Abstract
The solid-liquid phase change process realizes a buffer system to adsorb and then release heat loads. This property can be used in thermal control and in thermal energy storage. In the first case, it allows to have an assigned temperature range where the system works and to reject high heat loads, mainly when they are intermittent. In the second case, it is used to obtain a constant supply compared to a continuous variation of the consumption demand which leads to waste of excess energy. The phase change materials (PCMs) are materials employed for solid-liquid phase change process. They present many advantages such as stability and high stored energy density. Nevertheless, the main drawback of these materials is the small value of the thermal conductivity, and it necessitates a long time for melting and implicates a broad difference of temperature in the system between the solid zone and liquid zone. To overcome this drawback, improvement techniques are implemented to optimize the system like the inserting of metal foam or the addition of highly conductive nanoparticles. The new material created with nanoparticles in the base PCM is called nano-PCM. In the present chapter, the study of these systems will be analyzed numerically after a review of current literature. The governing equation models will be described in the cases of base PCM, nano-PCM, PCM, and nano-PCM in metal foam. Some results related to the main applications of the different systems will be provided in order to underline their advantages and disadvantages.
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Nomenclature
Nomenclature
a | Coefficient term | Eq. 33 |
A_{mush} | Mushy zone costant | kgm^{−3} s^{−1} |
b | Parameter term | Eq. 33 |
c | Specific heat | Jkg^{−1} K^{−1} |
C_{F} | Inertial drag factor | – |
d_{f} | Ligament diameter | m |
d_{p} | Pore diameter | m |
E | Specific enthalpy | Jkg^{−1} |
Fo | Fourier number | \( \frac{kt^2}{\rho {c}_p{L}_R^2} \) |
\( \overrightarrow{g} \) | Gravity acceleration | ms^{−2} |
h | Sensible enthalpy | J |
h_{sf} | Local heat transfer coefficient | Wm^{−2} K^{−1} |
H | Enthalpy | J |
ΔH | Latent heat content | Jkg^{−1} |
H_{L} | Latent Heat of material | Jkg^{−1} |
k | Thermal conductivity | Wm^{−1} K^{−1} |
K | Permeability | m^{2} |
Nu_{i,d} | Interstitial Nusselt number | \( \frac{h_{sf}{d}_f}{k} \) |
p | Relative pressure | Pa |
Pr | Prandtl number | \( \frac{\mu {c}_p}{k} \) |
q | Performance parameter | \( \frac{E_t-{E}_{t-\Delta t}}{H_L} \) |
Ra | Rayleigh number | \( \frac{\rho^2{c}_p g\beta \Delta {TL}_R^3}{\mu k} \) |
Re_{d} | Ligament Reynolds number | \( \frac{\rho {Vd}_f}{\mu} \) |
Ste | Stefan number | \( \frac{c_p\Delta T}{H_L} \) |
\( \overrightarrow{S} \) | Source term | Eq. 2 |
T | Temperature | K |
T_{solidus} | Solidus temperature | K |
T_{liquidus} | Liquidus temperature | K |
V,\( \overrightarrow{V} \) | Velocity, velocity vector | ms^{−1} |
1.1 Greek Symbols
α_{sf} | Surface Area density | m^{−1} |
β | Liquid fraction | – |
γ | Thermal expansion coefficient | K^{−1} |
ε | Porosity | – |
η | Dimensionless coordinate | x/L_{R} |
μ | Viscosity of material | kgm^{−1} s^{−1} |
ξ | Dimensionless coordinate | y/L_{R} |
ρ | Density | kgm^{−3} |
ω | Pore size | Pore per Inch (PPI) |
ψ | Volume fraction of nano-PCM | – |
1.2 Subscripts
0 | Operating |
eff | Effective |
m | Metal foam |
nanoparticles | Nanoparticle |
nanopcm | Nano-PCM |
pcm | Phase change material |
t | Time |
1-t | Time step |
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Buonomo, B., Ercole, D., Manca, O., Nardini, S. (2017). Nanoparticles and Metal Foam in Thermal Control and Storage by Phase Change Materials. In: Kulacki, F. (eds) Handbook of Thermal Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-32003-8_39-1
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DOI: https://doi.org/10.1007/978-3-319-32003-8_39-1
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