Journal of Mechanical Science and Technology

, Volume 29, Issue 9, pp 3819–3830 | Cite as

Melting of nanoparticles-enhanced phase change material (NEPCM) in vertical semicircle enclosure: numerical study

  • Mahmoud JourabianEmail author
  • Mousa Farhadi


Convection melting of ice as a Phase change material (PCM) dispersed with Cu nanoparticles, which is encapsulated in a semicircle enclosure is studied numerically. The enthalpy-based Lattice Boltzmann method (LBM) combined with a Double distribution function (DDF) model is used to solve the convection-diffusion equation. The increase in solid concentration of nanoparticles results in the enhancement of thermal conductivity of PCM and the decrease in the latent heat of fusion. By enhancing solid concentration of nanoparticles, the viscosity of nanofluid increases and convective heat transfer dwindles. For all Rayleigh numbers investigated in this study, the insertion of nanoparticles in PCM has no effect on the average Nusselt number.


Convection Lattice Boltzmann method Melting front Nanoparticles Phase change Semicircle 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. M. Khodadadi and S. F. Hosseinizadeh, Nanoparticleenhanced phase change materials (NEPCM) with great potential for improved thermal energy storage, Int. Commun. Heat Mass Transfer, 34 (5) (2007) 534–543.CrossRefGoogle Scholar
  2. [2]
    C. J. Ho and J. Y. Gao, Preparation and thermophysical properties of nanoparticle-in-paraffin emulsion as phase change material, Int. Commun. Heat Mass Transfer, 36 (5) (2009) 467–470.CrossRefGoogle Scholar
  3. [3]
    S. Kuravi, K. M. Kota, J. Du and L. C. Chow, Numerical investigation of flow and heat transfer performance of nanoencapsulated phase change material slurry in microchannels, ASME J. Heat Transfer, 131 (6) (2009) 1–9.CrossRefGoogle Scholar
  4. [4]
    L. Fan and J. M. Khodadadi, An experimental investigation of enhanced thermal conductivity and expedited unidirectional freezing of cyclohexane-based nanoparticle suspensions utilized as nano-enhanced phase change materials (NePCM), Int. J. Therm. Sci., 62 (2012) 120–126.CrossRefGoogle Scholar
  5. [5]
    S. Jesumathy, M. Udayakumar and S. Suresh, Experimental study of enhanced heat transfer by addition of CuO nanoparticle, Heat Mass Transfer, 48 (6) (2012) 965–978.CrossRefGoogle Scholar
  6. [6]
    S. Kashani, A. A. Ranjbar, M. Abdollahzadeh and S. Sebti, Solidification of nano-enhanced phase change material (NEPCM) in a wavy cavity, Heat Mass Transfer, 48 (7) (2012) 1155–1166.CrossRefGoogle Scholar
  7. [7]
    S. F. Hosseinizadeh, A. A. R. Darzi and F. L. Tan, Numerical investigations of unconstrained melting of nanoenhanced phase change material (NEPCM) inside a spherical container, Int. J. Therm. Sci., 51 (2012) 77–83.CrossRefGoogle Scholar
  8. [8]
    Z. Rao, S. Wang and F. Peng, Molecular dynamics simulations of nano-encapsulated and nanoparticle-enhanced thermal energy storage phase change materials, Int. J. Heat Mass Transfer, 66 (2013) 575–584.CrossRefGoogle Scholar
  9. [9]
    Y. Zeng, L. W. Fan, Y. Q. Xiao, Z. T. Yu and K. F. Cen, An experimental investigation of melting of nanoparticleenhanced phase change materials (NePCMs) in a bottomheated vertical cylindrical cavity, Int. J. Heat Mass Transfer, 66 (2013) 111–117.CrossRefGoogle Scholar
  10. [10]
    K. E. Omari, T. Kousksou and Y. L. Guer, Impact of shape of container on natural convection and melting inside enclosures used for passive cooling of electronic devices, Applied Therm. Eng., 31 (14–15) (2011) 3022–3035.CrossRefGoogle Scholar
