A review on phase-change materials: Mathematical modeling and simulations

Renewable and Sustainable Energy Reviews

Volumn 15, Issue 1, 2011, Pages 112-130

  Dutil, Yvan ^a   Rousse, Daniel R ^a   Salah, Nizar Ben ^b   Lassue, Stéphane ^c   Zalewski, Laurent ^c  

^a ÉCOLE DE TECHNOLOGIE SUPÉRIEURE   (Canada)

^b UNIVERSITY OF TUNIS   (Tunisia)

^c UNIVERSITÉ D'ARTOIS   (France)

Author keywords

Component; Latent heat; Mathematical modeling; Numerical simulations; Phase change materials; Power demand; Power system economics; Thermal energy storage

Indexed keywords

COMPONENT; MATHEMATICAL MODELING; NUMERICAL SIMULATION; POWER DEMANDS; POWER SYSTEM ECONOMICS;

COMPUTER SIMULATION; ECONOMICS; ENERGY EFFICIENCY; FLYWHEELS; HEAT STORAGE; LATENT HEAT; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PHASE TRANSITIONS; RESEARCH; STORAGE (MATERIALS); THERMODYNAMICS;

PHASE CHANGE MATERIALS;

EID: 78149416685     PISSN: 13640321     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.rser.2010.06.011     Document Type: Review

References (253)

