# Looking for Energy Losses of a Rotary Permanent Magnet Magnetic Refrigerator to Optimize Its Performances

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{H}) equal to 22 °C [35]. Furthermore, ‘8MAG’ showed a maximum second-law efficiency of 2.4% at T

_{H}= 22 °C and a temperature span of 3.3 K. These results are comparable to the performance of the magnetic refrigerator prototype presented by Capovilla et al. [42].

## 2. The Prototype and the Experimental Measurement System

## 3. Energy Losses Model

#### 3.1. Mechanical Model

_{gd}) acts on this component, with a magnitude dependent on the working temperatures of the regenerators (hot and cold end). In detail, the magnitude of the resistant torque follows an oscillating trend, according to the alternative attraction and rejection of the magnets during the AMR cycle. This oscillation reduces with the increase of the rotational frequency due to the inertial phenomena related to the distribution of the rotating mass of the magnets. However, other two energy losses must be considered in ‘8MAG’ related to the drive shaft, and therefore to the rotary valve.

_{ec}) that leads to increase the work needed to move the magnetic assembly. Moreover, the friction caused by the sliding of the bearings and seals of the rotary valve represents an additional resistant torque (TO

_{fr}) on the drive shaft. Observing Figure 2, it is possible to write the following torque balance equation at steady-state conditions (neglecting the inertial term)

_{ec}, was performed by a mathematical model composed by three sub-model: the static magnetic field model (SMF), the stationary eddy currents power dissipation model (SECP), and the stationary thermal model (ST). The friction term (${\dot{W}}_{fr}\left(\omega \right)$) was estimated by a semi-empirical approach, using technical data of the bearings and seals of the rotary valve and measuring the resistant torque ($T{o}_{fr}\left(\omega \right)$) to the rotary valve without the MCW and regenerators. Hence, it was possible to measure the resistant torque related to friction effects.

#### 3.1.1. Static Magnetic Field Model

_{r}) of 1370 mT.

^{−1}), $B$ is the magnetic flux density (T), $E$ is the electric field intensity (V m

^{−1}), ${D}_{E}$ the electric flux density (C m

^{−2}), $J$ is the electric current density (A m

^{−2}) and ${\rho}_{q}$ is the volume charge density (C m

^{−3}). The considered constitutive relations are shown in Equations (4)–(6)

^{−1}), $P$ is the electric polarization (in C m

^{−2}), ${\mu}_{0}$ is the vacuum permeability (in H m

^{−1}), $M$ is the magnetization (in A m

^{−1}) and $\sigma $ is the electrical conductivity. The boundary conditions at the material interfaces and physical boundaries are represented by the equations

#### 3.1.2. Stationary Eddy Currents Power Dissipation Model

#### 3.1.3. Stationary Thermal Model

^{−2}K

^{−1}, considering the following experimental correlation for the convective heat transfer coefficient (${h}_{c}$) expressed in W m

^{−2}K

^{−1}, as a function of the rotating frequency f (in Hz)

#### 3.1.4. Semi-Empirical Evaluation of Friction Losses

#### 3.2. Thermal Model

## 4. Model Validation

#### 4.1. Mechanical Model Validation

_{z}. A good agreement was found between experiments and simulation, highlighting that the model can reproduce magnetic field distribution, peaks, and valleys. Locally comparing measured and simulated data, a narrow absolute error emerged (−0.09 T), whereas the maximum relative error is of about 15%. The comparison between experiments and simulation of some representative points is shown in Table 2.

#### 4.2. Thermal Model Validation

## 5. Results and Discussion

^{−1}, and operating frequency ($f$) for three different levels of cooling power (50 W, 100 W, and 200 W) at a hot source temperature of 22 °C. From Figure 15, it is evident that COP decreases with the operating frequency increasing (at a constant cooling power) since the mechanical power required to move the magnets increases. The same trend can be noticed also considering the volumetric flow rate, even if it is less marked. However, the experimental tests showed that ‘8MAG’ can achieve a maximum COP of about 2.5 with a cooling power equal to 200 W and a temperature span of 2 K. These results represent the baseline of the ‘8MAG’ performance and they are used as a comparison to evaluate the possible improvements which could be achieved reducing the mechanical and thermal losses calculated by the models described in Section 3, regarding eddy currents and intrinsic thermal load of the rotary valve.

