743_b0015) 2021; 298(12):117203 Wan (10.1016/j.tsep.2023.101743_b0070) 2018; 126 Feldman (10.1016/j.tsep.2023.101743_b0085) 1989; 18(3–4) Senobar (10.1016/j.tsep.2023.101743_b0125) 2020; 32 Adler (10.1016/j.tsep.2023.101743_b0180) 1996; 187 Naveenkumar (10.1016/j.tsep.2023.101743_b0040) 2020; 33 Mustafa (10.1016/j.tsep.2023.101743_b0060) 2022; 57 Perrier (10.1016/j.tsep.2023.101743_b0195) 1999; 88 Song (10.1016/j.tsep.2023.101743_b0245) 2019; 170 Yao (10.1016/j.tsep.2023.101743_b0170) 2016; 92 Tian (10.1016/j.tsep.2023.101743_b0215) 2015; 90 Shi (10.1016/j.tsep.2023.101743_b0205) 2002; 1(1):4 Kabir (10.1016/j.tsep.2023.101743_b0055) 2021; 180 Hashin (10.1016/j.tsep.2023.101743_b0145) 1962; 33 Sadati (10.1016/j.tsep.2023.101743_b0220) 2021; 127 Rozanna (10.1016/j.tsep.2023.101743_b0080) 2005; 1(4):495–513 Junaid (10.1016/j.tsep.2023.101743_b0010) 2021; 252 Li (10.1016/j.tsep.2023.101743_b0005) 2021; 22 Huang (10.1016/j.tsep.2023.101743_b0240) 2015; 86 Carson (10.1016/j.tsep.2023.101743_b0160) 2005; 48 Iasiello (10.1016/j.tsep.2023.101743_b0095) 2020; 1599 10.1016/j.tsep.2023.101743_b0130 Landauer (10.1016/j.tsep.2023.101743_b0155) 1952; 23 Poonia (10.1016/j.tsep.2023.101743_b0045) 2022 Salvatore (10.1016/j.tsep.2023.101743_b0165) 2002; 55(4):B62 Dinesh (10.1016/j.tsep.2023.101743_b0100) 2020; 28 10.1016/j.tsep.2023.101743_b0135 |
| References_xml | – volume: 174 year: 2020 ident: b0075 article-title: Intelligent bidirectional thermal regulation of phase change material incorporated in thermal protective clothing publication-title: Appl. Therm. Eng. – volume: 160 year: 2022 ident: b0050 article-title: Extracting energy from ocean thermal and salinity gradients to power unmanned underwater vehicles: State of the art, current limitations, and future outlook publication-title: Renew. Sustain. Energy Rev. – volume: 212 year: 2022 ident: b0120 article-title: Enhancing PCMs thermal conductivity: A comparison among porous metal foams, nanoparticles and finned surfaces in triplex tube heat exchangers publication-title: Appl. Therm. Eng. – volume: 57 year: 2022 ident: b0060 article-title: PCM embedded radiant chilled ceiling as a solution to shift the cooling peak load-focusing on solidification process acceleration publication-title: Journal of Building Engineering – volume: 37 start-page: 1257 year: 2008 end-page: 1266 ident: b0250 article-title: Geometric conditions for fractal super carbon nanotubes with strict self-similarities publication-title: Chaos Solitons Fractals – volume: 86 start-page: 309 year: 2015 end-page: 317 ident: b0240 article-title: Theoretical study on effective thermal conductivity of salt/expanded graphite composite material by using fractal method publication-title: Appl. Therm. Eng. – volume: 170 start-page: 752 year: 2019 end-page: 762 ident: b0245 article-title: Prediction of the solid effective thermal conductivity of fatty acid/carbon material composite phase change materials based on fractal theory publication-title: Energy – volume: 88 start-page: 137 year: 1999 end-page: 164 ident: b0195 article-title: Generalizing the fractal model of soil structure: the pore–solid fractal approach publication-title: Geoderma – volume: 42 start-page: 11674 year: 2016 end-page: 11681 ident: b0230 article-title: High porous yttria-stabilized zirconia with aligned pore channels: Morphology directionality influence on heat transfer publication-title: Ceram. Int. – volume: 18(3–4) start-page: 201 year: 1989 end-page: 216 ident: b0085 article-title: Fatty acids and their mixtures as phase-change materials for thermal energy storage[J] publication-title: Solar Energy