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Influence of Optical Thickness on the Melting of a Phase Change Material in a Thermal Energy Storage Module


Thermal energy storage using phase change material (PCM) is needed for renewable power generation using solar energy. In the present investigation, the discrete-ordinate method is used to numerically investigate the radiative transport in a two-dimensional finned cylinder containing an absorbing-emitting PCM. The enthalpy-porosity method is used to track the melting-solidification interface. This study investigated the effects of the optical thickness of the phase change material and the temperature at the outer surface of the finned cylinder on the melting process. The results obtained show that thermal radiation decreases the melting time and accelerates the phase transition process. Besides, the results showed that the use of fins along with a radiation absorber in the PCM decreases the melting time by 65% compared with only fins.

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c p :

Specific heat at constant pressure (J/kg K)

g :

Gravitational acceleration (m/s2)

h :

Sensible enthalpy (J/kg)

P :


q t :

Total heat transfer rate at the inner shell wall (W)

q r :

Radiation heat transfer rate (W)

r :

Radial coordinate (m)


Stefan number, Ste = cp(TwTm)/λ

t :

Time (s)

T :

Temperature (K)

v :

Velocity (m/s)

α :

Thermal diffusivity (m2/s)

β :

Thermal expansion coefficient (1/K)

θ :

Angular coordinate

κ a :

Absorption coefficient (m−1)

λ :

Latent heat (J/kg)

µ :

Dynamic viscosity (kg/m s)

ρ :

Density (kg/m3)

σ s :

Scattering coefficient (m−1)

τ :

Optical thickness, τ = (κa + σs)R






Radial direction



θ :

Angular direction


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Correspondence to Muhammad Mustafizur Rahman.

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Belaed, M., Rahman, M.M. & Guldiken, R. Influence of Optical Thickness on the Melting of a Phase Change Material in a Thermal Energy Storage Module. JOM 72, 2089–2095 (2020).

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