Skip to main content
SpringerLink
Log in

Numerical method and model for calculating thermal storage time for an annular tube with phase change material

  • Published:
Journal of Central South University Aims and scope Submit manuscript

Abstract

For calculating the thermal storage time for an annular tube with phase change material (PCM), a novel method is proposed. The method is suitable for either low-temperature PCM or high-temperature PCM whose initial temperature is near the melting point. The deviation fit is smaller than 8% when the time is below 2×104 s. Comparison between the predictions and the reported experimental data of thermal storage time at same conditions is investigated and good agreements have been got. Based on this method, the performance of the thermal storage unit and the role of natural convection are also investigated. Results show a linear relation between the maximum amount of stored heat and thermal storage time, and their ratio increases with the height of the thermal storage unit. As the thickness of the cavity increases, natural convection plays an increasingly important role in promoting the melting behavior of paraffin. When the thickness of the cavity is small, natural convection restrains the melting behavior of paraffin.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. TYAGI V V, KAUSHIK S C, TYAGI S K, AKIYAMA T. Development of phase change materials based microencapsulated technology for buildings: A review [J]. Renewable & Sustainable Energy Reviews, 2011, 15(2): 1373–1391.

    Article  Google Scholar 

  2. KENISARIN M M. High-temperature phase change materials for thermal energy storage [J]. Renewable & Sustainable Energy Reviews, 2010, 14(3): 955–970.

    Article  Google Scholar 

  3. ZHANG Xue-lai, YU Shu-xuan, YU Mei, LIN Yuan-pei. Experimental research on condensing heat recovery using phase change material [J]. Applied Thermal Engineering, 2011, 31: 3736–3740.

    Article  Google Scholar 

  4. FENG Guo-hui, CHEN Qi-zhen, HUANG Kai-liang, NIU Run-ping, WANG Lin. Cool storage time of phase change wallboard room in summer [J]. Journal of Central South University of Technology, 2009, 16(12): 75–79.

    Google Scholar 

  5. ZHAO Fang, CHEN Zhen-qian, SHI Ming-heng. Numerical study on freezing-thawing phase change heat transfer in biological tissue embedded with two cryoprobes [J]. Journal of Central South University of Technology, 2009, 16(2): 326–331.

    Article  Google Scholar 

  6. AADMI M, KARKRI M, HAMMOUTI M E. Heat transfer characteristics of thermal energy storage of a composite phase change materials: Numerical and experimental investigations [J]. Energy, 2014, 72(7): 381–392.

    Article  Google Scholar 

  7. HUANG Kai-liang, FENG Guo-hui, ZHANG Jian-shun. Experimental and numerical study on phase change material floor in solar water heating system with a new design [J]. Solar Energy, 2014, 105: 126–138.

    Article  Google Scholar 

  8. SUN Xiao-qin, ZHANG Quan, MEDINA M A, KYOUNG O L. Energy and economic analysis of a building enclosure outfitted with a phase change material board (PCMB) [J]. Energy Conversion & Management, 2014, 83: 73–78.

    Article  Google Scholar 

  9. DUTIL Y, ROUSSE D R, SALAH N B, LASSUE S, ZALEWSKI L. A review on phase-change materials: Mathematical modeling and simulations [J]. Renewable & Sustainable Energy Reviews, 2011, 15(1): 112–130.

    Article  Google Scholar 

  10. MA Zhan-hua, ZHANG Yu-wen. Solid velocity correction schemes for a temperature transforming model for convection phase change [J]. International Journal of Numerical Methods for Heat & Fluid Flow, 2006, 16(2): 204–225.

    Article  Google Scholar 

  11. CAO Y, FAGHRI A. A numerical analysis of phase-change problems including natural convection [J]. Journal of Heat Transfer, 1990, 112, 3(3): 812–816.

    Article  Google Scholar 

  12. VOLLER V R, CROSS M, MARKATOS N C. An enthalpy method for convection/diffusion phase change [J]. International Journal for Numerical Methods in Engineering, 1987, 24(1): 271–284.

    Article  MATH  Google Scholar 

  13. GARTLING D K. Finite element analysis of convective heat transfer problems with change of phase [C]// Conference on Numerical Methods in Laminar and Turbulent Flow, Swansea, UK: NMLTF, 1978.

