Low computational cost semi-analytical magnetostatic model for magnetocaloric refrigeration systems

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.