Heat and Mass Transfer

, Volume 55, Issue 12, pp 3547–3559 | Cite as

Numerical investigation of paraffin wax solidification in spherical and rectangular cavity

  • Debasree GhoshEmail author
  • Chandan Guha
  • Joyjeet Ghose


The solid-liquid phase change processes are very sensitive to thermal boundary conditions. The phase change processes are also dominated by the shape of the cavity and thermo-physical properties of phase change materials. The transient experimental studies of unconstrained phase change processes are very difficult. Therefore, the numerical simulation is chosen to study the solidification phase change process in a rectangular and a spherical cavity. In this work, the solidification process of paraffin wax is simulated in a spherical cavity and a rectangular cavity for different thermal boundary conditions. The different sizes of cavities are taken to show the impact of shape on the solidification process. The simulations results are obtained using enthalpy-porosity model for free surface solidification process. The commercial software Ansys-fluent 16.2 is used to solve the numerical model. The model used for simulation is validated in previous work for melting in a spherical cavity [1] The result shows the solidification time is minimum for highest Stefan number. It also reveals that the solidification process is slow as the thickness of the solid zone increases. This is because of decreasing effect of natural convection and increasing effect of conductive resistance of solidified phase change material. The conduction dominated process makes the solidification slower as the thermal conductivity of paraffin wax is low. Different shapes of cavity, effects the solidification time. This research shows that though the size of spherical cavity is higher than that of rectangular cavity, the solidification time is much lower for spherical cavity.

List of symbols


Phase volume fraction of mth fluid


Velocity component in ith direction (m/s)


Cartesian component


Time (s)


Density of PCM (kg/m3)


Viscosity of PCM (kg.m/s)


Specific heat of liquid PCM (J/kg.K)


Pressure (N/m2)


Gravitational force (m/s2)


Momentum source (kg/m2.s2)


Enthalpy (kJ/kg)


Thermal conductivity (W/m.K)


Temperature (K)


Wall temperature of the cavity (K)


Mean melting temperature of PCM (K)


Mushy zone constant


Liquid fraction


Solidus temperature (K)


Liquids temperature(K)


Stefan number



  1. 1.
    Debasree Ghosh CG (2019) Numerical and experimental investigation of paraffin wax melting in spherical cavity. Heat Mass Transf 55:1427–1437. CrossRefGoogle Scholar
  2. 2.
    Ismail KARJRH, Silva RCR, Jesus AB, Paixão LC (2014) Experimentally validated two dimensional numerical model for the solidification of PCM along a horizontal long tube. Int J Therm Sci 75:184–193CrossRefGoogle Scholar
  3. 3.
    Ismail KARJRH (2000) Solidification of pcm inside a spherical capsule. Energ Conversion Manag 41:173–187CrossRefGoogle Scholar
  4. 4.
    Yuxiang Hong W-BY, Huang S-M, Dua J (2018) Can the melting behaviors of solid-liquid phase change be improved by inverting the partially thermal-active rectangular cavity? Int J Heat Mass Transf 126:571–578CrossRefGoogle Scholar
  5. 5.
    Sharma RKPG, Sahu JN, Metselaar HSC, Mahlia TMI (2014) Numerical study for enhancement of solidification of phase change materials using trapezoidal cavity. Powder Technol 268:38–47CrossRefGoogle Scholar
  6. 6.
    Chakraborty SNC, Kumar P, Dutta P (2003) Studies on turbulent momentum, heat and species transport during binary alloy solidification in a top-cooled rectangular cavity. Int J Heat Mass Transf 46:1115–1137CrossRefGoogle Scholar
  7. 7.
    Shyy WYP, Hunter GB, Wei DY, Chen MH (1992) Modeling of turbulent transport and solidification during continuous ingot casting. Int J Heat Mass Transf 35:1229–1245CrossRefGoogle Scholar
  8. 8.
    Ezan MAMK (2016) Numerical investigation of transient natural convection heat transfer of freezing water in a square cavity. Int J Heat Fluid Flow 61:438–448CrossRefGoogle Scholar
  9. 9.
    Stickland MTTJS, MacKenzie J (2007) An experimental investigation of natural convection with solidification in a differentially heated cavity. Int J Heat Mass Transf 50:36–44CrossRefGoogle Scholar
  10. 10.
    Assis EGZ, Letan R (2009) Numerical and experimental study of solidification in a spherical shell. J Heat Transf 131:1–5CrossRefGoogle Scholar
  11. 11.
    Assis E, K L, Ziskind G, Letan R (2007) Numerical and experimental study of melting in a spherical Shell. Int J Heat Mass Transf 50:1790–1804CrossRefGoogle Scholar
  12. 12.
    Vogel JJFMJ (2016) Naturalconvectioninhightemperature flatplate latent heat thermal energy storage systems. Appl Therm Eng 184:184–196. CrossRefGoogle Scholar
  13. 13.
    Meng ZNPZ (2017) Experimental and numerical investigation of a tube-in-tank latent thermal energy storage unit using composite PCM. Appl Energy 190:524–539. CrossRefGoogle Scholar
  14. 14.
    Archibold ARMMR, Goswami DY, Stefanakos EK (2014) Analysis of heat transfer and fluid flow during melting inside a spherical container for thermal energy storage. Appl Therm Eng 64:396–407. CrossRefGoogle Scholar
  15. 15.
    Niyas HSP, Muthukumar P (2017) Performance investigation of a lab scale latent heat storage prototype numerical results. Energ Conversion Manag 135:188–199. CrossRefGoogle Scholar
  16. 16.
    Kozak YGZ (2017) Novel enthalpy method for modeling of PCM melting accompanied by sinking of the solid phase. Int J Heat Mass Transf 112:568–586CrossRefGoogle Scholar
  17. 17.
    Pahamli YMJH, Ranjbar AA, Bahrampoury R (2016) Analysis of the effect of eccentricity and operational parameters in PCM-filled single-pass shell and tube heat exchangers. Renew Energy 97:344–357. CrossRefGoogle Scholar
  18. 18.
    Mohamed Fadl PCE (2019) Numerical investigation of the influence of mushy zone parameter Amush on heat transfer characteristics in vertically and horizontally oriented thermal energy storage systems. Appl Therm Eng 151:90–99CrossRefGoogle Scholar
  19. 19.
    Mathura Kumar DJK (2017) Influence of mushy zone constant on Thermohydraulics of a PCM. Energy Procedia 109:314–321CrossRefGoogle Scholar
  20. 20.
    Simone Arena EC, Gasia J, Cabeza LF, Cau G (2017) Numerical simulation of a finned-tube LHTES system: influence of the mushy zone constant on the phase change behaviour. Energy Procedia 126:517–524CrossRefGoogle Scholar
  21. 21.
    A.W. D (2005) Introduction to computational fluid dynamics.. Cambrige University PressGoogle Scholar
  22. 22.
    Patankar SV (1980) Numerical heat transfer and fluid flow hemisphere. Washington, DCGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Chemical EngineeringBirla Institute of TechnologyRanchiIndia
  2. 2.Department of Chemical EngineeringJadavpur UniversityKolkataIndia
  3. 3.Department of Production EngineeringBirla Institute of TechnologyRanchiIndia

Personalised recommendations