Materials – volume: 15 start-page: 438 year: 2016 end-page: 443 ident: b0255 article-title: Fractal model of thermal conductivity of GA-based composite phase change material with hole sub-model publication-title: J. Therm. Sci. Technol. – volume: 32 year: 2020 ident: b0125 article-title: Nanoparticles and metal foams for heat transfer enhancement of phase change materials: A comparative experimental study[J] publication-title: The Journal of Energy Storage – volume: 16 start-page: 22 year: 2012 end-page: 29 ident: b0200 article-title: Fractal Models for the Effective Thermal Conductivity of Bidispersed Porous Media[J] publication-title: J. Thermophys Heat Transfer – volume: 28(6) start-page: 939 year: 2003 end-page: 948 ident: b0090 article-title: Some fatty acids used for latent heat storage: thermal stability and corrosion of metals with respect to thermal cycling[J] publication-title: Renew. Energy – volume: 73 start-page: 86 year: 2013 end-page: 94 ident: b0260 article-title: Thermal characterization of nitrates and nitrates/expanded graphite mixture phase change materials for solar energy storage publication-title: Energ. Conver. Manage. – volume: 180 year: 2021 ident: b0055 article-title: Design and Development of a PCM-Based Two-Phase Heat Exchanger Manufactured Additively for Spacecraft Thermal Management Systems publication-title: Int. J. Heat Mass Transf. – reference: Shouju LI, Liu Y, Sun W, Wang YJIJoMPC. ESTIMATION OF THERMAL CONDUCTIVITY OF POROUS MATERIAL WITH FEM AND FRACTAL GEOMETRY. 2009. – volume: 259 year: 2020 ident: b0025 article-title: Energy and exergy analysis of wind farm integrated with compressed air energy storage using multi-stage phase change material[J] publication-title: J. Clean. Prod. – volume: 33 start-page: 4159 year: 2020 end-page: 4162 ident: b0040 article-title: A comparative study on role of phase change materials in thermal efficiency enhancement of passive solar still publication-title: Mater. Today:. Proc. – volume: 366 year: 2022 ident: b0105 article-title: Nanoparticles effect on freezing of PCM utilizing finite element approach publication-title: J. Mol. Liq. – volume: 1(4):495–513 year: 2005 ident: b0080 article-title: Fatty Acids as Phase Change Materials (PCMs) for Thermal Energy Storage: A Review[J] publication-title: Int. J. Green Energy – volume: 252 year: 2021 ident: b0010 article-title: Inorganic phase change materials in thermal energy storage: A review on perspectives and technological advances in building applications publication-title: Energ. Buildings – volume: 92 start-page: 589 year: 2016 end-page: 602 ident: b0170 article-title: Experimental determination and fractal modeling of the effective thermal conductivity of autoclaved aerated concrete: Effects of moisture content publication-title: Int. J. Heat Mass Transf. – volume: 7(182) start-page: 478 year: 2014 end-page: 480 ident: b0150 article-title: A Treatise On Electricity and Magnetism[J] publication-title: Nature – volume: 126 start-page: 636 year: 2018 end-page: 648 ident: b0070 article-title: Numerical analysis of cooling effect of hybrid cooling clothing incorporated with phase change material (PCM) packs and air ventilation fans publication-title: Int. J. Heat Mass Transf. – volume: 48 start-page: 2150 year: 2005 end-page: 2158 ident: b0160 article-title: Thermal conductivity bounds for isotropic, porous materials publication-title: Int. J. Heat Mass Transf. – reference: Hsu C T, Cheng P, Wong K W. A lumped-parameter model for stagnant thermal conductivity of spatially periodic porous media[J]. 