Energy and Exergy Analyses of an Active Magnetic Refrigerator

Abstract

In this paper, a thermodynamic model for predicting the performance of active magnetic refrigerator (AMR) is developed using energy and exergy analyses. Through this model, the cooling power, total power consumption, as well as the coefficient of performance (COP), exergy efficiency and exergy destruction rates of an AMR are determined. The effects of increasing mass flow rate on the COP, exergy efficiency and exergy destruction rates of the system are investigated. The results are presented to show that when mass flow rate increases, the COP and exergy efficiency curves reach their maximum values and then slightly decreases with increasing mass flow rate. The rate of exergy destruction increases with increasing mass flow rate due to the pump power requirements. The numerical results show that in order to reach optimal performance, mass flow rate must be adjusted carefully regarding to different operating conditions.

Nomenclature

Ac:

Cross-sectional area m²

a_sf :

Specific surface area m²/m³

c:

Specific heat J kg K⁻¹

COP:

Coefficient of performance

D:

Diameter of the regenerator section m

d_P :

Diameter of the particles μm

$\dot{\mathrm{E}}\mathrm{x}$ :

Exergy flow rate (W)

h:

Convection coefficient (W m⁻² K⁻¹)

H:

Magnetic field A m⁻¹

H_max :

Maximum magnetic field A m⁻¹

k:

Thermal conductivity W m⁻¹ K⁻¹

L:

Length of the regenerator m

m:

Mass kg

$\dot{\mathrm{m}}$ :

Mass flow rate kg s⁻¹

M:

Magnetic intensity A m⁻¹

Nu:

Nusselt number

Pr:

Prandtl number

$\dot{Q}$ :

Heat transfer rate, W

Re:

Reynolds number dimensionless

s:

Specific entropy (J kg⁻¹ K⁻¹)

t:

Time coordinate s

t₁ :

Magnetization time step (s)

t₂ :

Isofield cooling time step (s)

t₃ :

Demagnetization time step (s)

t₄ :

Isofield heating time step (s)

T:

Temperature K

u:

Local velocity m/s

V:

Volume L

X:

Axial position m

$\dot{W}$ :

Work kJ s⁻¹

ΔP:

Pressure drop Pa

ε :

Porosity of the regenerator bed

μ ₀ :

Permeability of free space (m kg s⁻² A⁻²)

ρ :

Density kg m⁻³

η :

Efficiency (−)

ad:

Adiabatic

C:

Cooling

D:

Demagnetization

des:

Destruction

ex:

Exergy

f:

Fluid

H:

Rejection

M:

Magnetic

P:

Pump

s:

Solid