  11. [11]
    O. Bertrand, B. Binet, H. Combeau, S. Couturier, Y. Delannoy, D. Gobin, M. Lacroix, P. Le Quéré, M. Médale, J. Mencinger, H. Sadat and G. Vieira, Melting driven by natural convection. A comparison exercise: first results, Int. J. Therm. Sci., 38 (1) (1999) 5–26.CrossRefGoogle Scholar
  12. [12]
    J. Mencinger, Numerical simulation of melting in twodimensional cavity using adaptative grid, J. Comput. Phys., 198 (1) (2004) 243–64.CrossRefzbMATHGoogle Scholar
  13. [13]
    L. Tan and N. Zabaras, A level set simulation of dendritic solidification with combined features of front-tracking and fixed-domain methods, J. Comput. Phys., 211 (1) (2006) 36–63.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    W. J. Boettinger, J. A. Warren, C. Beckermann and A. Karma, Phase-field simulation of solidification, Annu. Rev. Mater. Res., 32 (2002) 163–194.CrossRefGoogle Scholar
  15. [15]
    A. R. Videla, C. L. Lin and J. D. Miller, Simulation of saturated fluid flow in packed particle beds—The lattice-Boltzmann method for the calculation of permeability from XMT images, J. Chinese Institute Chemical Engineers, 39 (2) (2008) 117–128.CrossRefGoogle Scholar
  16. [16]
    D. Gao and Z. Chen, Lattice Boltzmann simulation of natural convection dominated melting in a rectangular cavity filled with porous media, Int. J. Therm. Sci., 50 (4) (2011) 493–501.CrossRefGoogle Scholar
  17. [17]
    M. Jourabian, M. Farhadi and A. A. R. Darzi, Lattice Boltzmann investigation for enhancing the thermal conductivity of ice using Al2O3 porous matrix, Int. J. Comput. Fluid Dyn., 26 (9-10) (2012) 451–462.MathSciNetCrossRefGoogle Scholar
  18. [18]
    A. A. Mehrizi, M. Farhadi, K. Sedighi and M. A. Delavar, Effect of fin position and porosity on heat transfer improvement in a plate porous media heat exchanger, J. Taiwan Institute Chemical Eng., 44 (3) (2013) 420–431.CrossRefGoogle Scholar
  19. [19]
    H. Nemati, M. Farhadi, K. Sedighi and A. A. R. Darzi, Lattice Boltzmann simulation of nanofluid in lid-driven cavity, Int. Commun. Heat Mass Transfer, 37 (10) (2010) 1528–1534.CrossRefGoogle Scholar
  20. [20]
    W. S. Jiaung, J. R. Ho and C. P. Kuo, Lattice-Boltzmann method for the heat conduction problem with phase change, Numer. Heat Transfer: Part B, 39 (2) (2001) 167–187.CrossRefGoogle Scholar
  21. [21]
    D. Chatterjee and S. Chakraborty, A hybrid lattice Boltzmann model for solid-liquid phase transition in presence of fluid flow, Phys. Lett. A, 351 (4–5) (2006) 359–367.CrossRefzbMATHGoogle Scholar
  22. [22]
    E. Semma, M. E. Ganaoui, R. Bennacer and A. A. Mohamad, Investigation of flows in solidification by using the lattice Boltzmann method, Int. J. Therm. Sci., 47 (3) (2008) 201–208.CrossRefGoogle Scholar
  23. [23]
    C. Huber, A. Parmigiani, B. Chopard, M. Manga and O. Bachmann, Lattice Boltzmann model for melting with natural convection, Int. J. Heat Fluid Flow, 29 (5) (2008) 1469–1480.CrossRefGoogle Scholar
  24. [24]
    E. Attar and C. Körner, Lattice Boltzmann model for thermal free surface flows with liquid-solid phase transition, Int. J. Heat Fluid Flow, 32 (1) (2011) 156–63.CrossRefGoogle Scholar
  25. [25]
    M. Jourabian, M. Farhadi, K. Sedighi, A. A. Rabienataj Darzi and Y. Vazifeshenas, Simulation of natural convection melting in a cavity with fin using lattice Boltzmann method, Int. J. Numer. Meth. Fluids, 70 (3) (2012) 313–325.MathSciNetCrossRefGoogle Scholar
  26. [26]
    M. Jourabian, M. Farhadi and A. A. R. Darzi, Simulation of natural convection melting in an inclined cavity using lattice Boltzmann method, Sci. Iran., 19 (4) (2012) 1066–1073.CrossRefGoogle Scholar