1. M.M. Farid, A.M. Khudhair, S.A.K. Razack, and S. Al-Hallaj A review on phase change energy storage: materials and applications Energy Convers Manage 45 9-10 2004 1597 1615
2. A. Sharma Review on thermal energy storage with phase change materials and applications Renew Sust Energy Rev 13 2 2009 318 345
3. Y. Zhang, G. Zhou, K. Lin, Q. Zhang, and H. Di Application of latent heat thermal energy storage in buildings: state-of-the-art and outlook Build Environ 42 6 2007 2197 2209
4. A.F. Regin, S.C. Solanki, and J.S. Saini Heat transfer characteristics of thermal energy storage system using PCM capsules: a review Renew Sust Energy Rev 12 9 2008 2438 2458
5. V.V. Tyagi, and D. Buddhi PCM thermal storage in buildings: a state of art Renew Sust Energy Rev 11 6 2007 1146 1166
6. S. Mondal Phase change materials for smart textiles-an overview Appl Therm Eng 28 11-12 2008 1536 1550
7. V.P. Sethi, and S.K. Sharma Survey and evaluation of heating technologies for worldwide agricultural greenhouse applications Solar Energy 82 9 2008 832 859
8. P. Verma, S.K. Varun, and Singal Review of mathematical modeling on latent heat thermal energy storage systems using phase-change material Renew Sust Energy Rev 12 4 2008 999 1031
9. B.P.E. Clapeyron, and M.M. Lamé Mémoire sur la solidification par refroidissement d'un globe liquide Ann Chim Phys 47 1831 250 256
10. M. Brillouin Sur quelques problmes non résolus de la Physique Mathématique classique Propagation de la fusion Ann l'inst Henri Poincaré 1 3 1930 285 308
11. J. Stefan Uber einige probleme der theorie der warmeleitung Sber Akad Wiss Wien 98 1889 473 484
12. G.W. Evans A note on the existence of a solution to a problem of Stefan Q Appl Math 9 1951 185 193
13. J. Douglas A uniqueness theorem for the solution of a Stefan problem Proc Am Math Soc 8 1957 402 408
14. J. Crank Free and moving boundary problems 1984 Clarendon Press Oxford
15. J.M. Hill One-dimensional Stefan problems: an introduction 1987 Longman Scientific Technical Harlow
16. H.S. Carslaw, and J.C. Jaeger Conduction of heat in solids 1959 Clarendon Press Oxford
17. V.J. Lunardini Heat transfer in cold climates 1981 Van Nostrand Reinhold New York
18. Z. Ma, and Y. Zhang Solid velocity correction schemes for a temperature transforming model for convection phase change Int J Numer Methods Heat 16 2 2006 204 225
19. C.R. Swaminathan, and V.R. Voller On the enthalpy method Int J Numer Methods Heat Fluid Flow 3 1993 233 244
20. V.R. Voller, M. Cross, and N.C. Markatos An enthalpy method for convection/diffusion phase change Int J Numer Methods Eng 24 1987 271 284
21. V. Alexiades, and A.D. Solomon Mathematical modeling of melting and freezing processes 1993 Hemisphere Publishing Corporation USA
22. B. Nedjar An enthalpy-based finite element method for nonlinear heat problems involving phase change Comput Struct 80 2002 9 21
23. L.W. Hunter, and J.R. Kuttler The enthalpy method for heat conduction problems with moving boundaries J Heat Transfer, Trans ASME 111 1989 239 242
24. M. Amdjadi, B. Fabre, and C. Meynadier Résolution unidimensionnelle d'un problme de Stefan par une méthode pas de temps variable. Application une bille de chliarolithe Rev Gén Therm Fr 339 1990 129 134
25. V.R. Voller Fast implicit finite-difference method for the analysis of phase change problems Numer Heat Transfer Part B 17 1990 155 169
26. C. Bonacina Numerical solution of phase-change problems Int J Heat Mass Transfer 16 1973 1825 1832
27. Y. Cao, and A. Faghri A numerical analysis of phase change problem including natural convection J Heat Transfer 112 1990 812 815
28. K. Morgan A numerical analysis of freezing and melting with convection Comput Methods Appl Eng 28 1981 275 284
29. M. Yang, and W.Q. Tao Numerical study of natural convection heat transfer in a cylindrical envelope with internal concentric slotted hollow cylinder Numer Heat Transfer, Part A 22 1992 289 305
30. A.D. Brent, V.R. Voller, and K.J. Reid Enthalpy-porosity technique for modeling convection-diffusion phase change: application to the melting of a pure metal Numer Heat Transfer 13 1988 297 318
31. D.K. Gartling Finite element analysis of convective heat transfer problems with change of phase K. Morgan, C. Taylor, C.A. Brebbia, Computer methods in fluids 1980 Pentech London 257 284
32. M. Okada Analysis of heat transfer during melting from a vertical wall Int J Heat Mass Transfer 27 1984 2057 2066
33. R.J. Braun, and B.T. Murray Adaptive phase-field computations of dendritic growth J Cryst Growth 174 1997 41 53
34. R.H. Nochetto, M. Paolini, and C. Verdi An adaptive finite element method for two-phase Stefan problems in two space dimensions, Part II: implementation and numerical experiments SIAM J Sci Comput 12 1991 1207 1244
35. N. Provatas, N. Goldenfeld, and J. Dantzig Efficient computation of dendritic microstructures using adaptive mesh refinement Phys Rev Lett 80 1998 3308 3311
36. N. Provatas, N. Goldenfeld, and J. Dantzig Adaptive mesh refinement computation of solidification microstructures using dynamic data structures J Comput Phys 148 1999 265 290
37. M. Ainsworth, and J.T. Oden A posteriori error estimation in finite element analysis, pure and applied mathematics 2000 Wiley-Interscience
38. J.A. Mackenzie, and M.L. Robertson The numerical solution of one-dimensional phase change problems using an adaptive moving mesh method J Comput Phys 161 2000 537 557
39. J.A. Mackenzie, and M.L. Robertson A moving mesh method for the solution of the one-dimensional phase-field equations J Comput Phys 181 2002 526 544
40. J.A. Mackenzie, and W.R. Mekwi On the use of moving mesh methods to solve PDEs T. Tang, J. Xu, Adaptive computations: theory and algorithms 2007 Science Press Beijing 242 278
41. Z. Tan, K.M. Lim, and B.C. Khoo An adaptive mesh redistribution method for the incompressible mixture flows using phase-field model J Comput Phys 225 2007 1137 1158