#### 5.1. COP Improvement by Reducing Eddy Currents

#### 5.2. COP Improvement by Reducing Parasitic Thermal Load

#### 5.3. Overall Achievable COP Improvement

^{−1}). Good improvements can be achieved also for lower cooling power, with maximum increases of the COP value of 0.65 and 0.8, with cooling power of 50 W and 100 W, respectively.

_{H}= 16 °C and a temperature span of 4.7 K, if the energy losses evaluated in this work can be reduced.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Barclay, J.A. Theory of an Active Magnetic Regenerative Refrigerator. United States. Available online: https://www.osti.gov/servlets/purl/6224820 (accessed on 26 July 2019).
- Steven Brown, J.; Domanski, P.A. Review of alternative cooling technologies. Appl. Therm. Eng.
**2014**, 64, 252–262. [Google Scholar] [CrossRef] - Rowe, A. Thermodynamics of active magnetic regenerators: Part I. Cryogenics
**2012**, 52, 111–118. [Google Scholar] [CrossRef] - Rowe, A. Thermodynamics of active magnetic regenerators: Part II. Cryogenics
**2012**, 52, 119–128. [Google Scholar] [CrossRef] - Aprea, C.; Greco, A.; Maiorino, A.; Masselli, C. The environmental impact of solid-state materials working in an active caloric refrigerator compared to a vapor compression cooler. Int. J. Heat Technol.
**2018**, 36, 1155–1162. [Google Scholar] [CrossRef] - Aprea, C.; Greco, A.; Maiorino, A.; Masselli, C. Magnetic refrigeration: An eco-friendly technology for the refrigeration at room temperature. J. Phys. Conf. Ser.
**2015**, 655, 012026. [Google Scholar] [CrossRef] - Greco, A.; Aprea, C.; Maiorino, A.; Masselli, C. A review of the state of the art of solid-state caloric cooling processes at room-temperature before 2019. Int. J. Refrig.
**2019**, 106, 66–88. [Google Scholar] [CrossRef] - Yu, B.; Liu, M.; Egolf, P.W.; Kitanovski, A. A review of magnetic refrigerator and heat pump prototypes built before the year 2010. Int. J. Refrig.
**2010**, 33, 1029–1060. [Google Scholar] [CrossRef] - Engelbrecht, K.; Pryds, N. Progress in magnetic refrigeration and future challenges. In Proceedings of the 6th IIF-IIR International Conference on Magnetic Refrigeration. International Institute of Refrigeration, Victoria, BC, Canada, 7–10 September2014. [Google Scholar]
- Lozano, J.A.; Engelbrecht, K.; Bahl, C.R.H.; Nielsen, K.K.; Eriksen, D.; Olsen, U.L.; Barbosa, J.R.; Smith, A.; Prata, A.T.; Pryds, N. Performance analysis of a rotary active magnetic refrigerator. Appl. Energy
**2013**, 111, 669–680. [Google Scholar] [CrossRef] - Rowe, A. Configuration and performance analysis of magnetic refrigerators. Int. J. Refrig.
**2011**, 34, 168–177. [Google Scholar] [CrossRef] - Rosario, L.; Rahman, M.M. Analysis of a magnetic refrigerator. Appl. Therm. Eng.
**2011**, 31, 1082–1090. [Google Scholar] [CrossRef] - Romero Gómez, J.; Ferreiro Garcia, R.; Carbia Carril, J.; Romero Gómez, M. Experimental analysis of a reciprocating magnetic refrigeration prototype. Int. J. Refrig.
**2013**, 36, 1388–1398. [Google Scholar] [CrossRef] - Lozano, J.A.; Engelbrecht, K.; Bahl, C.R.H.; Nielsen, K.K.; Barbosa, J.R.; Prata, A.T.; Pryds, N. Experimental and numerical results of a high frequency rotating active magnetic refrigerator. Int. J. Refrig.
