DATE: 2019.06 We have given a lecture to the class in the course of "Refrigeration Systems" in ODTÜ. Refrigeration technology has an important role over various areas such as medicine, food, manufacturing, and it is a very important element for a comfortable life for the society. It directly affects the people’s life by permiting to store the medicines and foods for long times, manufacturing with very high accuracy, air conditioning applications, etc. Although refrigeration technology have lots of benefits which has been mentioned above, conventional vapor compression/expansion systems have some weaknesses. Refrigerant fluids that are used in the traditional cooling/refrigeration applications have important effects over the global warming and ozone depletion. To be able to overcome these disadvantages of the refrigeration applications, new thecnologies which does not use harmful matirals such as traditional refrigerants are investigated. One of these developing technologies is magnetic refrigeration systems. Magnetic refrigeration systems are commonly used in the low temperature applications and it also has usage in air conditioning applications, aerospace technologies and telecommunication technologies. Magnetic refrigeration has lots of advantages such that: 1. It uses very small amount of energy compared to compressor work inlet of a similar size vapor compression/expansion system. 2. It is highly more compact and makes less noise than the traditional systems. 3. It has a lower operating and maintenance cost. 4. It is environment friendly and does not cause the global warming or ozone depletion. Although the magnetic refrigeration has lots of benefits which have been described above, because of its high initial cost and need of the very rare materials in the system, it is not very common recent days, however, it has a high potential for the future.

1. Magnetic Refrigeration
06.12.2019
A.B. Karsan, D.A. Yılmaz, S. Baykul
1. Introduction
Refrigeration technology has an important role over various areas such as medicine, food, manufacturing,
and it is a very important element for a comfortable life for the society. It directly affects the people’s life
by permiting to store the medicines and foods for long times, manufacturing with very high accuracy, air
conditioning applications, etc.
Although refrigeration technology have lots of benefits which has been mentioned above, conventional
vapor compression/expansion systems have some weaknesses. Refrigerant fluids that are used in the
traditional cooling/refrigeration applications have important effects over the global warming and ozone
depletion. To be able to overcome these disadvantages of the refrigeration applications, new thecnologies
which does not use harmful matirals such as traditional refrigerants are investigated. One of these
developing technologies is magnetic refrigeration systems.
Magnetic refrigeration systems are commonly used in the low temperature applications and it also has
usage in air conditioning applications, aerospace technologies and telecommunication technologies.
Magnetic refrigeration has lots of advantages such that:
1. It uses very small amount of energy compared to compressor work inlet of a similar size vapor
compression/expansion system.
2. It is highly more compact and makes less noise than the traditional systems.
3. It has a lower operating and maintenance cost.
4. It is environment friendly and does not cause the global warming or ozone depletion.
Although the magnetic refrigeration has lots of benefits which have been described above, because of its
high initial cost and need of the very rare materials in the system, it is not very common recent days,
however, it has a high potential for the future.

2. 2. Magnetocaloric Effect
Magnetic refrigeration systems are based on magnetocaloric effect (MCE) of a material which is the
temperature change related to the behavior phase change of the material under a magnetic field in a certain
temperature interval. This effect is observed for the first time by the German scientist E. Warburg in 1881.
He noticed a temperature raise on an iron sample under when applied a magnetic field over the sample
and a temperature decrease when the magnetic field is removed (Bohigas, 2000; Zimm, 2007). Material
which shows this behavior under a magnetic field is called as Magnetocaloric Materials (MCM).
MCE could be observed in all transition metals and lanthanide-series elements which also could have
ferromagnetic behavior in addition to their magnetocaloric behavior or not. The main reason of this
temperature increase under a magnetic field is when an MCM is under a magnetic field , the magnetic
moments of these metal atoms tries to align parallel to the field and the thermal energy is emitted till the
magnetic moments of the all atoms become parallel to the field. This emitted thermal energy causes an
increase of temperature. After removing the magnetic field, the magnetic moments of the atoms return to
a random orientation and MCM cools down (Gschneidner, 1998). This effect is basically demonstrated in
Fig 1.
Figure 1: Demonstration of magnetic moment of atoms under a magnetic field [3]