1995. – volume: 52 start-page: 91 year: 2004 end-page: 99 ident: b0190 article-title: Theoretical prediction of the thermal conductivity and temperature variation inside mars soil analogues[J] publication-title: Planet. Space Sci. – volume: 179 start-page: 353 year: 2018 end-page: 361 ident: b0110 article-title: Silica fume/capric acid-palmitic acid composite phase change material doped with CNTs for thermal energy storage publication-title: Sol. Energy Mater. Sol. Cells – volume: 68 start-page: 3872 year: 1990 end-page: 3883 ident: b0175 article-title: Thermal conductivity of random media and regular fractals[J] publication-title: J. Appl. Phys. – volume: 298(12):117203 year: 2021 ident: b0015 article-title: Nonuniform metal foam design and pore-scale analysis of a tilted composite phase change material system for photovoltaics thermal management[J] publication-title: Appl. Energy – reference: Wei G, Xing L, Du X, et al. Research status and selection of phase change thermal energy storage materials for CSP systems[J]. Zhongguo Dianji Gongcheng Xuebao/Proceedings of the Chinese Society of Electrical Engineering 2014；34(3):325-335. – volume: 187 start-page: 195 year: 1996 end-page: 213 ident: b0180 article-title: Transports in fractal porous media publication-title: J. Hydrol. – volume: 23 start-page: 779 year: 1952 end-page: 784 ident: b0155 article-title: The Electrical Resistance of Binary Metallic Mixtures[J] publication-title: J.appl.phys – volume: 55(4):B62 year: 2002 ident: b0165 article-title: Random heterogeneous materials[J] publication-title: Interdiscip. Appl. Math. – volume: 608 start-page: 1497 year: 2022 end-page: 1513 ident: b0035 article-title: Morphology-controlled fabrication of magnetic phase-change microcapsules for synchronous efficient recovery of wastewater and waste heat publication-title: J. Colloid Interface Sci. – volume: 90 start-page: 1007 year: 2015 end-page: 1014 ident: b0215 article-title: A comprehensive characterization on the structural and thermophysical properties of sintered ore particles toward waste heat recovery applications publication-title: Appl. Therm. Eng. – volume: 51 start-page: 537 year: 1998 end-page: 585 ident: b0185 article-title: Real Porous Media: Local Geometry andMacroscopic Properties[J] publication-title: Appl. Mech. Rev. – volume: 34 start-page: 801 year: 2007 end-page: 808 ident: b0140 article-title: Effect of orientation for phase change material (PCM)-based heat sinks for transient thermal management of electric components publication-title: Int. Commun. Heat Mass Transfer – start-page: 119 year: 2021 end-page: 139 ident: b0210 article-title: Fractal analysis on conductive heat transfer in porous media[J] publication-title: Modelling of Flow and Transport in Fractal Porous Media – volume: 127 year: 2021 ident: b0220 article-title: Low thermal conductivity measurement using thermoelectric technology - Mathematical modeling and experimental analysis publication-title: Int. Commun. Heat Mass Transfer – volume: 32 start-page: 2201 year: 2007 end-page: 2210 ident: b0115 article-title: Thermal conductivity improvement of stearic acid using expanded graphite and carbon fiber for energy storage applications publication-title: Renew. Energy – volume: 1599 year: 2020 ident: b0095 article-title: Simulations of paraffine melting inside metal foams at different gravity levels with preliminary experimental validation[J] publication-title: J. Phys. Conf. Ser. – reference: Mahmoud M, Ramadan M, Pullen K, Abdelkareem MA, Wilberforce T, Olabi A-G, et al. Waste Heat Recovery Applications Incorporating Phase Change Materials. In: Encyclopedia of Smart Materials. Olabi A-G (editor). Oxford: Elsevier 2022; pp. 513-521. – year: 2022 ident: b0045 article-title: Performance evaluation of PCM based solar concentrator type desalination device – volume: 119 start-page: 448 year: 2020 end-page: 456 ident: b0065 article-title: Improving the performance of household refrigerating appliances through the integration of phase change materials in the context of the new global refrigerator standard IEC 62552:2015 publication-title: Int. J. Refrig – volume: 28 year: 2020 ident: b0100 article-title: Comparison of energy absorption characteristics of PCM-metal foam systems with different pore size distributions publication-title: J. Storage Mater. – volume: 1(1):4 year: 2002 ident: b0205 article-title: A Fractal Model for Evaluating Heat Conduction in Porous Media[J] publication-title: Journal of Thermal Science and Technology – volume: 22 year: 2021 ident: b0005 article-title: Review on tailored phase change behavior of hydrated salt as phase change materials for energy storage publication-title: Mater. Today Energy – volume: 333 year: 2022 ident: b0225 article-title: Theoretical relation of the structure and thermal properties of gradient thermal insulator aerogels using fractal geometry publication-title: Microporous Mesoporous Mater. – volume: 36 start-page: 2157 year: 2003 ident: b0235 article-title: A self-similarity model for effective thermal conductivity of porous media[J] publication-title: J. Phys. D Appl. Phys. – volume: 33 start-page: 3125 year: 1962 end-page: 3131 ident: b0145 article-title: A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials[J] publication-title: J. Appl. Phys. – volume: 119 start-page: 448 year: 2020 ident: 10.1016/j.tsep.2023.101743_b0065 article-title: Improving the performance of household refrigerating appliances through the integration of phase change materials in the context of the new global refrigerator standard IEC 62552:2015 publication-title: Int. J. Refrig doi: 10.1016/j.ijrefrig.2020.07.025 – volume: 42 start-page: 11674 issue: 10 year: 2016 ident: 10.1016/j.tsep.2023.101743_b0230 article-title: High porous yttria-stabilized zirconia with aligned pore channels: Morphology directionality influence on heat transfer publication-title: Ceram. Int. doi: 10.1016/j.ceramint.2016.04.078 – volume: 57 year: 2022 ident: 10.1016/j.tsep.2023.101743_b0060 article-title: PCM embedded radiant chilled ceiling as a solution to shift the cooling peak load-focusing on solidification process acceleration publication-title: Journal of Building Engineering doi: 10.1016/j.jobe.2022.104894 – ident: 10.1016/j.tsep.2023.101743_b0030 doi: 10.1016/B978-0-12-815732-9.00074-7 – volume: 28(6) start-page: 939 year: 2003 ident: 10.1016/j.tsep.2023.101743_b0090 article-title: Some fatty acids used for latent heat storage: thermal stability and corrosion of metals with respect to thermal cycling[J] publication-title: Renew. Energy – volume: 179 start-page: 353 year: 2018 ident: 10.1016/j.tsep.2023.101743_b0110 article-title: Silica fume/capric acid-palmitic acid composite phase change material doped with CNTs for thermal energy storage publication-title: Sol. Energy Mater. Sol. Cells doi: 10.1016/j.solmat.2017.12.036 – volume: 51 start-page: 537 issue: 9 year: 1998 ident: 10.1016/j.tsep.2023.101743_b0185 article-title: Real Porous Media: Local Geometry andMacroscopic Properties[J] publication-title: Appl. Mech. Rev. doi: 10.1115/1.3099022 – volume: 92 start-page: 589 year: 2016 ident: 10.1016/j.tsep.2023.101743_b0170 article-title: Experimental determination and fractal modeling of the effective thermal conductivity of autoclaved aerated concrete: Effects of