**2014**, 37, 92–98. [Google Scholar] [CrossRef] - Aprea, C.; Greco, A.; Maiorino, A.; Masselli, C. The energy performances of a rotary permanent magnet magnetic refrigerator. Int. J. Refrig.
**2016**, 61, 1–11. [Google Scholar] [CrossRef] - Aprea, C.; Greco, A.; Maiorino, A.; Mastrullo, R.; Tura, A. Initial experimental results from a rotary permanent magnet magnetic refrigerator. Int. J. Refrig.
**2014**, 43, 111–122. [Google Scholar] [CrossRef] - Lozano, J.A.; Capovilla, M.S.; Trevizoli, P.V.; Engelbrecht, K.; Bahl, C.R.H.; Barbosa, J.R. Development of a novel rotary magnetic refrigerator. Int. J. Refrig.
**2016**, 68, 187–197. [Google Scholar] [CrossRef] - Eriksen, D.; Engelbrecht, K.; Bahl, C.R.H.; Bjørk, R.; Nielsen, K.K.; Insinga, A.R.; Pryds, N. Design and experimental tests of a rotary active magnetic regenerator prototype. Int. J. Refrig.
**2015**, 58, 14–21. [Google Scholar] [CrossRef] - Huang, B.; Lai, J.W.; Zeng, D.C.; Zheng, Z.G.; Harrison, B.; Oort, A.; van Dijk, N.H.; Brück, E. Development of an experimental rotary magnetic refrigerator prototype. Int. J. Refrig.
**2019**, 104, 42–50. [Google Scholar] [CrossRef] - Albertini, F.; Bennati, C.; Bianchi, M.; Branchini, L.; Cugini, F.; De Pascale, A.; Fabbrici, S.; Melino, F.; Ottaviano, S.; Peretto, A.; et al. Preliminary Investigation on a Rotary Magnetocaloric Refrigerator Prototype. Energy Procedia
**2017**, 142, 1288–1293. [Google Scholar] [CrossRef] - Gimaev, R.; Spichkin, Y.; Kovalev, B.; Kamilov, K.; Zverev, V.; Tishin, A. Review on magnetic refrigeration devices based on HTSC materials. Int. J. Refrig.
**2019**, 100, 1–12. [Google Scholar] [CrossRef] - Plaznik, U.; Tušek, J.; Kitanovski, A.; Poredoš, A. Numerical and experimental analyses of different magnetic thermodynamic cycles with an active magnetic regenerator. Appl. Therm. Eng.
**2013**, 59, 52–59. [Google Scholar] [CrossRef] - Kitanovski, A.; Plaznik, U.; Tušek, J.; Poredoš, A. New thermodynamic cycles for magnetic refrigeration. Int. J. Refrig.
**2014**, 37, 28–35. [Google Scholar] [CrossRef] - Lucia, U. General approach to obtain the magnetic refrigeretion ideal coefficient of performance. Phys. A Stat. Mech. Its Appl.
**2008**, 387, 3477–3479. [Google Scholar] [CrossRef] - Trevizoli, P.V.; Nakashima, A.T.; Peixer, G.F.; Barbosa, J.R. Évaluation de la performance d’un régénérateur magnétique actif pour les applications de refroidissement—Partie I: Analyse expérimentale et performance thermodynamique. Int. J. Refrig.
**2016**, 72, 192–205. [Google Scholar] [CrossRef] - Aprea, C.; Greco, A.; Maiorino, A.; Masselli, C. A comparison between rare earth and transition metals working as magnetic materials in an AMR refrigerator in the room temperature range. Appl. Therm. Eng.
**2015**, 91, 767–777. [Google Scholar] [CrossRef] - Aprea, C.; Greco, A.; Maiorino, A. A dimensionless numerical analysis for the optimization of an active magnetic regenerative refrigerant cycle. Int. J. Energy Res.