  27. [27]
    M. Jourabian, M. Farhadi, K. Sedighi, A. A. R. Darzi and Y. Vazifeshenas, Melting of NEPCM within a cylindrical tube: numerical study using the lattice Boltzmann method, Numer. Heat Transfer Part A, 61 (12) (2012) 929–948.Google Scholar
  28. [28]
    M. Eshraghi and S. D. Felicelli, An implicit lattice Boltzmann model for heat conduction with phase change, Int. J. Heat Mass Transfer, 55 (9–10) (2012) 2420–2428.CrossRefGoogle Scholar
  29. [29]
    M. Jourabian, M. Farhadi and A. A. Rabienataj Darzi, Outward melting of ice enhanced by Cu nanoparticles inside cylindrical horizontal annulus: lattice Boltzmann approach, Appl. Math. Modelling, 37 (20–21) (2013) 8813–8825.MathSciNetCrossRefGoogle Scholar
  30. [30]
    M. Jourabian, M. Farhadi and A. A. Rabienataj Darzi, Convection-dominated melting of phase change material in partially heated cavity: lattice Boltzmann study, Heat Mass Transfer, 49 (4) (2013) 555–565.CrossRefGoogle Scholar
  31. [31]
    R. Huang, H. Wu and P. Cheng, A new lattice Boltzmann model for solid-liquid phase change, Int. J. Heat Mass Transfer, 59 (2013) 295–301.CrossRefzbMATHGoogle Scholar
  32. [32]
    A. A. R. Darzi, M. Farhadi and M. Jourabian, Lattice Boltzmann simulation of heat transfer enhancement during melting by using nanoparticles, IJST Trans. Mech. Eng., 37 (1) (2013) 23–37.Google Scholar
  33. [33]
    M. Jourabian, M. Farhadi, A. A. R. Darzi and A. Abouei, Lattice Boltzmann simulation of melting phenomenon with natural convection from an eccentric annulus, Therm. Sci., 17 (3) (2013) 877–890.CrossRefGoogle Scholar
  34. [34]
    J. M. Fuentes, F. Kuznik, K. Johannes and J. Virgone, Development and validation of a new LBM-MRT hybrid model with enthalpy formulation for melting with natural convection, Phys. Lett. A, 378 (4) (2014) 4374–4381.Google Scholar
  35. [35]
    A. A. R. Darzi, M. Farhadi, M. Jourabian and Y. Vazifeshenas, Natural convection melting of NEPCM in a cavity with an obstacle using lattice Boltzmann method, Int. J. Numer. Meth. Heat Fluid Flow, 24 (1) (2014) 221–236.CrossRefGoogle Scholar
  36. [36]
    H. K. Kang, M. Tsutahara, K. D. Ro and Y. H. Lee, Numerical simulation of shock wave propagation using the finite difference lattice Boltzmann method, KSME Int. J., 16 (10) (2002) 1327–1335.Google Scholar
  37. [37]
    S. Alapati, S. Kang and Y. K. Suh, Parallel computation of two-phase flow in a microchannel using the lattice Boltzmann method, J. Mech. Sci. Tech., 23 (9) (2009) 2492–2501.CrossRefGoogle Scholar
  38. [38]
    L. S. Kim, H. K. Jeong, M. Y. Ha and K. C. Kim, Numerical simulation of droplet formation in a micro-channel using the lattice Boltzmann method, J. Mech. Sci. Tech., 22 (4) (2008) 770–779.CrossRefGoogle Scholar
  39. [39]
    H. Sajjadi, M. B. Abbassi and GH. R. Kefayati, Lattice Boltzmann simulation of turbulent natural convection in a square cavity using Cu/water nanofluid, J. Mech. Sci. Tech., 27 (8) (2013) 2341–2349.CrossRefGoogle Scholar
  40. [40]
    R. Benzi, S. Succi and M. Vergassola, The lattice Boltzmann equation: Theory and applications, Phys. Reports, 222 (3) (1992) 145–197.CrossRefGoogle Scholar
  41. [41]
    S. Chen and G. D. Doolen, Lattice Boltzmann method for fluid flows, Annual Rev. Fluid Mech., 30 (1998) 329–364.MathSciNetCrossRefGoogle Scholar
  42. [42]
    S. Succi, The Lattice Boltzmann equation for fluid dynamics and beyond, clarendon, New York, USA (2001).Google Scholar
  43. [43]
