This paper presents a numerical model conceived for a multi-physics evaluation of a magnetic refrigeration system. The model takes into account the variable magnetic field, the characteristics of the magnetocaloric materials (MCM) as well as the efficiency of the fluid flow heat transfer between the hot and the cold sources via the MCM. This model allows us to optimize these elements and to determine their impact on the overall performance of a magnetocaloric device. We present here a finite-difference model of AMRR cycles for a sub-unit of MCM crossed by micro-channels of fluid connected to cold and hot regenerative receivers. Thus, the calculation of the output parameters such as the temperature span, and thermal power passing from the cold receiver to the hot receiver has been performed. The influence of the geometry of the MCM and the fluid flow were investigated over the working domain highlighting the current technological achievements and indicating possible improvements.