**2013**, 37, 1475–1487. [Google Scholar] [CrossRef] - Gao, X.Q.; Shen, J.; He, X.N.; Tang, C.C.; Li, K.; Dai, W.; Li, Z.X.; Jia, J.C.; Gong, M.Q.; Wu, J.F. Improvements of a room-temperature magnetic refrigerator combined with Stirling cycle refrigeration effect. Int. J. Refrig.
**2016**, 67, 330–335. [Google Scholar] [CrossRef] - He, X.N.; Gong, M.Q.; Zhang, H.; Dai, W.; Shen, J.; Wu, J.F. Design and performance of a room-temperature hybrid magnetic refrigerator combined with Stirling gas refrigeration effect. Int. J. Refrig.
**2013**, 36, 1465–1471. [Google Scholar] [CrossRef] - Aprea, C.; Greco, A.; Maiorino, A. GeoThermag: A geothermal magnetic refrigerator. Int. J. Refrig.
**2015**, 59, 75–83. [Google Scholar] [CrossRef] - Lucas, C.; Koehler, J. Experimental investigation of the COP improvement of a refrigeration cycle by use of an ejector. Int. J. Refrig.
**2012**, 35, 1595–1603. [Google Scholar] [CrossRef] - Aprea, C.; Greco, A.; Maiorino, A. An application of the artificial neural network to optimise the energy performances of a magnetic refrigerator. Int. J. Refrig.
**2017**, 82, 238–251. [Google Scholar] [CrossRef] - Qian, S.; Yuan, L.; Yu, J.; Yan, G. Variable load control strategy for room-temperature magnetocaloric cooling applications. Energy
**2018**, 153, 763–775. [Google Scholar] [CrossRef] - Qian, S.; Yuan, L.; Yu, J. An online optimum control method for magnetic cooling systems under variable load operation. Int. J. Refrig.
**2019**, 97, 97–107. [Google Scholar] [CrossRef] - Aprea, C.; Cardillo, G.; Greco, A.; Maiorino, A.; Masselli, C. A rotary permanent magnet magnetic refrigerator based on AMR cycle. Appl. Therm. Eng.
**2016**, 101, 699–703. [Google Scholar] [CrossRef] - Lei, T.; Engelbrecht, K.; Nielsen, K.K.; Veje, C.T. Study of geometries of active magnetic regenerators for room temperature magnetocaloric refrigeration. Appl. Therm. Eng.
**2017**, 111, 1232–1243. [Google Scholar] [CrossRef] [Green Version] - Arnold, D.S.; Tura, A.; Ruebsaat-Trott, A.; Rowe, A. Design improvements of a permanent magnet active magnetic refrigerator. Int. J. Refrig.
**2014**, 37, 99–105. [Google Scholar] [CrossRef] - Monfared, B. Design and optimization of regenerators of a rotary magnetic refrigeration device using a detailed simulation model. Int. J. Refrig.
**2018**, 88, 260–274. [Google Scholar] [CrossRef] - Li, Z.; Shen, J.; Li, K.; Gao, X.; Guo, X.; Dai, W. Assessment of three different gadolinium-based regenerators in a rotary-type magnetic refrigerator. Appl. Therm. Eng.
**2019**, 153, 159–167. [Google Scholar] [CrossRef] - Klinar, K.; Tomc, U.; Jelenc, B.; Nosan, S.; Kitanovski, A. New frontiers in magnetic refrigeration with high oscillation energy-efficient electromagnets. Appl. Energy
**2019**, 236, 1062–1077. [Google Scholar] [CrossRef] - Czernuszewicz, A.; Kaleta, J.; Kołosowski, D.; Lewandowski, D. Experimental study of the effect of regenerator bed length on the performance of a magnetic cooling system. Int. J. Refrig.
**2019**, 97, 49–55. [Google Scholar] [CrossRef] - Capovilla, M.S.; Lozano, J.A.; Trevizoli, P.V.; Barbosa, J.R. Performance evaluation of a magnetic refrigeration system. Sci. Technol. Built Environ.
**2016**, 22, 534–543. [Google Scholar] [CrossRef]