    Google Scholar 

  14. BINET B, LACROIX M. Melting from heat sources flush mounted on a conducting vertical wall [J]. International Journal of Numerical Methods for Heat & Fluid Flow, 2000, 10(3): 286–307.

    Article  MATH  Google Scholar 

  15. VOLLER V R. An overview of numerical methods for solving phase change problems [J]. Advances in Numerical Heat Transfer, 1997, 1(9): 341–380.

    Google Scholar 

  16. KOZAK Y, ROZENFELD T, ZISKIND G. Close-contact melting in vertical annular enclosures with a non-isothermal base: Theoretical modeling and application to thermal storage [J]. International Journal of Heat & Mass Transfer, 2014, 72(3): 114–127.

    Article  Google Scholar 

  17. AGYENIM F, EAMES P, SMYTH M. Experimental study on the melting and solidification behaviour of a medium temperature phase change storage material (Erythritol) system augmented with fins to power a LiBr/H2O absorption cooling system [J]. Renewable Energy, 2011, 36(1): 108–117.

    Article  Google Scholar 

  18. LIU Chang, GROULX D. Experimental study of the phase change heat transfer inside a horizontal cylindrical latent heat energy storage system [J]. International Journal of Thermal Sciences, 2014, 82: 100–110.

    Article  Google Scholar 

  19. MESALHY O, LAFDI K, ELGAFY A, BOWMAN K. Numerical study for enhancing the thermal conductivity of phase change material (PCM) storage using high thermal conductivity porous matrix [J]. Energy Conversion & Management, 2005, 46(6): 847–867.

    Article  Google Scholar 

  20. SHARIFI N, BERGMAN T L, ALLEN M J, FAGHRI A. Melting and solidification enhancement using a combined heat pipe, foil approach [J]. International Journal of Heat & Mass Transfer, 2014, 78: 930–941.

    Article  Google Scholar 

  21. ALLEN M J, SHARIFI N, FAGHRI A, BERGMAN T L. Effect of inclination angle during melting and solidification of a phase change material using a combined heat pipe-metal foam or foil configuration [J]. International Journal of Heat & Mass Transfer, 2015, 80: 767–780.

    Article  Google Scholar 

  22. SARI A, KAYGUSUZ K. Thermal performance of palmitic acid as a phase change energy storage material [J]. Energy Conversion & Management, 2002, 43(6): 863–876.

    Article  Google Scholar 

  23. TRP A. An experimental and numerical investigation of heat transfer during technical grade paraffin melting and solidification in a shelland-tube latent thermal energy storage unit [J]. Solar Energy, 2005, 79(6): 648–660.

    Article  Google Scholar 

  24. ANISUR M R, KIBRIA M A, MAHFUZ M H, SAIDUR R, MESTSELAAR I H S C. Cooling of air using heptadecane phase change material in shell and tube arrangement: Analytical and experimental study [J]. Energy & Buildings, 2014, 85: 98–106.

    Article  Google Scholar 

  25. LIU Zhen-yu, YAO Yuan-peng, WU Hui-ying. Numerical modeling for solid–liquid phase change phenomena in porous media: Shell-and-tube type latent heat thermal energy storage [J]. Applied Energy, 2013, 112: 1222–1232.

    Article  Google Scholar 

  26. LAFDI K, MESALHY O, ELGAFY A. Graphite foams infiltrated with phase change materials as alternative materials for space and terrestrial thermal energy storage applications [J]. Carbon, 2008, 46(1): 159–168.

    Article  Google Scholar 

  27. SUN Xiao-qin, ZHANG Quan, MEDINA M A, KYOUNG O L. Experimental observations on the heat transfer enhancement caused by natural convection during melting of solid–liquid phase change materials (PCMs) [J]. Applied Energy, 2015.

    Google Scholar 

  28. TAN F L, HOSSEINIZADEH S F, KHODADADI J M, FAN L. Experimental and computational study of constrained melting of phase change materials (PCM) inside a spherical capsule [J]. International Journal of Heat & Mass Transfer, 2009, 52: 3464–3472.