42. M. Lacroix, and V.R. Voller Finite different solutions of solidification phase change problems: transformed versus fixed grids Numer Heat Transfer, Part B 17 1990 25 41
43. R. Viswanath, and Y. Jaluria A comparison of different solution methodologies for melting and solidification problems in enclosures Numer Heat Transfer, Part B: Fundam 24 1993 77 105
44. O. Bertrand, and B. Binet Melting driven by natural convection. A comparison exercise: first results Int J Therm Sci 38 1999 5 26
45. N. Shamsundar, and E.M. Sparrow Analysis of multidimensional conduction phase change via the enthalpy model J Heat Transfer, Trans ASME 1975 333 340
46. N. Shamsundar, and E.M. Sparrow Effect of density change on multidimensional conduction phase change J Heat Transfer, Trans ASME 98 1976 550 557
47. N. Shamsundar, and R. Srinivasan Analysis of energy storage by phase change with an array of cylindrical tubes Thermal energy storage and heat transfer in solar energy systems vol. 35 1978 American Society of Mechanical Engineers New York
48. N. Shamsundar, and E. Rooz Numerical methods for moving boundary problems Handbook of Numerical Heat Transfer 1988 Wiley-Interscience
49. N. Shamsundar Comparison of numerical methods for diffusion problems with moving boundaries O.G. Wilson, A.D. Solomon, T.T. Boggs, Moving boundary problems 1978 Academic Press New York
50. M.A. Hamdan, and F.A. Elwerr Thermal energy storage using a phase change material Solar Energy 56 2 1996 183 189
51. C. Benard, G. Gobin, and F. Martinez Melting in rectangular enclosures: experiments and numerical simulations J Heat Transfer, Trans ASME 107 1985 794 802
52. M. Lacroix Computation of heat transfer during melting of a pure substance from an isothermal wall Numer Heat Transfer, Part B 15 1989 191 210
53. M. Lacroix Contact melting of a phase change material inside a heated parallelepedic capsule Energy Convers Manage 42 2001 35 44
54. B. Binet, and M. Lacroix Numerical study of natural-convection dominated melting inside uniformly and discretely heated rectangular cavities J Numer Heat Transfer Part A 33 1998 207 224 (Pubitemid 128620542)
55. B. Binet, and M. Lacroix Étude numérique de la fusion dans des enceintes rectangulaires chauffées uniformément ou discrtement par les parois latérales conductrices Int J Therm Sci 37 1998 607 620
56. P. Brousseau, and M. Lacroix Study of the thermal performance of a multi-layer PCM storage unit Energy Convers Manage 37 1996 599 609
57. P. Brousseau, and M. Lacroix Numerical simulation of a multi-layer latent heat thermal energy storage system Int J Energy Res 22 1998 1 15
58. M. Costa, A. Oliva, C.D. Perez Segarra, and R. Alba Numerical simulation of solid-liquid phase change phenomena Comput Methods Appl Mech Eng 91 1991 1123 1134
59. M. Costa, A. Oliva, and C.D. Perez-Segarra Three-dimensional numerical study of melting inside an isothermal horizontal cylinder Numer Heat Transfer, Part A 32 1997 531 553
60. M.M. Farid, and R.M. Husian An electrical storage heater using phase change method of heat storage Energy Convers Manage 30 1990 219 230
61. M.M. Farid, F.A. Hamad, and M. Abu-Arabi Phase change cool storage using dimethyl-sulfoxide Energy Convers Manage 39 1998 819 826
62. D.J. Morrison, and S.I. Abdul Khalik Effect of phase change energy storage on the performance of air-based and liquidbased solar heating systems Solar Energy 20 1978 57 67
63. R. Marshall, and C. Dietsche Comparisons of paraffin wax storage subsystem models using liquid heat transfer media Solar Energy 29 1982 503 511 (Pubitemid 13478986)
64. J.A. Bailey, J.C. Mulligan, C.K. Liao, S.I. Guceri, and M.K. Reddy Research on solar energy storage subsystem utilizing the latent heat of phase change of paraffin hydrocarbons for the heating and cooling of buildings. Report to the National Science Foundation for Grant GI-4438 1976 North Carolina State University USA
65. E. Halawa, F. Bruno, and W. Saman Numerical analysis of a PCM thermal storage system with varying wall temperature Energy Convers Manage 46 2005 2592 2604
66. M. Costa, D. Buddhi, and A. Oliva Numerical simulation of a latent heat thermal energy storage system with enhanced heat conduction Energy Convers Manage 39 3-4 1998 319 330
67. S.V. Patankar Numerical heat transfer and fluid flow 1980 Hemisphere Publishing Corporation Washington, DC
68. S.M. Vakilaltojjar, and W. Saman Analysis and modeling of a phase change storage system for air conditioning applications Appl Therm Eng 21 2001 249 263
69. P. Dolado, A. Lázaro, B. Zalba, and J.M. Marín Numerical simulation of material behaviour of an energy storage unit with phase change materials for air conditioning applications between 17 °C and 40 °C ECOSTOCK 10th international conference on thermal energy storage Stockton 2006
70. M. Zukowski Mathematical modeling and numerical simulation of a short term thermal energy storage system using phase change material for heating applications Energy Convers Manage 48 2007 155 165
71. P.D. Silva, L.C. Goncalves, and L.O. Pires Transient behavior of a latent heat thermal energy store: numerical and experimental studies Appl Energy 73 2002 83 98
72. M. Vynnycky, and S. Kimura An analytical and numerical study of coupled transient natural convection and solidification in a rectangular enclosure Int J Heat Mass Transfer 50 25-26 2007 5204 5214
73. B. Zivkovic, and I. Fujii An Analysis of isothermal phase change of phase change material within rectangular and cylindrical containers Solar Energy 70 1 2001 51 61
74. A. Najjar, and A. Hasan Modeling of greenhouse with PCM energy storage Energy Convers Manage 49 2008 3338 3342
75. D.R. Laybourn Thermal energy storage with encapsulated ice ASHRAE, Part 1 94 1988 1971 1988
76. T. Hirata, Y. Makino, and Y. Kaneko Analysis of close-contact melting for octadecane and ice inside isothermally heated horizontal rectangular capsule Int J Heat Mass Transfer 34 12 1991 3097 3106
77. S.K. Roy, and S. Sengupta Melting of a free solid in a spherical enclosure: effects of subcooling J Solar Energy Eng 111 1989 32 36