moisture content publication-title: Int. J. Heat Mass Transf. doi: 10.1016/j.ijheatmasstransfer.2015.08.103 – volume: 68 start-page: 3872 issue: 8 year: 1990 ident: 10.1016/j.tsep.2023.101743_b0175 article-title: Thermal conductivity of random media and regular fractals[J] publication-title: J. Appl. Phys. doi: 10.1063/1.346274 – volume: 18(3–4) start-page: 201 year: 1989 ident: 10.1016/j.tsep.2023.101743_b0085 article-title: Fatty acids and their mixtures as phase-change materials for thermal energy storage[J] publication-title: Solar Energy Materials doi: 10.1016/0165-1633(89)90054-3 – volume: 33 start-page: 3125 issue: 10 year: 1962 ident: 10.1016/j.tsep.2023.101743_b0145 article-title: A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials[J] publication-title: J. Appl. Phys. doi: 10.1063/1.1728579 – volume: 298(12):117203 year: 2021 ident: 10.1016/j.tsep.2023.101743_b0015 article-title: Nonuniform metal foam design and pore-scale analysis of a tilted composite phase change material system for photovoltaics thermal management[J] publication-title: Appl. Energy – volume: 22 year: 2021 ident: 10.1016/j.tsep.2023.101743_b0005 article-title: Review on tailored phase change behavior of hydrated salt as phase change materials for energy storage publication-title: Mater. Today Energy – volume: 16 start-page: 22 issue: 1 year: 2012 ident: 10.1016/j.tsep.2023.101743_b0200 article-title: Fractal Models for the Effective Thermal Conductivity of Bidispersed Porous Media[J] publication-title: J. Thermophys Heat Transfer doi: 10.2514/2.6669 – volume: 212 year: 2022 ident: 10.1016/j.tsep.2023.101743_b0120 article-title: Enhancing PCMs thermal conductivity: A comparison among porous metal foams, nanoparticles and finned surfaces in triplex tube heat exchangers publication-title: Appl. Therm. Eng. doi: 10.1016/j.applthermaleng.2022.118623 – volume: 160 year: 2022 ident: 10.1016/j.tsep.2023.101743_b0050 article-title: Extracting energy from ocean thermal and salinity gradients to power unmanned underwater vehicles: State of the art, current limitations, and future outlook publication-title: Renew. Sustain. Energy Rev. doi: 10.1016/j.rser.2022.112283 – volume: 88 start-page: 137 issue: 3 year: 1999 ident: 10.1016/j.tsep.2023.101743_b0195 article-title: Generalizing the fractal model of soil structure: the pore–solid fractal approach publication-title: Geoderma doi: 10.1016/S0016-7061(98)00102-5 – volume: 366 year: 2022 ident: 10.1016/j.tsep.2023.101743_b0105 article-title: Nanoparticles effect on freezing of PCM utilizing finite element approach publication-title: J. Mol. Liq. doi: 10.1016/j.molliq.2022.120168 – ident: 10.1016/j.tsep.2023.101743_b0020 – volume: 170 start-page: 752 year: 2019 ident: 10.1016/j.tsep.2023.101743_b0245 article-title: Prediction of the solid effective thermal conductivity of fatty acid/carbon material composite phase change materials based on fractal theory publication-title: Energy doi: 10.1016/j.energy.2018.12.162 – volume: 48 start-page: 2150 issue: 11 year: 2005 ident: 10.1016/j.tsep.2023.101743_b0160 article-title: Thermal conductivity bounds for isotropic, porous materials publication-title: Int. J. Heat Mass Transf. doi: 10.1016/j.ijheatmasstransfer.2004.12.032 – volume: 127 year: 2021 ident: 10.1016/j.tsep.2023.101743_b0220 article-title: Low thermal conductivity measurement using thermoelectric technology - Mathematical modeling and experimental analysis publication-title: Int. Commun. Heat Mass Transfer doi: 10.1016/j.icheatmasstransfer.2021.105534 – volume: 187 start-page: 195 issue: 1 year: 1996 ident: 10.1016/j.tsep.2023.101743_b0180 article-title: