**5. Magnetostatic study**

From the definition of the MCE, it is obvious that the performance of a magnetic refrigeration system depends mainly on the efficiency of the MCE material and the strength of the magnetic field. Thus the study of magnetic field sources dedicated to magnetic refrigeration systems is of a paramount importance. In this section we will pay a particular attention to the design of these sources using the finite element method.

The field sources described throughout this section are built with permanent magnets (Neodymium Iron Boron) with a remanent magnetization of 1.46 *Br* = T and a magnetic permeability of 1.064 μ*<sup>r</sup>* = . The MCE material used is gadolinium with isotropic magnetic permeability 2 μ*<sup>r</sup>* = . In this study, MCE solid blocks are considered. However, in actuality to ensure a better heat exchange between the MCE material and the exchanging fluid, other forms are considered (plates, powder, etc). The yoke, when it exists, is made of XC10 steel.
