Nanoparticles and Metal Foam in Thermal Control and Storage by Phase Change Materials

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.

Nomenclature

a	Coefficient term	Eq. 33
Amush	Mushy zone costant	kgm−3 s−1
b	Parameter term	Eq. 33
c	Specific heat	Jkg−1 K−1
CF	Inertial drag factor	–
df	Ligament diameter	m
dp	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
hsf	Local heat transfer coefficient	Wm−2 K−1
H	Enthalpy	J
ΔH	Latent heat content	Jkg−1
HL	Latent Heat of material	Jkg−1
k	Thermal conductivity	Wm−1 K−1
K	Permeability	m2
Nui,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	$\frac{\rho^2{c}_p g\beta \Delta {TL}_R^3}{\mu k}$
Red	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
Tsolidus	Solidus temperature	K
Tliquidus	Liquidus temperature	K
V,$\overrightarrow{V}$	Velocity, velocity vector	ms−1

1.1 Greek Symbols

αsf	Surface Area density	m−1
β	Liquid fraction	–
γ	Thermal expansion coefficient	K−1
ε	Porosity	–
η	Dimensionless coordinate	x/LR
μ	Viscosity of material	kgm−1 s−1
ξ	Dimensionless coordinate	y/LR
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