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Numerical investigation of paraffin wax solidification in spherical and rectangular cavity

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Abstract

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.

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Abbreviations

α m :

Phase volume fraction of mth fluid

u i :

Velocity component in ith direction (m/s)

x i :

Cartesian component

t :

Time (s)

ρ :

Density of PCM (kg/m3)

μ :

Viscosity of PCM (kg.m/s)

C p :

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

p :

Pressure (N/m2)

g i :

Gravitational force (m/s2)

S i :

Momentum source (kg/m2.s2)

h :

Enthalpy (kJ/kg)

k :

Thermal conductivity (W/m.K)

T :

Temperature (K)

Tw :

Wall temperature of the cavity (K)

Tm :

Mean melting temperature of PCM (K)

C :

Mushy zone constant

γ:

Liquid fraction

T s :

Solidus temperature (K)

T l :

Liquids temperature(K)

St:

Stefan number

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Authors and Affiliations

  1. Department of Chemical Engineering, Birla Institute of Technology, Mesra, Ranchi, India

    Debasree Ghosh

  2. Department of Chemical Engineering, Jadavpur University, Kolkata, India

    Chandan Guha

  3. Department of Production Engineering, Birla Institute of Technology, Mesra, Ranchi, India

    Joyjeet Ghose

Authors
  1. Debasree Ghosh
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  2. Chandan Guha
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  3. Joyjeet Ghose
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Correspondence to Debasree Ghosh.

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Ghosh, D., Guha, C. & Ghose, J. Numerical investigation of paraffin wax solidification in spherical and rectangular cavity. Heat Mass Transfer 55, 3547–3559 (2019). https://doi.org/10.1007/s00231-019-02680-4

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