**Figure 1.**Prototype core details in cross-section (

**a**) and 3-D view of MCW (

**b**): (1) permanent magnet assembly; (2) magnets support; (3) shaft-rotary valve combination; (4) regenerators; (5) magneto caloric wheel (MCW); (6) cold sub-valve and (7) hot sub-valve.

**Figure 3.**Modelled geometries (

**a**), domain of the simulations (

**b**), and meshes of magnets and the MCW (

**c**).

**Figure 5.**Magnetic flux distribution (

**a**–

**c**), induced current density (

**b**–

**d**), and resistive losses (

**b**–

**d**) for two different positions of the magnets.

**Figure 6.**Temperature distribution on the MCW surface for a rotating frequency of 0.72 Hz, an ambient temperature of 20 °C and different heat transfer coefficients: 20 (

**a**) and 30 (

**b**) W m

^{−2}K

^{−1}. In the figures, the area of interest for the simulation is evidenced (black dotted lines).

**Figure 7.**Experimental resistant torque by friction effects (left y-axis) and correlated power dissipated (right y-axis) for different operating frequency.

**Figure 9.**Comparison between experimental (symbols) and simulation (full line) results of resistant torque (black symbols and full line on the left y-axis, only losses contribution) and mechanical power losses (grey symbols and full line on the right y-axis).

**Figure 10.**Temperature sensors positioning on the surface of the MCW. Sensors 1 and 2 were placed on the top and bottom surface of the MCW, respectively.

**Figure 11.**Surface temperature of the MCW in six different representative points as a function of operating frequency: experimental (symbols) vs. simulated (full lines) results.

**Figure 12.**An example of simulation results for a rotating frequency of 17 Hz (that corresponds to 1000 rpm) and for a hot source temperature T

_{H}of 22 °C.

**Figure 13.**Comparison of experimental measurements and model results of (

**a**,

**b**) surface temperatures of both sub-valves (${T}_{RV,C}$, ${T}_{RV,H}$) and (

**c**,

**d**) outlet water temperatures (${T}_{RV,C,out},\text{}{T}_{RV,H,out}$) for T

_{H}= 22 °C and different operating frequency.

**Figure 14.**Parasitic thermal load of the rotary valve simulated by the thermal model with different operating frequencies and hot source temperatures.

**Figure 15.**COP of ‘8MAG’ as a function of volumetric flow rate and operating frequency at T

_{H}= 22 °C and different cooling power (50 W, 100 W, and 200 W, from the top to the bottom). Temperature spans are in the range between 1 K and 8.5 K.

**Figure 16.**‘8MAG’ COP changing by reducing ECL on the MCW for different operating conditions at T

_{H}= 22 °C. Temperature spans are in the range between 1 K and 8.5 K.

**Figure 17.**‘8MAG’ COP changing by reducing thermal losses in the rotary valve for different operating conditions at T

_{H}= 22 °C. Temperature spans are in the range between 1 K and 8.5 K.

**Figure 18.**‘8MAG’ COP changing by reducing both thermal losses in the rotary valve and ECL on the MCW for different operating conditions at T

_{H}= 22 °C. Temperature spans are in the range between 1 K and 8.5 K.

Measurement | Instrument Type | Accuracy |
---|---|---|

Temperature | RTD 4 wires | 0.1 K |

Torque | Torque transducer | 0.5% |

Angular velocity | Optical encoder | 0.01° s^{−1} |

Magnetic field | Hall probe | 0.4% |

Water flow | Electromagnetic flowmeter | 0.5% |

Electrical power | Electromagnetic wattmeter | 0.2% |

X (cm) | y (cm) | B_{z_sim} (T) | B_{z_exp} (T) | Absolute Error (T) | Relative Error (%) |
---|---|---|---|---|---|

0 | 100 | 0.297 | 0.350 | −0.053 | −15.1 |

0 | −180 | −1.270 | −1.180 | −0.090 | 7.5 |

0 | −200 | −1.069 | −1.085 | 0.020 | −1.5 |

−100 | −180 | −0.827 | −0.800 | −0.030 | 3.4 |

−150 | 0 | 0.085 | 0.075 | 0.010 | 12.8 |

${\mathit{T}}_{\mathit{R}\mathit{V},\mathit{C}}$ | ${\mathit{T}}_{\mathit{R}\mathit{V},\mathit{H}}$ | ${\mathit{T}}_{\mathit{R}\mathit{V},\mathit{C},\mathit{o}\mathit{u}\mathit{t}}$ | ${\mathit{T}}_{\mathit{R}\mathit{V},\mathit{H},\mathit{o}\mathit{u}\mathit{t}}$ | |
---|---|---|---|---|

Relative error range (%) | 1.7–4.4 | 0.2–4.2 | 0.1–1.6 | 0.4–11.4 |

Absolute max error (°C) | 0.7 | 0.9 | 0.3 | 2.5 |

**Table 4.**Average ‘8MAG’ COP for different cooling power and hot source temperatures (T

_{H}). These values were obtained by an average among the experimental data at different volumetric flow rates and operating frequencies. Temperature spans are in the range between 1 K and 8.5 K.

