Skip to main content

Large-Scale Experimental Study of a Phase Change Material: Shape Identification for the Solid–Liquid Interface


This study describes the development of an experimental setup that tracks the evolution of the melting and freezing fronts of a Phase Change Material (PCM), in this case paraffin. The results obtained enable the examination of the shape and movement of the melting front of the PCM. Two modes of heat transfer were identified during the melting process: conduction when melting began and natural convection, which becomes dominant in the remainder of the cycle. Monitoring of the melt over time shows that the melt fraction, expressed as the ratio of the molten volume and solid volume, is proportional to the difference between the imposed temperature and the melting temperature. Experimental results confirm the linearity proposed by other researchers.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15


A :

Aspect ratios (\(\mathrm{{A}} = {\mathrm{{H}} {\cdot } \mathrm{{L}}}^{-1}\))

c :

Specific heat at constant pressure (\(\mathrm{{J}}{\cdot }\mathrm{kg}^{-1}{\cdot }\mathrm{{K}}^{-1})\)

\(h_{sl}\) :

Latent heat of melting/solidification of PCM \((\mathrm{{J}}{\cdot } \mathrm{{kg}}^{-1})\)

Fo :

Fourier number \((\mathrm{{Fo}} = {\upalpha }{\cdot }\mathrm{{t{\cdot }L}}^{-2})\)

H :

Height of the rectangular enclosure (m)

k :

Thermal conductivity \((\mathrm{{W{\cdot }m}}^{-1}{\cdot }\mathrm{{K}}^{-1})\)

L :

Length of the rectangular enclosure (m)

Ra :

Rayleigh number \((\hbox {Ra} = \mathrm{{g}}{\cdot }{\upbeta }\,(\mathrm{{T}}_{\mathrm{h}}-\mathrm{{T}}_{\mathrm{m}}){\cdot }\mathrm{{L}}^{3}{\cdot }({\upalpha }{\cdot }{{\upnu }})^{-1})\)

Ste :

Stefan number \((\hbox {Ste} = \mathrm{{C}}{\cdot }(\mathrm{{T}}_{\mathrm{h}}-\mathrm{{T}}_{\mathrm{m}}){\cdot }\mathrm{{h}}_{\mathrm{sl}}^{-1})\)

t :

Time (s)

T :

Temperature \((^{\circ }\hbox {C})\)

V :

Volume of the PCM liquid \((\hbox {m}^{3})\)

\(V_{0}\) :

Total volume of the PCM \((\hbox {m}^{3})\)

xy :

Cartesian coordinates of the enclosure (m)

\(\alpha \) :

Thermal diffusivity \((\mathrm{{m}}^{2}{\cdot }\mathrm{{s}}^{-1})\)

\(\beta \) :

Thermal expansion coefficient \((\hbox {K}^{-1})\)

\(\nu \) :

Kinematic viscosity \((\mathrm{{m}}^{2}{\cdot }\mathrm{{s}}^{-1})\)

\(\rho \) :

Density \((\mathrm{{kg}}{\cdot }\mathrm{{m}}^{-3})\)






Insulating material




Melting point




  1. A. Sharma, V.V. Tyagi, C.R. Chen, D. Buddhi, Renew. Sustain. Energy Rev. 13, 318 (2009)

    Article  Google Scholar 

  2. F. Agyenim, N. Hewitt, P. Eames, M. Smyth, Renew. Sustain. Energy Rev. 14, 615 (2010)

    Article  Google Scholar 

  3. R. Baetens, B.P. Jelle, A. Gustavsen, Energy Build. 42, 1361 (2010)

    Article  Google Scholar 

  4. M.M. Kenisarin, Renew. Sustain. Energy Rev. 14, 955 (2010)

    Article  Google Scholar 

  5. L.F. Cabeza, A. Castell, C. Barreneche, A. De Gracia, A.I. Fernández, Renew. Sustain. Energy Rev. 15, 1675 (2011)

    Article  Google Scholar 

  6. F. Kuznik, D. David, K. Johannes, J.J. Roux, Renew. Sustain. Energy Rev. 15, 379 (2011)

    Article  Google Scholar 

  7. E. Oró, A. De Gracia, A. Castell, M.M. Farid, L.F. Cabeza, Appl. Energy 99, 513 (2012)

    Article  Google Scholar 

  8. D. Zhou, C.Y. Zhao, Y. Tian, Appl. Energy 92, 593 (2012)

    Article  Google Scholar 

  9. A. Waqas, Z. Ud Din, Renew. Sustain. Energy Rev 18, 607 (2013)

    Article  Google Scholar 

  10. Y. Dutil, D. Rousse, N.B. Salah, S. Lassue, L. Zalewski, Renew. Sustain. Energy Rev. 15, 112–130 (2011)

    Article  Google Scholar 

  11. Y. Dutil, D. Rousse, S. Lassue, L. Zalewski, A. Joulin, J. Virgone, F. Kuznik, K. Johannes, J.-P. Dumas, J.-P. Bédécarrats, A. Castell, L.F. Cabeza, Renew. Energy 61, 132 (2014)

