Exergoeconomic Analysis of a Cascade Active Magnetic Regenerative Refrigeration System

Abstract

In this paper, an exergoeconomic analysis of a cascade active magnetic regenerative (AMR) refrigeration system operating on a regenerative Brayton cycle is conducted with respect to various system design parameters. The finite difference method is used in order to solve the set of governing equations, which are highly nonlinear and coupled. In exergy analysis, a thermodynamic model is developed in order to determine exergy destruction rates and calculate the exergy efficiency of the system. In the economic analysis, investment cost rates are calculated with respect to equipment costs, which are determined by cost correlations for each system component, and capital recovery factors. Thus, by combining the two analyses, an exergoeconomic model is created whereby the exergy streams are identified and cost equations are allocated for each component. The results of both exergetic and exergoeconomic analyses show that increasing the fluid mass flow rate decreases the exergy efficiency, and increasing the specific exergetic cooling rate decreases the cost per unit of cooling.

Nomenclature

A_c :

Cross-sectional area, m ²

a_sf :

Specific surface area, m²/m³

c:

Specific heat capacity, 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 

MCE:

Magnetocaloric effect

MCM:

Magnetocaloric material

Nu:

Nusselt number

Pr:

Prandtl number

 $\dot{Q}$ :

Heat transfer rate, W

Re:

Reynolds number

s:

Specific entropy (J kg⁻¹ K⁻¹)

t:

Time coordinate, s

T:

Temperature, K

t₁ :

Magnetization time step (s)

t₂ :

Isofield cooling time step (s)

t₃ :

Demagnetization time step (s)

t₄ :

Isofield heating time step (s)

V:

Volume, L

x:

Axial position, m

x :

Mass fraction

 $\dot{W}$ :

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 (-)

μ:

The specific exergy cooling of the system (W T⁻¹ L⁻¹)

ad:

Adiabatic

C:

Cold or refrigeration temperature

D:

Demagnetization

des:

Destruction

ex:

Exergy

f:

Fluid

H:

Hot or heat rejection temperature

I:

First stage of the cascade system

II:

Second stage of the cascade system

M:

Magnetization

P:

Pump

s:

Solid

t₁ :

Magnetization process

t₂ :

Isofield cooling process

t₃ :

Demagnetization process

t₄ :

Isofield heating process

wg:

Water–glycol mixture