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The analysis of the active magnetic refrigeration (AMR) cycle for different waveforms of both the magnetic field and the velocity of the heat transfer fluid is an essential challenge in designing and implementing heating and cooling systems based on the magnetocaloric effect. One of the most important issue is the correct modelling of the magnetic and thermal behavior of the active magnetocaloric materials (MCM) in order to estimate precisely cooling capacity of the magnetocaloric system. As the multiphysics coupling implies successive calls for both the thermal and the magnetic modelling subroutines, the execution time of these subroutines has to be as short as possible. For this purpose, a new magnetostatic model based on reluctance network has been performed to calculate the internal magnetic field and the internal magnetic flux density of the active magnetocaloric material (gadolinium, Gd) inside the air gap of the magnetic circuit. Compared to a 3D Finite Element Model (FEM), our magnetostatic semi-analytical model leads to a sharp drop of the computation time, while offering a similar precision for all magnetic quantities in the whole magnetocaloric system.

Compared to conventional vapor-compression refrigeration systems, magnetic refrigeration is a promising and potential alternative technology. The magnetocaloric effect (MCE) is used to produce heat and cold sources through a magnetocaloric material (MCM). The material is submitted to a magnetic field with active magnetic regenerative refrigeration (AMRR) cycles. Initially, this effect was widely used for cryogenic applications to achieve very low temperatures. However, this technology must be improved to replace vapor-compression devices operating around room temperature. Therefore, over the last 30 years, a lot of studies have been done to obtain more efficient devices. Thus, the modeling is a crucial step to perform a preliminary study and optimization. In this paper, after a large introduction on MCE research, a state-of-the-art of multi-physics modeling on the AMRR cycle modeling is made. To end this paper, a suggestion of innovative and advanced modeling solutions to study magnetocaloric regenerator is described.