COP_{ref} | COP_{ec} | COP_{Qc,loss} | COP_{ec+Qc,loss} | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

T_{H} [°C] | Ave | Max | Min | Ave | Max | Min | Ave | Max | Min | Ave | Max | Min | |

${\dot{\mathit{Q}}}_{\mathit{c}}\mathbf{=}\mathbf{50}W$ | 16 | 0.35 | 0.68 | 0.15 | 0.45 | 0.75 | 0.29 | 0.61 | 1.08 | 0.25 | 0.79 | 1.19 | 0.46 |

28.6% | 10.3% | 93.3% | 74.3% | 58.8% | 66.7% | 125.7% | 75.0% | 206.7% | |||||

22 | 0.35 | 0.68 | 0.15 | 0.45 | 0.75 | 0.29 | 0.64 | 1.09 | 0.28 | 0.83 | 1.21 | 0.51 | |

28.6% | 10.3% | 93.3% | 82.9% | 60.3% | 86.7% | 137.1% | 77.9% | 240.0% | |||||

32 | 0.38 | 0.69 | 0.15 | 0.49 | 0.79 | 0.28 | 0.64 | 1.04 | 0.26 | 0.85 | 1.25 | 0.48 | |

28.9% | 14.5% | 86.7% | 68.4% | 50.7% | 73.3% | 123.7% | 81.2% | 220.0% | |||||

${\dot{\mathit{Q}}}_{\mathit{c}}\mathbf{=}\mathbf{100}W$ | 16 | 0.66 | 1.22 | 0.28 | 0.83 | 1.35 | 0.52 | 0.94 | 1.64 | 0.37 | 1.18 | 1.82 | 0.70 |

25.8% | 10.7% | 85.7% | 42.4% | 34.4% | 32.1% | 78.8% | 49.2% | 150.0% | |||||

22 | 0.66 | 1.22 | 0.28 | 0.83 | 1.35 | 0.52 | 0.97 | 1.65 | 0.40 | 1.22 | 1.83 | 0.75 | |

25.8% | 10.7% | 85.7% | 47.0% | 35.2% | 42.9% | 84.8% | 50.0% | 167.9% | |||||

32 | 0.75 | 1.35 | 0.37 | 0.95 | 1.51 | 0.64 | 1.02 | 1.66 | 0.56 | 1.33 | 1.87 | 0.99 | |

26.7% | 11.9% | 73.0% | 36.0% | 23.0% | 51.4% | 77.3% | 38.5% | 167.6% | |||||

${\dot{\mathit{Q}}}_{\mathit{c}}\mathbf{=}\mathbf{200}W$ | 16 | 1.52 | 2.53 | 0.89 | 1.81 | 2.80 | 1.21 | 1.83 | 2.96 | 1.11 | 2.18 | 3.28 | 1.51 |

19.1% | 10.7% | 36.0% | 20.4% | 17.0% | 24.7% | 43.4% | 29.6% | 69.7% | |||||

22 | 1.52 | 2.53 | 0.89 | 1.81 | 2.80 | 1.21 | 1.86 | 2.97 | 1.15 | 2.23 | 3.29 | 1.57 | |

19.1% | 10.7% | 36.0% | 22.4% | 17.4% | 29.2% | 46.7% | 30.0% | 76.4% | |||||

32 | 1.58 | 1.97 | 1.21 | 1.83 | 2.22 | 1.44 | 1.86 | 2.26 | 1.47 | 2.16 | 2.54 | 1.76 | |

15.8% | 12.7% | 19.0% | 17.7% | 14.7% | 21.5% | 36.7% | 28.9% | 45.5% |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Maiorino, A.; Mauro, A.; Del Duca, M.G.; Mota-Babiloni, A.; Aprea, C.
Looking for Energy Losses of a Rotary Permanent Magnet Magnetic Refrigerator to Optimize Its Performances. *Energies* **2019**, *12*, 4388.
https://doi.org/10.3390/en12224388

**AMA Style**

Maiorino A, Mauro A, Del Duca MG, Mota-Babiloni A, Aprea C.
Looking for Energy Losses of a Rotary Permanent Magnet Magnetic Refrigerator to Optimize Its Performances. *Energies*. 2019; 12(22):4388.
https://doi.org/10.3390/en12224388

**Chicago/Turabian Style**

Maiorino, Angelo, Antongiulio Mauro, Manuel Gesù Del Duca, Adrián Mota-Babiloni, and Ciro Aprea.
2019. "Looking for Energy Losses of a Rotary Permanent Magnet Magnetic Refrigerator to Optimize Its Performances" *Energies* 12, no. 22: 4388.
https://doi.org/10.3390/en12224388