78. S.K. Roy, and S. Sengupta Gravity-assisted melting in a spherical enclosure: effects of natural convection Int J Heat Mass Transfer 33 1990 1135 1147
79. H. Ettouney, H. El-Dessouky, and A. Al-Ali Heat transfer during phase change of paraffin wax stored in spherical shells ASME J Solar Energy Eng 127 2005 357 365
80. A. Barba, and M. Spriga Discharge mode for encapsulated PCMs in storage tanks Solar Energy 74 2003 141 148
81. J.M. Khodadadi, and Y. Zhang Effects of buoyancy-driven convection on melting within spherical containers Int J Heat Mass Transfer 44 2001 1605 1618
82. S.A. Fomin, and T.S. Saitoh Melting of unfixed material in spherical capsule with nonisothermal wall Int J Heat Mass Transfer 42 1999 4197 4205
83. S.A. Fomin, and A.V. Wilchinsky Shape-factor effect on melting in an elliptic capsule Int J Heat Mass Transfer 45 14 2002 3045 3054
84. A.V. Wilchinsky, S.A. Fomin, and T. Hashida Contact melting inside an elastic capsule Int J Heat Mass Transfer 45 2002 4097 4106
85. Adref KT. A theoretical and experimental study of phase change in encapsulated ice store. Ph.D. thesis. England, UK: Department of Mechanical Engineering, Sheffield University; 1995.
86. K.T. Adref, and I.W. Eames Freezing of water within spherical enclosures: an experimental study Proceedings international conference on energy research development, vol. 2 Kuwait 1998 643 659
87. S. Lin, and Z. Jiang An improved quasi-steady analysis for solving freezing problems in a plate, a cylinder and a sphere ASME J Heat Transfer 125 2003 1123 1128
88. L. Bilir, and Z. Ilken Total solidification time of a liquid phase change material enclosed in cylindrical/spherical containers Appl Therm Eng 25 2005 1488 1502
89. K.A.R. Ismail, and J.R. Henriquez Solidification of PCM inside a spherical capsule Energy Convers Manage 41 2000 173 187
90. K.A.R. Ismail, J.R. Henriquez, and T.M. da Silva A parametric study on ice formation inside a spherical capsule Int J Therm Sci 42 2003 881 887
91. E. Assis, L. Katsman, G. Ziskind, and R. Letan Numerical and experimental study of melting in a spherical shell Int J Heat Mass Transfer 50 9-10 2007 1790 1804
92. Y.P. Shih, and T.C. Chou Analytical solution for freezing a saturated liquid inside or outside spheres Chem Eng Sci 26 1971 1787 1793
93. I.R. Pedroso, and G.A. Domoto Perturbation solutions for spherical solidification of saturated liquids J Heat Transfer 95 1 1973 42 46
94. J.M. Hill, and A. Kucera Freezing a saturated liquid inside a sphere Int J Heat Mass Transfer 26 11 1983 1631 1637
95. L.A. London, and R.A. Seban Rate of ice formation Trans ASME 65 1943 771 778
96. M. Veerappan, S. Kalaiselvam, S. Iniyan, and R. Goic Phase change characteristic study of spherical PCMs in solar energy storage Solar Energy 83 2009 1245 1252
97. I.W. Eames, and K.T. Adref Freezing and melting of water in spherical enclosures of the type used in thermal (ice) storage systems Appl Therm Eng 22 2002 733 745
98. A.F. Regin, S.C. Solanki, and J.S. Saini Experimental and numerical analysis of melting of PCM inside a spherical capsule Proceedings of the 9th AIAA/ASME joint thermophysics and heat transfer conference (CD ROM). Paper AIAA 2006-3618 San Francisco, CA 2006 12
99. G. Poots On the application of integral methods to the solution of problems involving the solidification of liquid initially at fusion temperature Int J Heat Mass Transfer 5 1962 525 531
100. Beckett PM. Ph.D. thesis. England: Hull University; 1971.
101. D.N. de, G. Allen, and R.T. Severn The application of the relaxation method to the solution of non-elliptic partial differential equations Q J Mech Appl Math 15 1962 53
102. L.C. Tao Generalized numerical solutions of freezing a saturated liquid in cylinders and spheres AIChE J 13 1 1967 165
103. D.S. Riley, F.I. Smith, and G. Poots The inward solidification of spheres and circular cylinders Int J Heat Mass Transfer 17 1974 1507 1516
104. V.J. Lunardini Heat transfer in cold climates 1981 Van Nostrand Reinhold Co. New York [Chapter 8]
105. V.R. Voller, and M. Cross Estimating the solidification/melting times of cylindrically symmetric regions Int J Heat Mass Transfer 24 9 1981 1457 1462
106. V. Shatikian, G. Ziskind, and R. Letan Numerical investigation of a PCM-based heat sink with internal fins Int J Heat Mass Transfer 48 2005 3689 3706
107. L. Katsman Melting and solidification of a phase-change material (PCM), Graduation Project 16-04 June 2004 Heat Transfer Laboratory, Department of Mechanical Engineering, Ben-Gurion University of the Negev
108. E. Assis, L. Katsman, G. Ziskind, and R. Letan Experimental and numerical investigation of phase change in a spherical enclosure Proceedings of the fourth European thermal sciences conference Birmingham, UK March 2004
109. F.L. Tan Constrained and unconstrained melting inside a sphere Int Commun Heat Mass Transfer 35 2008 466 475
110. F.L. Tan, S.F. Hosseinizadeh, J.M. Khodadadi, and L. Fan Experimental and computational study of constrained melting of phase change materials (PCM) inside a spherical capsule Int J Heat Mass Transfer 52 2009 3464 3472
111. A. Trp An experimental and numerical investigation of heat transfer during technical grade paraffin melting and solidification in a shell-and-tube latent thermal energy storage unit Solar Energy 79 2005 648 660
112. A. Trp, K. Lenic, and B. Frankovic Analysis of the influence of operating conditions and geometric parameters on heat transfer in water-paraffin shell-and-tube latent thermal energy storage unit Int J Heat Mass Transfer 50 9-10 2007 1790 1804
113. Z.X. Gong, and A.S. Mujumdar Finite-element analysis of cyclic heat transfer in a shell-and-tube latent heat energy storage exchanger Appl Therm Eng 17 6 1997 583 591
114. H. El-Dessouky, and F. Al-Juwayhel Effectiveness of a thermal energy storage system using phase-change materials Energy Convers Manage 38 6 1997 601 617