Transports in fractal porous media publication-title: J. Hydrol. doi: 10.1016/S0022-1694(96)03096-X – volume: 32 start-page: 2201 issue: 13 year: 2007 ident: 10.1016/j.tsep.2023.101743_b0115 article-title: Thermal conductivity improvement of stearic acid using expanded graphite and carbon fiber for energy storage applications publication-title: Renew. Energy doi: 10.1016/j.renene.2006.11.011 – volume: 73 start-page: 86 year: 2013 ident: 10.1016/j.tsep.2023.101743_b0260 article-title: Thermal characterization of nitrates and nitrates/expanded graphite mixture phase change materials for solar energy storage publication-title: Energ. Conver. Manage. doi: 10.1016/j.enconman.2013.04.007 – volume: 252 year: 2021 ident: 10.1016/j.tsep.2023.101743_b0010 article-title: Inorganic phase change materials in thermal energy storage: A review on perspectives and technological advances in building applications publication-title: Energ. Buildings doi: 10.1016/j.enbuild.2021.111443 – volume: 37 start-page: 1257 issue: 5 year: 2008 ident: 10.1016/j.tsep.2023.101743_b0250 article-title: Geometric conditions for fractal super carbon nanotubes with strict self-similarities publication-title: Chaos Solitons Fractals doi: 10.1016/j.chaos.2008.01.005 – volume: 32 year: 2020 ident: 10.1016/j.tsep.2023.101743_b0125 article-title: Nanoparticles and metal foams for heat transfer enhancement of phase change materials: A comparative experimental study[J] publication-title: The Journal of Energy Storage doi: 10.1016/j.est.2020.101911 – ident: 10.1016/j.tsep.2023.101743_b0130 doi: 10.1115/1.2822515 – volume: 180 year: 2021 ident: 10.1016/j.tsep.2023.101743_b0055 article-title: Design and Development of a PCM-Based Two-Phase Heat Exchanger Manufactured Additively for Spacecraft Thermal Management Systems publication-title: Int. J. Heat Mass Transf. doi: 10.1016/j.ijheatmasstransfer.2021.121782 – volume: 34 start-page: 801 issue: 7 year: 2007 ident: 10.1016/j.tsep.2023.101743_b0140 article-title: Effect of orientation for phase change material (PCM)-based heat sinks for transient thermal management of electric components publication-title: Int. Commun. Heat Mass Transfer doi: 10.1016/j.icheatmasstransfer.2007.03.008 – volume: 174 year: 2020 ident: 10.1016/j.tsep.2023.101743_b0075 article-title: Intelligent bidirectional thermal regulation of phase change material incorporated in thermal protective clothing publication-title: Appl. Therm. Eng. doi: 10.1016/j.applthermaleng.2020.115340 – start-page: 119 year: 2021 ident: 10.1016/j.tsep.2023.101743_b0210 article-title: Fractal analysis on conductive heat transfer in porous media[J] publication-title: Modelling of Flow and Transport in Fractal Porous Media doi: 10.1016/B978-0-12-817797-6.00005-1 – volume: 333 year: 2022 ident: 10.1016/j.tsep.2023.101743_b0225 article-title: Theoretical relation of the structure and thermal properties of gradient thermal insulator aerogels using fractal geometry publication-title: Microporous Mesoporous Mater. doi: 10.1016/j.micromeso.2022.111722 – volume: 36 start-page: 2157 issue: 17 year: 2003 ident: 10.1016/j.tsep.2023.101743_b0235 article-title: A self-similarity model for effective thermal conductivity of porous media[J] publication-title: J. Phys. D Appl. Phys. doi: 10.1088/0022-3727/36/17/321 – volume: 55(4):B62 year: 2002 ident: 10.1016/j.tsep.2023.101743_b0165 article-title: Random heterogeneous materials[J] publication-title: Interdiscip. Appl. Math. – year: 2022 ident: 10.1016/j.tsep.2023.101743_b0045 – volume: 23 start-page: 779 issue: 7 year: 1952 ident: 10.1016/j.tsep.2023.101743_b0155 article-title: The