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Numerical study of the melting process of spherical phase change material with variable thermal conductivity

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Abstract

This paper addresses the melting of phase change solid sphere, which motivates researchers to develop new thermal energy storage (TES) systems techniques. Phase change materials can store or release large amounts of heat in short intervals of time, thus improving the thermal performance of cooling and heating systems in buildings and regulate the temperature of PV systems, batteries and other electronic components. We have considered a convective spherical Stefan problem with thermal conductivity as a function of time and temperature. The heat balance integral method (HBIM) is used to find the problem’s solution numerically. The temperature profile is approximated by using n degree polynomial. The influence of governing parameters on the location of melting front and temperature profile is discussed thoroughly. The parameters depict that transition from solid to liquid phase becomes fast for higher values of Stefan number while the transition rate slows down for larger values of Peclet number. The melting rate increases from 20% to 80% when Stefan number rises from 0.1 to 1.0 at a particular time. Moreover, a comparative study of the proposed model with some existing models is being done. It is observed that moving melting front for the assumed problem undergoes a fast melting process.

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Abbreviations

r :

Radial distance (m)

\(R_0\) :

Radius of sphere (m)

t :

Time (s)

R(t):

Moving melting front position

\(\rho\) :

Density \(({\text{Kg} \text{ m }}^{-3})\)

c :

Specific heat \(({\text{J} \text{ kg }}^{-1}{\text{ K }}^{-1})\)

k :

Thermal conductivity

h :

Latent heat (\({\text{J} \text{ kg }}^{-1}\))

\(T_{\rm m}\) :

Melting temperature (K)

T :

Temperature (K)

Pe:

Peclet number

\(\delta\) :

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

Ste:

Stefan number

\(\theta\) :

Transformed temperature

\(k_0\) :

Reference thermal conductivity \(({\text{W} \text{ m }}^{-1}{\text{ K }}^{-1})\)

u :

Velocity \(({\text{ ms }}^{-1})\)

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Acknowledgements

This work is supported by SERB-POWER SPG/2021/000591 funded by Science and Engineering Research Board (SERB) and by the DST-FIST (Govt. of India) for the grant SR/FIST/MS-1/2017/13.

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  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, 147004, India

    Tanvi Singla, B. Kumar & Sapna Sharma

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  1. Tanvi Singla
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Correspondence to Sapna Sharma.

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Singla, T., Kumar, B. & Sharma, S. Numerical study of the melting process of spherical phase change material with variable thermal conductivity. Indian J Phys 98, 1355–1363 (2024). https://doi.org/10.1007/s12648-023-02886-7

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