115. J. Prakash, H.P. Garg, and G. Datta A solar water heater with a built-in latent heat storage Energy Convers Manage 25 1 1985 51 56
116. N.K. Bansa, and D. Buddhi An analytical study of a latent heat storage system in a cylinder Energy Convers Manage 33 4 1982 235 242
117. M.M. Farid Solar energy storage with phase change J Solar Energy Res 4 1986 11 29
118. M.M. Farid, and A. Kanzawa Thermal performance of a heat storage module using PCM's with different melting temperatures: mathematical modeling Trans ASME, J Solar Energy Eng 111 1989 152 157
119. M.M. Farid, Y. Kim, and A. Kanzawa Thermal performance of heat storage module using PCM's with different melting temperatures: experimental Trans ASME, J Solar Energy Eng 112 1990 125 131
120. B.J. Jones, D. Sun, S. Krishnan, and S.V. Garimella Experimental and numerical study of melting in a cylinder Int J Heat Mass Transfer 49 2006 2724 2738
121. M. Esen, and T. Ayhan Development of a model compatible with solar assisted cylindrical energy storage tank and variation of stored energy with time for different phase change materials Energy Convers Manage 37 12 1996 1775 1785
122. H. Visser Energy storage in phase-change materials-development of a component model compatible with TRNSYS, Final report, Contract no. 2462-84-09 ED ISPNL 1986 Delft University of Technology, Department of Applied Physics Delft
123. Esen M. Numerical simulation of cylindrical energy storage tank containing phase change material on the solar assisted heat pump system and comparing with experimental results. Doctoral thesis. Turkey: Department of Mechanical Engineering, Karadeniz Technical University, Trabzon; 1994.
124. L. Jian-you Numerical and experimental investigation for heat transfer in triplex concentric tube with phase change material for thermal energy storage Solar Energy 82 2008 977 985
125. T. Saitoh, and K. Hirose High-performance of phase change thermal energy storage using spherical capsules Chem Eng Commun 41 1986 39 58
126. Y. Zhang, Su Yan, Y. Zhu, and X. Hu A General model for analyzing the thermal performance of the heat charging and discharging process of latent heat thermal energy storage systems Trans ASME, J Sol Energy Eng 123 2001 232 236
127. C.K. Jotshi, D.Y. Goswami, and J.J. Tomilnson Proceedings of the 1992 ASES annual conference USA 1992
128. H.P. Garg, A.C. Mullick, and A.K. Bhargava Solar thermal energy storage 1985 D. Reidel Publishing Company Dordrecht p. 241-2
129. R. Naumann, and H.H. Emons Results of thermal analysis for investigation of salt hydrates as latent heat-storage materials J Therm Anal 35 1989 1009 1031
130. A. Benmansour, M.A. Hamdan, and A. Bengeuddach Experimental and numerical investigation of solid particles thermal energy storage unit Appl Therm Eng 26 5-6 2006 513 518
131. J.P. Dumas, J.P. Bédécarrats, F. Strub, and B. Falcon Modelization of a tank filled with spherical nodules containing a phase change material Proceedings of the 10th international heat transfer conference, vol. 7 Brighton 1994 239 244
132. J.P. Bédécarrats, F. Strub, B. Falcon, and J.P. Dumas Experimental and numerical analysis of the supercooling in a phase-change energy storage Proceedings of the 19th international congress of refrigeration, vol. IIIa The Hague, The Netherlands, August 20-25 1995 46 53
133. J.P. Bédécarrats, and J.P. Dumas Study of the crystallization of nodules containing a phase change material for cool thermal storage Int J Heat Mass Transfer 40 1 1997 149 157 [in French]
134. T. Kousksou, J.P. Bédécarrats, J.P. Dumas, and A. Mimet Dynamic modeling of the storage of an encapsulated ice tank Appl Therm Eng 25 2005 1534 1548
135. T. Kousksou, J.P. Bédécarrats, F. Strub, and J. Castaing-Lasvignottes Numerical simulation of fluid flow and heat transfer in a phase change thermal energy storage Int J Energy Technol Policy 6 1/2 2008 143 158
136. J.P. Bédécarrats, J. Castaing-Lasvignottes, F. Strub, and J.P. Dumas Study of a phase change energy storage using spherical capsules. Part I: Experimental results Energy Convers Manage 50 2009 2527 2536
137. J.P. Bédécarrats, J. Castaing-Lasvignottes, F. Strub, and J.P. Dumas Study of a phase change energy storage using spherical capsules. Part II: Numerical modelling Energy Convers Manage 50 2009 2537 2546
138. M. Cheralathan, R. Velraj, and S. Renganarayanan Effect of porosity and the inlet heat transfer fluid temperature variation on the performance of cool thermal energy storage system Heat Mass Transfer 43 2007 833 842
139. C. Arkar, and S. Medved Influence of accuracy of thermal property data of a phase change material on the result of a numerical model of a packed bed latent heat storage with spheres Thermochim Acta 438 1-2 2005 192 201
140. J. Wei, Y. Kawaguchi, S. Hirano, and H. Takeuchi Study on a PCM heat storage system for rapid heat supply Appl Therm Eng 25 2005 2903 2920
141. R.V. Seeniraj, and N. Lakshmi Narasimhan The thermal response of a cold LHTS unit with heat leak through side walls Int Commun Heat Mass Transfer 32 2005 1375 1386
142. K.A.R. Ismail, and J.R. Henriquez Numerical and experimental study of spherical capsules packed bed latent heat storage system Appl Therm Eng 22 2002 1705 1716
143. K.A.R. Ismail, and R. Stuginsky A parametric study on possible fixed bed models for PCM and sensible heat storage Appl Therm Eng 19 1999 757 788
144. S.L. Chen One dimensional analysis of energy storage in packed capsules ASME J Sol Energy Eng 114 1992 127 130
145. S.L. Chen, and J.S. Yue A simplified analysis for cold storage in porous capsules with solidification ASME J Energy Resour Technol 113 1991 108 116
146. L.C.C. Goncalves, and S.D. Probert Thermal energy storage: dynamic performance characteristics of cans each containing a phase change material, assembled as a packed bed Appl Energy 45 1993 117 155
147. G.A. Adebiyi, E.C. Nsofor, W.G. Steele, and A.A. Jalalzadeh-Azar Parametric study on the operating efficiencies of a packed bed for high-temperature sensible heat storage J Solar Energy Eng 120 1 1998 2 13