    Article  Google Scholar 

  12. N. Hannoun, V. Alexiades, T.Z. Mai, Num. Heat Transf, Part B: Fundam 44, 253 (2003)

    Article  ADS  Google Scholar 

  13. T.A. Campbell, J.N. Koster, J. Cryst. Growth. 140, 414 (1994)

    Article  ADS  Google Scholar 

  14. C. Gau, R. Viskanta, Int. J. Heat Mass Transf. 27, 113 (1984)

    Article  Google Scholar 

  15. C. Gau, R. Viskanta, J. Heat Transf. 108, 174 (1986)

    Article  Google Scholar 

  16. I. Wintruff, C. Günther, A.G. Class, Numerical Heat Transfer, Part B: Fundam. 39, 127 (2001)

    Article  ADS  Google Scholar 

  17. O. Bertrand, B. Binet, H. Combeau, S. Couturier, Y. Delannoy, D. Gobin, M. Lacroix, P. Le Quéré, M. Médale, J. Mencinger, H. Sadat, G. Vieira, Int. J. Therm. Sci. 38, 5 (1999)

    Article  Google Scholar 

  18. D. Gobin, P. Le Quéré, Comp. Ass. Mech. Eng. Sci. 7, 289 (2000)

    MATH  Google Scholar 

  19. J. Szekely, P.S. Chabra, Metall. Mater. Trans. B. 1, 1195 (1970)

    ADS  Google Scholar 

  20. F.M. Chiesa, R.I.L. Guthrie, J. Heat Transf. 96, 377 (1974)

    Article  Google Scholar 

  21. R.H. Marshall, Therm. Storage. Heat Transf. Solar Energy Syst. 61 (1978)

  22. N.W. Hale, R. Viskanta Jr, Lett. Heat Mass Transf. 5, 329 (1978)

    Article  Google Scholar 

  23. V.P. Carey, B. Gebhart, J. Fluid Mech. 107, 37 (1981)

    Article  ADS  Google Scholar 

  24. P.D. Van Buren, R. Viskanta, Int. J. Heat Mass Transf. 23, 568 (1980)

    Article  Google Scholar 

  25. C.-J. Ho, R. Viskanta, J. Heat Transf. 106, 12 (1984)

    Article  Google Scholar 

  26. F. Wolff, R. Viskanta, Int. J. Exp. Heat Transf. 1, 17 (1987)

    Article  ADS  Google Scholar 

  27. C. Beckermann, R. Viskanta, J. Heat Transf. 111, 416 (1989)

    Article  Google Scholar 

  28. M. Bareiss, H. Beer, Int. Commun. Heat Mass transfer. 11, 323 (1984)

    Article  Google Scholar 

  29. M. Okada, Proc. ASME/JSME Therm. Eng. Jt. Conf. 1, 281 (1983)

    Google Scholar 

  30. M.M. Sorour, M.A. Hassab, M.B. Madi, F.T. Kandil, Int. Commun. Heat Mass Transf. 14, 167 (1987)

    Article  Google Scholar 

  31. Z. Zhang, A. Bejan, J. Heat Mass Transf. 32, 1063 (1989)

    Article  Google Scholar 

  32. Z. Zhang, A. Bejan, Int. J. Heat Mass Transf. 32, 2447 (1989)

    Article  Google Scholar 

  33. K.J. Choi, J.S. Hong, Int. J. Exp. Heat Transf. 3, 49 (1990)

    Article  ADS  Google Scholar 

  34. Y. Wang, A. Amiri, K. Vafai, Int. J. Heat Mass Transf. 42, 3659 (1999)

    Article  Google Scholar 

  35. P.D. Silva, L.C. Goncalves, L. Pires, Appl. Energy 73, 83 (2002)

    Article  Google Scholar 

  36. H. Yin, J.N. Koster, J. Alloy. Compd. 52, 175 (2003)

    Article  Google Scholar 

  37. Z. Younsi, L. Zalewski, S. Lassue, D. Rousse, A. Joulin, Int J. Thermophys. 32, 674 (2011)

    Article  ADS  Google Scholar 

  38. L. Kumar, B.S. Manjunath, R.J. Patel, S.G. Markandeya, R.G. Agrawal, A. Agrawal, Y. Kashyap, P.S. Sarkar, A. Sinha, K.N. Iyer, S.V. Prabhu, Int. J. Therm. Sci. 61, 15 (2012)

    Article  Google Scholar 

  39. H. Shokouhmand, B. Kamkari, Exp. Therm. Fluid. Sci. 50, 201 (2013)

    Article  Google Scholar 

  40. B. Kamkari, H. Shokouhmand, F. Bruno, Int. J. Heat Mass Transf. 72, 186 (2014)

    Article  Google Scholar 

  41. N.C. Barford, in Experimental Measurements: Precision, Error and Truth, 2nd edn, Repr. (Wiley, Chichester, 1990)

  42. B. Binet, M. Lacroix, Int. J. Numer. Method. Heat. Fluid Flow 10, 286 (2000)

    Article  MATH  Google Scholar 

Download references


The authors gratefully acknowledge the Natural Sciences and Engineering Research Council of Canada (NSERC) for financial support. The authors also thank the partners of the t3e research group, who support the project.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Belgacem Dhifaoui.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kadri, S., Dhifaoui, B., Dutil, Y. et al. Large-Scale Experimental Study of a Phase Change Material: Shape Identification for the Solid–Liquid Interface. Int J Thermophys 36, 2897–2915 (2015).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Phase change material
  • Experimental work
  • Solid–liquid interface
  • Melting process