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Successive melting and solidification of paraffin–alumina nanomaterial in a cavity as a latent heat thermal energy storage

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Latent heat thermal energy storage (LHTES) plays a main role in many industrial applications, especially in high-powered electronics cooling systems and providing the thermal energy demand when the energy supply is unavailable. In this study, the LHTES cycle process, including successive melting and solidification, investigates in a two-dimensional annular space of a square cavity filled with nanomaterial of paraffin–alumina as a nanoPCM. In the melting process, all sidewalls of the cavity are insulated. Meanwhile, a constant heat rate generates homogeneously within the central heat source. At the end of melting, the heat generation gets off, while a time-reducing temperature lower than the paraffin melting point imposes on the sidewalls, and then, solidification triggers. The numerical simulation was accomplished using control volume method and the governing equations solved using the SIMPLE algorithm. The enthalpy-porosity method was employed to model the phase-change front. The value of thermal conductivity and the viscosity of the nanofluid have been experimentally measured before the numerical modeling. In this study, the effect of volume fraction of nanoparticles (0–0.03) has been investigated on the successive melting and solidification rate for a constant Rayleigh number of 5.74 × 105. The results show that adding nanoparticles to the PCM equal to the volume fractions of 0.01 and 0.02 improves melting rate, but the nanofluid with the volume fraction of 0.03 represents a poor heat transfer rate during melting even weaker than those for nanofluid with the volume fraction of 0.01. It also observed that the nanomaterial with the volume fraction of φ = 0.03 represents the highest solidification rate. However, taking the overall performance of successive melting and solidification system into account, the nanofluid with the volume fraction of 0.02 remarked the most effective heat transfer rate in comparison with the other examined cases.

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b :

Enthalpy-porosity coefficient (kg m−3 s−1)

B :

Dimensionless enthalpy-porosity coefficient

B z :

Boltzmann constant

c :

Specific heat (J kg−1 K−1)

f :

Liquid fraction

g :

Gravity (m s−2)

h :

Enthalpy (J kg−1 K−1)

L, l :

Cavity and heat source dimension (m)

k :

Thermal conductivity (W m−1 K−1)

Nu :

Nusselt number, \(- k_{\text{nf}} /k_{\text{f}} (T_{\text{s}} - T_{\text{m}} )\partial T/\partial n\)

p :

Pressure (N m−2)

P :

Dimensionless pressure

Pr :

Prandtl number, \(Pr = \nu_{\text{f}} /\alpha_{\text{f}}\)


Heat generation rate (W m−3)

Ra :

Rayleigh number, \(g\beta_{\text{f}} q^{{{\prime \prime \prime }}} l^{5} /\nu_{\text{f}} \alpha_{\text{f}} k_{\text{s}}\)

Ste :

Stefan number, \(c_{\text{f}} q^{{{\prime \prime \prime }}} l^{2} /h_{\text{nf}} k_{\text{s}}\)

T :

Temperature (K)

T m, T s :

Melting and solidification points (K)

T h, T c :

Hot and cold temperatures (K)

t :

Time (s)

u, v :

Velocity in the x, y direction (m s−1)

U, V :

Dimensionless velocity

x, y :

Cartesian coordinate (m)

X, Y :

Dimensionless Cartesian coordinate


Cavity liquid fraction


Phase-change material


Nano-enhanced PCM

α :

Thermal diffusivity (m2 s−1)

β :

Expansion coefficient (K−1)

μ :

Dynamic viscosity (N s m−2)

ν :

Kinematic viscosity (m2 s−1)

θ :

Dimensionless temperature

ρ :

Density (kg m−3)

ϕ :

Volume fraction

σ :

Electrical conduction (S m−1)


Dimensionless time

f, s:

Fluid and solid


Melting point


Fluid PCM with nanoparticles


Solid PCM with nanoparticles




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Correspondence to R. Yadollahi Farsani.

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Yadollahi Farsani, R., Raisi, A. & Mahmoudi, A. Successive melting and solidification of paraffin–alumina nanomaterial in a cavity as a latent heat thermal energy storage. J Braz. Soc. Mech. Sci. Eng. 41, 368 (2019).

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