148. J. Yagi, and T. Akiyama Storage of thermal energy for effective use of waste heat from industries J Mater Process Technol 48 1995 793 804
149. T. Watanabe, and A. Kanzava Second law optimization of a latent heat storage system with PCMs having different melting points Heat Recov Syst CHP 15 7 1995 641 653
150. T. Watanabe, H. Hikuchi, and A. Kanzawa Enhancement of charging and discharging rates in a latent heat storage system by use of PCM with different melting temperature Heat Recov Syst CHP 13 1 1993 57 66
151. D. MacPhee, and I. Dincer Thermodynamic analysis of freezing and melting processes in a bed of spherical PCM capsules J Solar Energy Eng 131 2009 031017-1
152. D. MacPhee, and I. Dincer Thermal modeling of a packed bed thermal energy storage system during charging Appl Therm Eng 29 2009 695 705
153. K. Sasaguchi, M. Yoshida, and S. Nakashima Heat transfer characteristics of a latent heat thermal energy storage unit with a finned tube: effect of fin configuration Heat Transfer-Jpn Res 19 1 1990 11 27
154. K. Sasaguchi Heat-transfer characteristics of a latent heat thermal energy storage unit with a finned tube Heat Transfer-Jpn Res 19 7 1990 619 637
155. M. Lacroix Study of the heat transfer behavior of a latent heat thermal energy storage unit with a finned tube Int J Heat Mass Transfer 36 8 1993 2083 2092 (Pubitemid 23672046)
156. M. Lacroix, and M. Benmadda Numer Heat Transfer, Part A: Appl 31 1 1997 71 86
157. Y. Zhang, and A. Faghri Heat transfer enhancement in latent heat thermal energy storage system by using an external radial finned tube J Enhance Heat Transfer 3 2 1996 119 127 (Pubitemid 126606942)
158. R. Velraj, R.V. Seeniraj, B. Hafner, C. Faber, and K. Schwarzer Experimental analysis and numerical modelling of inward solidification on a finned vertical tube for a latent heat storage unit Solar Energy 60 5 1997 281 290
159. A.W. Date Novel strongly implicit enthalpy formulation for multidimensional Stefan problems Numer Heat Transfer, Part B 21 1992 231 251
160. R. Velraj, and R.V. Seeniraj Heat transfer studies during solidification of PCM inside an internally finned tube J Heat Transfer 121 1999 493 497
161. R.V. Seeniraj, R. Velraj, and N. Lakshmi Narasimhan Thermal analysis of a finned-tube LHTS module for a solar dynamic power system Heat Mass Transfer 38 4-5 2002 409 417
162. Lamberg P. Mathematical modelling and experimental investigation of melting and solidification in a finned phase change material storage. Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Department of Mechanical Engineering, Helsinki University of Technology; 2003.
163. P. Lamberg, and K. Sirén Analytical model for melting in a semi-infinite PCM storage with an internal fin Heat Mass Transfer 39 2003 167 176
164. P. Lamberg, and K. Sirén Approximate analytical model for solidification in a finite PCM storage with internal fins Appl Math Model 27 2003 491 513
165. P. Lamberg Approximate analytical model for two-phase solidification problem in a finned phase-change material storage Appl Energy 77 2004 131 152
166. A. Castell, C. Solé, M. Medrano, J. Roca, D. García, and L.F. Cabeza Effect of using external vertical fins in phase change material modules for domestic hot water tanks International conference on renewable energies and power quality (ICREPQ'06) Palma de Mallorca 2006
167. H. Mehling, L.F. Cabeza, S. Hippeli, and S. Hiebler PCM module to improve hot water heat stores with stratification Renew Energy 28 2003 699 711
168. L.F. Cabeza, M. Nogues, J. Roca, J. Illa, S. Hiebler, and H. Mehling PCM-module to improve hot water heat stores with stratification: first tests in a complete solar system R. Dománski, M. Jaworski, M. Rebow, 9th international conference on thermal energy storage, vol. 1 2003 Institute of Heat Engineering 273 278
169. K.S. Reddy Thermal modeling of PCM-based solar integrated collector storage water heating system J Solar Energy Eng 129 2007 458 464
170. M. Gharebaghi, and I. Sezai Enhancement of heat transfer in latent heat storage modules with internal fins Numer Heat Transfer, Part A 53 2008 749 765
171. K.A.R. Ismail, J.R. Henríquez, L.F.M. Moura, and M.M. Ganzarolli Ice formation around isothermal radial finned tubes Energy Convers Manage 41 2000 585 605
172. K.A.R. Ismail, C.L.F. Alves, and M.S. Modesto Numerical and experimental study on the solidification of PCM around a vertical axially finned isothermal cylinder Appl Therm Eng 21 2001 53 77
173. N. Kayansayan, and M. Ali Acar Ice formation around a finned-tube heat exchanger for cold thermal energy storage Int J Therm Sci 45 2006 405 418
174. R. Akhilesh, A. Narasimhan, and C. Balaji Method to improve geometry for heat transfer enhancement in PCM composite heat sinks Int J Heat Mass Transfer 48 2005 2759 2770
175. V. Shatikian, G. Ziskind, and R. Letan Numerical investigation of a PCM-based heat sink with internal fins: constant heat flux Int J Heat Mass Transfer 51 2008 1488 1493
176. V. Shatikian, G. Ziskind, and R. Letan Heat accumulation in a PCM-based heat sink with internal fins 5th European thermal-sciences conference The Netherlands 2008
177. I. Běhunek, and P. Fiala Phase change materials for thermal management of IC packages Radioengineering 16 2 2007 50 55
178. K.C. Nayak, S.K. Saha, K. Srinivasan, and P. Dutta A numerical model for heat sinks with phase change materials and thermal conductivity enhancers Int J Heat Mass Transfer 49 11-12 2006 1833 1844
179. S.K. Saha, K. Srinivasan, and P. Dutta Studies on optimum distribution of fins in heat sinks filled with phase change materials J Heat Transfer 130 2008 034505-1
180. R. Kandasamy, X. Wang, and A.S. Mujumdar Transient cooling of electronics using phase change material(PCM)-based heat sinks Appl Therm Eng 28 2008 1047 1057
181. C. Hirt, and B. Nichols Volume of fluid (VOF) method for the dynamics of free boundaries J Comput Phys 39 1981 201