    Article  MATH  Google Scholar 

  29. LONGEON M, SOUPART A, BRUCH A. Experimental and numerical study of annular PCM storage in the presence of natural convection [J]. Applied Energy, 2013, 112(4): 175–184.

    Article  Google Scholar 

  30. KHILLARKAR D B, GONG Z X, MUJUMDAR A S. Melting of a phase change material in concentric horizontal annuli of arbitrary cross-section [J]. Applied Thermal Engineering, 2000, 20(10): 893–912.

    Article  Google Scholar 

  31. MAHDAOUI M, KOUSKSOU T, BLANCHER S, MSSAD A A, RHAFIKI T E, MOUQALLID M. A numerical analysis of solid–liquid phase change heat transfer around a horizontal cylinder [J]. Applied Mathematical Modelling, 2014, 38(3): 1101–1110.

    Article  MathSciNet  Google Scholar 

  32. HOSSEINIZADEH S F, DARZI A A R, TAN F L. Numerical investigations of unconstrained melting of nano-enhanced phase change material (Nepcm) inside a spherical container [J]. International Journal of Thermal Sciences, 2012, 51(4): 77–83.

    Article  Google Scholar 

  33. ZHUO Cong-shan, ZHONG Cheng-wen. LES-based filter-matrix lattice Boltzmann model for simulating turbulent natural convection in a square cavity [J]. International Journal of Heat & Fluid Flow, 2013, 42(4): 10–22.

    Article  Google Scholar 

  34. WANG Jun. Regenerative experimental and theoretical study of the melting wax [D]. Xi’an: Xi’an Jiaotong University, 2002. (in Chinese)

    Google Scholar 

  35. LORENTE S, BEJAN A, NIU J L. Phase change heat storage in an enclosure with vertical pipe in the center [J]. International Journal of Heat & Mass Transfer, 2014, 72(3): 329–335.

    Article  Google Scholar 

  36. BRENT A D, VOLLER V R, REID K J. Enthalpy-porosity technique for modeling convection-diffusion phase change: Application to the melting of a pure metal [J]. Numerical Heat Transfer Applications, 1988, 13(3): 297–318.

    Google Scholar 

  37. VOLLER V R, PRAKASH C. A fixed grid numerical modelling methodology for convection-diffusion mushy region phase-change problems [J]. International Journal of Heat & Mass Transfer, 1987, 30(87): 1709–1719.

    Article  Google Scholar 

  38. SHOKOUHMAND H, KAMKARI B. Experimental investigation on melting heat transfer characteristics of lauric acid in a rectangular thermal storage unit [J]. Experimental Thermal & Fluid Science, 2013, 50(6): 201–212.

    Article  Google Scholar 

  39. PAL D, JOSHI Y K. Melting in a side heated tall enclosure by a uniformly dissipating heat source [J]. International Journal of Heat & Mass Transfer, 2000, 44(2): 375–387.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Complex Nonferrous Metal Resources Clean Utilization, Kunming University of Science and Technology, Kunming, 650093, China

    Fan-han Liu  (刘泛函), Jian-xin Xu  (徐建新) & Hua Wang  (王华)

  2. Faculty of Metallurgical and Energy Engineering, Kunming University of Science and Technology, Kunming, 650093, China

    Fan-han Liu  (刘泛函), Hui-tao Wang  (王辉涛) & Hua Wang  (王华)

  3. Quality Development Institure, Kunming University of Science and Technology, Kunming, 650093, China

    Jian-xin Xu  (徐建新)

Authors
  1. Fan-han Liu  (刘泛函)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian-xin Xu  (徐建新)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hui-tao Wang  (王辉涛)
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hua Wang  (王华)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian-xin Xu  (徐建新).

Additional information

Foundation item: Projects(51666006, 51406071, 51174105, 51366005) supported by the National Natural Science Foundation of China; Project(2014CB460605) supported by the National Basic Research Program of China

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Fh., Xu, Jx., Wang, Ht. et al. Numerical method and model for calculating thermal storage time for an annular tube with phase change material. J. Cent. South Univ. 24, 217–226 (2017). https://doi.org/10.1007/s11771-017-3422-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-017-3422-z

Key words

Search

Navigation