**4. Conclusions**

In this study, the effect of different parameters, such as the fluid flow rate, porosity, spherical particle diameter, temperature span, and frequency, on the active magnetic refrigeration system was evaluated. As a result, the optimal parameter was obtained in each working condition. In this research, it was shown that the temperature span is inversely related to the refrigeration capacity and coefficient of performance. At high-fluid-flow rates, increasing the frequency makes it possible to increase the coefficient of performance and refrigeration capacity. The spherical particle diameter is one of the parameters that influence the performance of the magnetic refrigeration system, which is inversely related to the pressure drop. Therefore, by conducting a parametric study on the mass flow rate of the fluid and the diameter of spherical particles in each working condition, the pressure drop can be controlled and evaluated. In this study, an efficient numerical method is proposed that reduce the computational time and minimize numerical errors.

The study showed that the magnetic refrigeration system efficiency is highly dependent on the selected parameters. According to the refrigeration capacity and coefficient of performance, the designer of a magnetic refrigeration system can extract the required parameters from the design charts. Design charts and tables are of particular importance for the design of a magnetic refrigeration system because of their time-saving capacity. Furthermore, without having to make complex calculations and creating additional costs, the desired parameter can be selected from the tables and design charts. Some of the items to be monitored that should be considered in designing a magnetic refrigeration system are presented in Table 5.

The limitations of this study include the lack of laboratory equipment to accurately measure the properties of the magnetocaloric material and build a prototype of AMR model. Some errors in system modeling are due to the assumptions of a uniform distribution of fluid flow in all regenerators, that there is no leakage in the system and there is no detectable magnetic hysteresis. These items are difficult to implement in the experimental model, which results in a discrepancy between the numerical model and experimental data, and leads to an overestimation of the outputs of the numerical model. AMR modeling is an immature field and requires further detailed research. Using new methods to calculate the actual magnetic field would result in customer demands being met with higher accuracy. **Author Contributions:** Methodology, software, validation, formal analysis, writing—original draft preparation, resources A.E.; Conceptualization, review, editing and project administration A.V.; supervision and technical support, B.A.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