182. X. Wang, A.S. Mujumdar, and C. Yap Effect of orientation for phase change material (PCM)-based heat sinks for transient thermal management of electric components Int Commun Heat Mass Transfer 34 2007 801 808
183. A. Wang, X. Liang, and J. Ren Constructal enhancement of heat conduction with phase change Int J Thermophys 27 1 2006 126 138
184. H.F. Erk, and M.P. Dudukovic Phase-change heat regenerators: modeling and experimental studies AIChE J 42 3 1996 791 808
185. O. Mesalhy, K. Lafdi, and A. Elgafy Carbon foam impregnated with phase change material (PCM) as a thermal barrier Proceeding of the conference of the American Carbon Society 2004 Brown University Providence, RI
186. O. Mesalhy, K. Lafdi, A. Elgafy, and K. Bowman Numerical study for enhancing the thermal conductivity of phase change material (PCM) storage using high thermal conductivity porous matrix Energy Convers Manage 46 2005 847 867
187. K. Lafdi, O. Mesalhy, and A. Elgafy Graphite foams infiltrated with phase change materials as alternative materials for space and terrestrial thermal energy storage applications Carbon 46 2008 159 168
188. D.B. Khillarkar, Z.X. Going, and A.S. Mujumdar Melting of a phase change material in concentric horizontal annuli of arbitrary cross-section Appl Therm Sci 20 2000 893 912
189. J. Fukai, Y. Hamada, Y. Morozumi, and O. Miyatake Effect of carbon-fiber brushes on conductive heat transfer in phase change materials Int J Heat Mass Transfer 45 2002 4781 4792
190. J. Fukai, Y. Hamada, Y. Morozumi, and O. Miyatake Improvement of thermal characteristics of latent heat thermal energy storage units using carbon-fiber brushes: experiments and modeling Int J Heat Mass Transfer 46 2003 4513 4525
191. Y. Hamada, W. Ohtsu, and J. Fukai Thermal response in thermal energy storage material around heat transfer tubes: effect of additives on heat transfer rates Solar Energy 75 2003 317 328
192. A. Elgafy, and K. Lafdi Effect of carbon nanofiber additives on thermal behaviour of phase change materials Carbon 43 2005 3067 3074
193. K. Lafdi, and M. Matzek Effect of nanofiber surface functionalization in carbon nano-fiber based nanocomposites systems Proceedings of 35th international SAMPE technical conference, Carbon nanomaterials session, vol. 35 Dayton, OH, USA 2003 p. 1
194. F. Frusteri, V. Leonardi, and G. Maggio Numerical approach to describe the phase change of an inorganic PCM containing carbon fibres Appl Therm Eng 26 2006 1883 1892
195. Zhang P, Ma ZW, Wang RZ. An overview of phase change material slurries: MPCS and CHS. Renew Sust Energy Rev; in press.
196. P. Charunyakorn, S. Sengupta, and S.K. Roy Forced convective heat transfer in microencapsulated phase change material slurries: flow in circular ducts Int J Heat Mass Transfer 34 3 1991 819 833
197. Y. Zhang, and A. Faghri Analysis of forced convection heat transfer in microencapsulated phase change material suspensions J Thermophys Heat Transfer 9 4 1995 727 732
198. M. Goel, S.K. Roy, and S. Sengupta Laminar forced convection heat transfer in microencapsulated phase change material suspensions Int J Heat Mass Transfer 37 4 1994 593 604
199. Alisetti EL. Forced convection heat transfer to phase change material slurries in circular ducts. Ph.D. thesis. University of Miami, Dpt of Mech Eng; 1998.
200. E.L. Alisetti, and S.K. Roy Forced convection heat transfer to phase change material slurries in circular ducts J Thermophys Heat Transfer 14 2000 115 118
201. S.K. Roy, and B.L. Avanic Turbulent heat transfer with phase change material suspensions Int J Heat Mass Transfer 44 12 2001 2277 2285
202. X. Hu, and Y. Zhang Novel insight and numerical analysis of convective heat transfer enhancement with microencapsulated phase change material slurries: laminar flow in a circular tube with constant heat flux Int J Heat Mass Transfer 45 2002 3163 3172
203. Y.L. Hao, and Y.-X. Tao A numerical model for phase-change suspension flow in microchannels Numer Heat Transfer, Part A 46 2004 55 77
204. K.Q. Xing, Y.-X. Tao, and Y.L. Hao Performance evaluation of liquid flow with PCM particles in microchannels ASME J Heat Transfer 127 2005 931 940
205. C.J. Ho, J.F. Lin, and S.Y. Chiu Heat transfer of solid-liquid phasechange material suspensions in circular pipes: effects of wall conduction Numer Heat Transfer, Part A 45 2004 171 190
206. H. Inaba, C. Dai, and A. Horibe Numerical simulation of Rayleigh-Bénard convection in non-Newtonian phase change-material slurry Int J Therm Sci 42 2003 471 480
207. H. Inaba, Y. Zhang, A. Horibe, and N. Haruki Numerical simulation of natural convection of latent heat phase-change-material microcapsulate slurry packed in a horizontal rectangular enclosure heated from below and cooled from above Heat Mass Transfer 43 2007 459 470
208. Cassidy D. Numerical and experimental investigations of mixed convection in solid-liquid flow for MicroPCM applications. Ph.D. thesis. North Carolina State University; 2008.
209. L. Royon, and G. Guiffant Forced convection heat transfer with slurry of phase change material in circular ducts: a phenomenological approach Energy Convers Manage 49 2008 928 932
210. R. Sabbah, M.M. Farid, and Said Al-Hallaj Micro-channel heat sink with slurry of water with micro-encapsulated phase change material: 3D-numerical study Appl Therm Eng 29 2008 445 454
211. S. Kuravi, K.M. Kota, J. Du, and L.C. Chow Numerical investigation of flow and heat transfer performance of nano-encapsulated phase change material slurry in microchannels J Heat Transfer 131 2009 062901-1
212. Y. Zhang, X. Hu, and X. Wang Theoretical analysis of convective heat transfer enhancement of microencapsulated phase change material slurries Heat Mass Transfer 40 2003 59 66
213. R. Zeng, X. Wang, B. Chen, Y. Zhang, J. Niu, and X. Wang Heat transfer characteristics of microencapsulated phase change material slurry in laminar flow under constant heat flux Appl Energy 86 2009 2661 2670
214. D. Sun, S.R. Annapragada, and S.V. Garimella Experimental and numerical study of melting of particle-laden materials in a cylinder Int J Heat Mass Transfer 52 13-14 2009 2966 2978
