This work aimed to study the coefficient of performance (COP) of an active magnetic regenerative refrigeration (AMRR) system by new analytical approaches of magnetic work Wm(B,x,y) and magnetocaloric effect MCE (T,B). Those approaches were applied to a permanent magnet magnetic refrigerator. The studied refrigeration system consisted of four regenerators, each of which was formed by parallel plates of gadolinium, a circulation pump, a rotating magnet, and two heat exchangers. The heat transfer fluids used were water and gallium. A resolution of the continuity equation, the amount of movement equation, and the heat equation were carried out in order to study the temperature profile in both the regenerator and the fluid. Furthermore, the authors deduced the temperatures at the inlet and the outlet of the heat exchangers in order to establish a thermal balance.