Electrical Resistance of Binary Metallic Mixtures[J] publication-title: J.appl.phys doi: 10.1063/1.1702301 – volume: 126 start-page: 636 year: 2018 ident: 10.1016/j.tsep.2023.101743_b0070 article-title: Numerical analysis of cooling effect of hybrid cooling clothing incorporated with phase change material (PCM) packs and air ventilation fans publication-title: Int. J. Heat Mass Transf. doi: 10.1016/j.ijheatmasstransfer.2018.05.155 – volume: 7(182) start-page: 478 year: 2014 ident: 10.1016/j.tsep.2023.101743_b0150 article-title: A Treatise On Electricity and Magnetism[J] publication-title: Nature – volume: 15 start-page: 438 year: 2016 ident: 10.1016/j.tsep.2023.101743_b0255 article-title: Fractal model of thermal conductivity of GA-based composite phase change material with hole sub-model publication-title: J. Therm. Sci. Technol. – volume: 33 start-page: 4159 year: 2020 ident: 10.1016/j.tsep.2023.101743_b0040 article-title: A comparative study on role of phase change materials in thermal efficiency enhancement of passive solar still publication-title: Mater. Today:. Proc. doi: 10.1016/j.matpr.2020.07.048 – volume: 259 year: 2020 ident: 10.1016/j.tsep.2023.101743_b0025 article-title: Energy and exergy analysis of wind farm integrated with compressed air energy storage using multi-stage phase change material[J] publication-title: J. Clean. Prod. doi: 10.1016/j.jclepro.2020.120906 – volume: 1(4):495–513 year: 2005 ident: 10.1016/j.tsep.2023.101743_b0080 article-title: Fatty Acids as Phase Change Materials (PCMs) for Thermal Energy Storage: A Review[J] publication-title: Int. J. Green Energy – ident: 10.1016/j.tsep.2023.101743_b0135 – volume: 1599 year: 2020 ident: 10.1016/j.tsep.2023.101743_b0095 article-title: Simulations of paraffine melting inside metal foams at different gravity levels with preliminary experimental validation[J] publication-title: J. Phys. Conf. Ser. doi: 10.1088/1742-6596/1599/1/012008 – volume: 28 year: 2020 ident: 10.1016/j.tsep.2023.101743_b0100 article-title: Comparison of energy absorption characteristics of PCM-metal foam systems with different pore size distributions publication-title: J. Storage Mater. – volume: 52 start-page: 91 issue: 1/3 year: 2004 ident: 10.1016/j.tsep.2023.101743_b0190 article-title: Theoretical prediction of the thermal conductivity and temperature variation inside mars soil analogues[J] publication-title: Planet. Space Sci. doi: 10.1016/j.pss.2003.08.009 – volume: 86 start-page: 309 year: 2015 ident: 10.1016/j.tsep.2023.101743_b0240 article-title: Theoretical study on effective thermal conductivity of salt/expanded graphite composite material by using fractal method publication-title: Appl. Therm. Eng. doi: 10.1016/j.applthermaleng.2015.04.049 – volume: 90 start-page: 1007 year: 2015 ident: 10.1016/j.tsep.2023.101743_b0215 article-title: A comprehensive characterization on the structural and thermophysical properties of sintered ore particles toward waste heat recovery applications publication-title: Appl. Therm. Eng. doi: 10.1016/j.applthermaleng.2015.07.071 – volume: 608 start-page: 1497 year: 2022 ident: 10.1016/j.tsep.2023.101743_b0035 article-title: Morphology-controlled fabrication of magnetic phase-change microcapsules for synchronous efficient recovery of wastewater and waste heat publication-title: J. Colloid Interface Sci. doi: 10.1016/j.jcis.2021.10.060 – volume: 1(1):4 year: 2002 ident: 10.1016/j.tsep.2023.101743_b0205 article-title: A Fractal Model for Evaluating Heat Conduction in Porous Media[J] publication-title: Journal of Thermal Science and Technology |
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