Active Magnetic Regeneration - Magnetocaloric Energy Conversion: From Theory to Applications - page 108

4.3 Numerical Modelling of an Active Magnetic
Regenerator

With the aim of analysing the operation of a magnetic refrigerator in detail, a
number of theoretical (numerical) models were developed. Since for more than
30 years, the principle of the AMR has been considered as the most ef cient way to

exploit the magnetocaloric effect, the vast majority of these models are actually
AMR models. The modelling approach is especially important since the AMR
process has a highly multidisciplinary nature and involves thermodynamics, heat
transfer,

uid dynamics, solid-state physics and magnetism problems. Its perfor-
mance strongly depends on various operational conditions (utilization factor,
operational frequency, magnetic

fl

uid,
performed thermodynamic cycle) as well as on the magnetocaloric and geometrical
characteristics of the AMR (the type and geometry of the magnetocaloric materials
used and the related losses). It is crucial to understand the fundamental loss
mechanisms, their relations and the performance limits in order to develop and
design an ef

eld change and its pro le, heat-transfer fl

cient AMR and a subsequent high-performance magnetic refrigerator.

4.3.1 A Brief Review of AMR Numerical Models

A detailed review of the AMR numerical models developed up to 2010 is presented
in Nielsen et al. [ 33 ]. In general, there are two established approaches to AMR
modelling: steady-state, time-independent modelling and dynamic, time-dependent
modelling. However, the overall goal of all AMR models is to predict the perfor-
mance of a particular AMR in terms of cooling power, temperature span, ef

ciency,

input magnetic work, etc.
The steady-state models are, in general, simpler, with the aim being to estimate
the AMR

s performance without a detailed knowledge of its dynamic characteris-
tics during operation. The basic assumption of such a model is an ideal thermo-
dynamic cycle for the magnetocaloric material, while the corresponding losses, like
the heat transfer losses between the heat-transfer

'

uid and the magnetocaloric
material, the viscous losses, the losses due to longitudinal thermal conductivity, etc.
are subsequently taken into account, through the appropriate correlations and cor-
rection factors. The major bene

fl

ciency.
However, the predictive capabilities of steady-state models are limited, as they are
unable to include the interactions between the loss mechanisms, which are the main
disadvantage if this model is to be used for the development and optimization of a
real AMR device [ 33 ]. Some of the steady-state models can be found in, e.g. [ 27 ,
34

t of these models is their computational ef

37 ].
With the aim of a detailed understanding of the AMR cycle and its properties, a
number of time-dependent numerical models were developed. They are based on
the energy equations of the magnetocaloric material and the heat-transfer

-

fl uid