215. W. Yueng Engineering analysis of heat transfer during melting in vertical rectangular enclosures Int J Heat Mass Transfer 32 1989 689 696
216. B. Webb, and R. Viskanta Analysis of heat transfer during melting of a pure metal from an isothermal vertical wall Numer Heat Transfer 9 1986 539 558
217. V.R. Voller Numer Heat Transfer, Part B 17 1990 155
218. L. Goodrich Int J Heat Mass Transfer 21 1978 615
219. Zalba B. Thermal energy storage with phase change. Experimental procedure. Ph.D. thesis. University of Zaragoza; 2002.
220. W.R. Humphries, and E.L. Griggs A design handbook for phase change thermal control and energy-storage devices. NASA Technical Paper 1977 p. 1074
221. L.R. Mack, and M.C. Hardee Natural convection between concentric spheres at low Rayleigh numbers Int J Heat Mass Transfer 11 1968 387 396
222. P.A. Bahrami, and T.G. Wang Analysis of gravity and conduction driven melting in a sphere ASME J Heat Transfer 19 1987 806 809
223. H. Hoshina, and T.S. Saitoh Numerical simulation on combined close-contact and natural convection melting in thermal energy storage spherical capsule Proceedings of the 34th national heat transfer symposium of Japan Sendai 1997 721 722
224. Yamada K. Numerical simulation of the latent heat thermal energy storage tank. Master thesis. Supervised by T.S. Saitoh, Tohoku University; 1997.
225. Esen M. Numerical simulation of cylindrical energy storage tank containing phase change material on the solar assisted heat pump system and comparing with experimental results. Ph.D. thesis. Trabzon, Turkey: Dept. of Mechanical Engineering, Karadeniz Technical University; 1994.
226. Y. Zhu, Y. Zhang, Y. Jiang, and Y. Kang Thermal storage and heat transfer in phase change material outside a circular tube with axial variation of the heat transfer fluid temperature ASME J Solar Energy Eng 121 1999 145 149
227. Y. Kang, Y. Zhang, Y. Jiang, and Y. Zhu A general model for analyzing the thermal characteristics of a class of latent heat thermal energy storage systems ASME J Solar Energy Eng 121 4 1999 185 193
228. Y. Kang, Y. Zhang, and Y. Jiang Simplified model for the heat transfer analysis of shell-and-tube with phase change material and its performance simulation Acta Energy Solaris Sinica 20 1 1999 20 25 [in Chinese]
229. Y. Kang, Y. Zhang, Y. Jiang, and Y. Zhu Analysis and theoretical model for the heat transfer characteristics of latent heat storage spherical packed bed J Tsinghua Univ 40 2 2000 106 109 [in Chinese]
230. Y. Jiang, Y. Zhang, and Y. Kang Heat transfer criterion of plate thermal storage systems J Tsinghua Univ 39 11 1999 86 89 [in Chinese]
231. J.P. Bédécarrats, F. Strub, B. Falcon, and J.P. Dumas Phase change thermal energy storage using spherical capsules: performance of a test plant Int J Refrig 19 1996 187 196
232. Y. Zhang, and A. Faghri Analytical solution of thermal energy storage system with conjugate laminar forced convection lnt J Heat Mass Transfer 39 4 1996 717 724
233. W.M. Kays, and M.W. Crawford Convective heat and mass transfer 2nd ed. 1980 McGraw-Hill New York
234. Y. Cao, and F. Faghi Performance characteristics of a thermal energy storage module Int J Heat Mass Transfer 36 1991 3851 3857
235. A. Castell Natural convection heat transfer coefficients in phase change material (PCM) modules with external vertical fins Appl Therm Eng 28 2008 1676 1686
236. A. Bejan Heat transfer 1993 John Wiley & Sons, Inc. New York
237. A.S. Ahuja Augmentation of heat transport in laminar flow of polystyrene suspensions: Part I J Appl Phys 46 8 1975 3408 3416
238. B.S. Petukhov Heat transfer and friction in turbulent pipe flow with variable physical properties J.P. Hartnett, T.F. Irvine jr. Advances in heat transfer vol. 6 1970 Academic Press New York 503 564
239. E.M. Sparrow, T.M. Hallman, and R. Siegel Turbulent Heat transfer in the thermal entrance region of a pie with uniform heat flux Appl Sci Res, Ser A 7 1957 37 52
240. J.P. Hartnett Experimental determination of thermal entrance length flow of water and of oil in a circular pipes Trans ASME 77 1955 1120 1211
241. Choi E. Forced convection heat transfer with water and phase-change material slurries: turbulent flow in a circular tube. Ph.D. thesis. PA: Drexel University; 1993.
242. E. Choi, Y.I. Cho, and H.G. Lorsch Forced convection heat transfer with phase change material slurries: turbulent flow in a circular tube Int J Heat Mass Transfer 17 1994 207 215
243. G. de Vahl Davis, and I.P. Jones Natural convection in a square cavity: a comparison exercise Int J Numer Methods Fluids 3 1983 227 248
244. H. Ozoe, and S.W. Churchill Hydrodynamic stability and natural convection in Ostwald-de Waele and Ellis fluids: the development of a numerical solution AIChE J 18 6 1972 1196 1206
245. R.B. Bird, W.E. Stewart, and E.N. Lightfoot Transport phenomena 1960 John Wiley & Sons New York
246. Gau C. Heat transfer during solid-liquid phase transformation of metals in rectangular cavities. Thesis. Purdue University; 1984.
247. C. Gau, and R. Viskanta Melting and solidification of a pure metal on a vertical wall J Heat Transfer 108 1986 174 181
248. F. Wolff, and R. Viskanta Melting of a pure metal from a vertical wall Exp Heat Transfer 1 1987 17 30
249. Ho CJ. Solid liquid phase change heat transfer in enclosures. Thesis. Purdue University; 1982.
250. C.J. Ho, and R. Viskanta Heat transfer during melting from an isothermal vertical wall J Heat Transfer 12 1984 12 19 (Pubitemid 14526174)
251. V. Voller, and C. Prakash A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems Int J Heat Mass Transfer 30 1987 1709 1719
252. G.A. Lane Solar heat storage: phase change material, vol. 1. Background and scientific principles 1986 CRC Press Boca Raton, FL, USA p. 163
253. K. Ahmet, A. Ozmerzi, and S. Bilgin Thermal performance of a water-phase change material solar collector Renew Energy 26 3 2002 391 399