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Maximization of performance of a PCM latent heat storage system with innovative cavity shape and optimum heating tube position

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Abstract

The melting behavior of a phase change material (lauric acid) placed in various shaped cavities having an inner heated tube is studied numerically. The present investigation concerns the influence of various shaped cavities and the position of the tube on the melting rate and heat transfer process of the phase change material. Finite element method has been employed to solve the governing differential equation along with boundary conditions. The PARADISO package solves the algebraic systems of equations deriving from spatial and temporal discretization. It is notably successful in solving unsymmetrical sparse matrixes using an LU-based decomposition strategy. The average Nusselt number in the inner tube is determined to confirm whether the melting process is convection dominant or conduction dominant. The result shows that the trapezoidal-shaped cavity with an eccentricity of inner tube can enhance the melting fraction compared to the annular-shaped cavity with a central inner tube, annular-shaped cavity with an eccentric inner tube, and trapezoidal-shaped cavity with a central inner tube by 67%, 12%, and 40%, respectively. The results show that the shape of the cavity and proper positioning of the inner tube can influence the melting phenomenon and therefore improves the charging rate appreciably.

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Abbreviations

\(A_{\text{mush}}\) :

Mushy zone constant, (kg m−3 s−1)

c p :

Specific heat at constant pressure, (J kg−1 K−1)

D(T) :

Delta-Dirac function

\(\vec{F}_{\text b}\) :

Body force due to buoyancy, (kg m−2 s−2)

g :

Gravitational acceleration, (m s−2)

H :

Heatlines function

k :

Thermal conductivity, (W m−1 K−1)

L f :

Latent heat of melting per unit mass (J kg−1)

P :

Pressure, (Pa)

S(T) :

Damping factor

T :

Temperature, (K)

T m :

Melting temperature, (K)

T w :

Wall temperature, (K)

∆T :

Melting temperature range, (K)

t :

Time, (s)

\(\vec{u}\) :

Velocity term used in x-direction, (m s−1)

\(\vec{v}\) :

Velocity term used in y-direction, (m s−1)

β :

Thermal expansion coefficient, (K−1)

µ :

Dynamic viscosity, (Pa.s)

ρ :

Density (kg m−3)

φ :

Melting fraction

MF:

Melt fraction

Avg Nu:

Average Nusselt number

F.M.T:

Full melting time

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Silchar, Assam, 788010, India

    Sourav Chatterjee & Dipankar Bhanja

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  1. Sourav Chatterjee
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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by S.C. and Dr. D.B. The first draft of the three manuscripts was written by S.C., and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Dipankar Bhanja.

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Chatterjee, S., Bhanja, D. Maximization of performance of a PCM latent heat storage system with innovative cavity shape and optimum heating tube position. J Therm Anal Calorim 148, 12549–12564 (2023). https://doi.org/10.1007/s10973-023-12607-1

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