    H. E. Patel, T. Pradeep, T. Sundararajan, A. Dasgupta, N. Dasgupta and S. K. Das, A micro-convection model for thermal conductivity of nanofluid, Pramana-J. Phys., 65 (5) (2005) 863–869.CrossRefGoogle Scholar
  44. [44]
    P. L. Bhatnagar, E. P. Gross and M. Krook, A model for collision processes in gases. I. small amplitude processes in charged and neutral one-component systems, Phys. Rev., 94 (1954) 511–525.CrossRefzbMATHGoogle Scholar
  45. [45]
    A. A. Mohamad, M. EL. Ganaoui and R. Bennacer, Lattice Boltzmann simulation of natural convection in an open ended cavity, Int. J. Therm. Sci., 48 (10) (2009) 1870–1875.CrossRefGoogle Scholar
  46. [46]
    X. He, S. Chen and G. D. Doolen, A novel thermal model for the lattice Boltzmann method incompressible limit, J. Comput. Phys., 146 (1) (1998) 282–300.MathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    G. McNamara and B. Alder, Analysis of the lattice Boltzmann treatment of hydrodynamics, Phys. A, 194 (1–4) (1993) 218–228.MathSciNetCrossRefzbMATHGoogle Scholar
  48. [48]
    N. Prasianakis and I. Karlin, Lattice Boltzmann method for thermal flow simulation on standard lattices, Phys. Rev. E, 76 (2007) 016702.CrossRefGoogle Scholar
  49. [49]
    A. Mezrhab, M. Bouzidi and P. Lallemand, Hybrid lattice-Boltzmann finite difference simulation of convective flows, Comput. Fluids, 33 (4) (2004) 623–641.CrossRefzbMATHGoogle Scholar
  50. [50]
    Z. Guo, B. Shi and C. Zheng, A coupled lattice BGK model for the Boussinesq equations, Int. J. Numer. Meth. Fluids, 39 (4) (2002) 325–342.MathSciNetCrossRefzbMATHGoogle Scholar
  51. [51]
    B. C. Shi and Z. L. Guo, Lattice Boltzmann model for nonlinear convection-diffusion equations, Phys. Rev. E, 79 (2009) 016701.CrossRefGoogle Scholar
  52. [52]
    R. Das, S. C. Mishra and R. Uppaluri, Retrieval of thermal properties in a transient conduction-radiation problem with variable thermal conductivity, Int. J. Heat Mass Transfer, 52 (11–12) (2009) 2749–2758.CrossRefzbMATHGoogle Scholar
  53. [53]
    M. Wang, J. Wang, N. Pan and S. Chen, Mesoscopic predictions of the effective thermal conductivity for micro scale random porous media, Phys. Rev. E, 75 (2007) 1–10.Google Scholar
  54. [54]
    Y. Y. Yan and Y. Q. Zu, Numerical simulation of heat transfer and fluid flow past a rotating isothermal cylinder - A LBM approach, Int. J. Heat Mass Transfer, 51 (9–10) (2008) 2519–2536.CrossRefzbMATHGoogle Scholar
  55. [55]
    Z. L. Guo, C. Zheng and B. C. Shi, An extrapolation method for boundary conditions in lattice Boltzmann method, Phys. Fluids, 14 (6) (2002) 2007–2010.CrossRefGoogle Scholar
  56. [56]
    D. Yu, R. Mei, L. S. Luo and W. Shyy, Viscous flow computations with the method of lattice Boltzmann equation, Prog. Aero. Sci., 39 (5) (2003) 329–367.CrossRefGoogle Scholar
  57. [57]
    R. Mei, D. Yu and W. Shyy, Force evaluation in the lattice Boltzmann method involving curved geometry, Phys. Rev. E, 65 (2002) 1–14.CrossRefGoogle Scholar
  58. [58]
    P. Jany and A. Bejan, Scaling theory of melting with natural convection in an enclosure, Int. J. Heat Mass Transfer, 31 (6) (1988) 1221–1235.CrossRefGoogle Scholar
  59. [59]
    Y. Feng, H. Li, L. Li, L. Bu and T. Wang, Numerical investigation on the melting of nanoparticle-enhanced phase change materials (NEPCM) in a bottom-heated rectangular cavity using lattice Boltzmann method, Int. J. Heat Mass Transfer, 81 (2015) 415–425.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Engineering and ArchitectureUniversity of TriesteTriesteItaly
  2. 2.Department of Mechanical EngineeringBabol Noshirvani University of TechnologyBabolIran

Personalised recommendations