Numerical analysis of thermal energy charging performance of spherical Cu@Cr@Ni phase-change capsules for recovering high-temperature waste heat


Metallic phase-change materials (PCMs) attract much attention due to their high thermal conductivity in thermal energy storage. Our previous work reported a kind of Cu@Cr@Ni bilayer capsules, which could endure at least 1000 thermal cycles between 1323 and 1423 K without leakage, and might be a potential high-temperature metallic PCM. This study numerically investigates the thermal energy charging performance of Cu@Cr@Ni capsules for recovering high-temperature waste heat at both constant and periodically fluctuant heat transfer fluid temperatures. It was revealed that only a short and slight sloped melting platform existed in the curve of outlet temperature due to the ultrahigh thermal conductivity of copper; with higher inlet velocities, the outlet and mean temperatures of such PCM increased and meanwhile the energy transfer efficiency decreased; the outlet and mean temperatures of the PCM and the liquid fraction in it were rather insensitive to the period of the inlet temperature fluctuation; and the amplitude of inlet temperature fluctuation, ±50 K, was sharply reduced to 5 K due to the thermal damping of the PCM.

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FIG. 1
FIG. 2
FIG. 3
FIG. 4
FIG. 5
FIG. 6
FIG. 7
FIG. 8


A :

Porosity function

C :

Porosity constant


Specific heat, J/(kg K)

g :

Gravitational acceleration

H :

Enthalpy, J

h :

Sensitive heat, J; surface heat transfer coefficient, W/(m2 K)

k :

Thermal conductivity, W/(mK)


Latent heat, J

L :

The specific latent heat, J/kg

P :

Pressure, Pa


Momentum source term

S b :

Buoyancy source term

Ra :

Rayleigh number

S h :

Energy source term


Sine function

t :

Time, s

T :

Temperature, K

u :

Velocity, m/s

\(\vec {u}\) :

Velocity vector


Nusselt number


Reynold number

n :


d :

Equivalent diameter

R :

Thermal resistance

x :

x coordinate

y :

y coordinate


Laplace operator


Thermal expansion coefficient, K−1


Density, kg/m3


Dynamic viscosity, kg/(m s)


Liquid fraction


Small constant to avoid division by zero


Energy transfer efficiency


The boundary layer thickness


Kinematic viscosity


Thermal diffusivity


Reference value


Initial value










Surface heat transfer coefficient


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This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 51274182, 51471158, 61274015, and U1407105). Partial work was also supported by Open Funding Project of the State Key Laboratory of Biochemical Engineering (Grant No. 2014KF-04), National Key Research and Development Program (Grant No. 2016YFC0700905), National Key Research and Development Program of China (Grant No. 2016YFB0601103), and the Instrument Developing Project of the Chinese Academy of Sciences (Grant No. YZ201520).

The Mole-8.5 Supercomputing System was developed by Institute of Process Engineering, Chinese Academy of Sciences.

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Correspondence to Zhijian Peng or Jianqiang Li.

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Li, H., Peng, Z., Ma, B. et al. Numerical analysis of thermal energy charging performance of spherical Cu@Cr@Ni phase-change capsules for recovering high-temperature waste heat. Journal of Materials Research 32, 1138–1148 (2017).

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