3. 3. Thermodynamics
3.1. Thermodynamics of the Magnetocaloric Effect
At the magnetic cooling and heat pump applications, thermodynamics helps to understand the relation
between magnetocaloric effect and .... Although the laws of thermodynamics still valid for magnetic
refrigeration applications there are little differences between conventional vapor compression/expansion
systems.
First law of thermodynamics could be seen in the Eq. (1). As conventional systems 𝑢 represents the specific
internal energy, 𝑄 is the total transferred heat and q is the heat flux. Different than the conventional
systems, magnetic work term, 𝑀$$⃗ 𝑑𝐵$⃗ is used instead of the shaft work.
𝑑𝑢 = 𝛿𝑄 −𝑀$$⃗ 𝑑𝐵$⃗ = −𝑑𝑖𝑣(𝛿𝑞⃗) −𝑀$$⃗ 𝑑𝐵$⃗
The second law of thermodynamics could be seen at Eq. (2). In the equation, 𝑠 is a state function which is
related to the specific entropy and 𝑠12345674 is a positive function related to the entropy production.
𝑑𝑠 = 𝑑𝑖𝑣 8
𝛿𝑞⃗
𝑇
: + 𝛿𝑠12345674
For a volume small enough, by considering thermodynamic equilibrium, second law of thermodynamics
could be shown as in Eq. (2). Note that 𝐻 represents the magnitude of the magnetic field and 𝑐> is the heat
capacity at constant magnetic field and is defined as 𝑇 𝜕𝑠/𝜕𝑇|> respectively.
𝑇𝑑𝑠 = 𝛿𝑄 + 𝑇𝛿𝑠12345674 = 𝑐> 𝑑𝑇 + 𝑇
𝛿𝑠
𝛿𝐻
𝑑𝐻
Temperature change in adiabatic conditions is the most important part in magnetic refrigeration cycle and
the second law of thermodynamics has a vital role while explaining this phenomena since the temperature
increase or decrease in adiabatic condition is depends on the irriversible effect of entropy proction only.
Therefore, temperature difference caused by magnetocaloric effect could be calculated by solving the ODE
which is given in Eq. (4).
𝑑𝑇
𝑑𝐻
= −
𝑇
𝑐>
𝛿𝑠
𝛿𝐻
+
𝑇
𝑐>
𝛿𝑠12345674
𝑑𝐻
In the Eq. (2), it could be seen that the entropy production is fed by two terms. The first term is a result of
heat transfer and other one is a result of the entropy production of the material. Since the second term is
not directly related to heat diffusion, it will be neglected at the following parts.
After neglecting the 𝑠12345674 term, three functions which are 𝛿𝑠/𝛿𝐻 (𝑇, 𝐻), 𝑐> (𝑇, 𝐻) and 𝑀 (𝑇, 𝐻)
should be determined. Note that, 𝑀 refers the magnetization. The experimental data about the relation
between three terms (𝑀, 𝑐> and 𝑇) could be seen in Fig. (2).
Figure 2: . Oxide Pr0.65 𝑆𝑟0.35 𝑀𝑛𝑂3 measured with a calorimeter and an extraction type magnetometer at CRISMAT laboratory (Caen – France) [4]

4. And finally, ordinary differential equation which is given in Eq. (4) could be solved numericaly by using
correlations taken from experimental data and Maxwell relations. Note that the correlated equations
should assure the first and second law of thermodynamics and it should be checked. The results of
numerical solution of Eq. (4) and Maxwell equations could be seen in Fig. (3).
Figure 3: Properties deduced from Fig. 3 with the resolution of ODE and Maxwell relations [4]
3.2. Thermodynamics of the Magnetic Refrigeration
To be able to use the MCE in cooling, refrigeration or heat pump applications, generally common
thermodynamic cycles are used. Similar to the traditional vapor compression refrigeration systems,
magnetic refrigeration system basically 4 different steps:
1. Adiabatic magnetization
2. Heat exchange under the constant magnetic field with the hot resevoire.
3. Adiabatic demagnetization
4. Heat exchance under the constant magnetic field with the cold resevoire.
While comparing to the traditional refrigeration systems, adiabatic vapor compression and expansion
replaced by the adiabatic magnetization and demagnetization. Also the heat excange at constant pressure
is replaced by the heat exchange under the constant magnetic field. A visual comparison of the vapor
compression/expansion cycle and magnetic refrigeration cyle could be seen in Fig. (4).
Figure 4: Comparison of a the vapor compression/expansion cycle and a magnetic refrigeration cyle [5]

5. Since the magnetocaloric effect is the driving phenomena in the magnetic refrigeration applications, the
performance of the system is directly related to performance characteristics of the magnetocaloric
materials which is characterized by 3 important parameters:
1. The adiabatic temperature change by the effect of the change in applied magnetic field (∆𝑇)
2. Isothermal entropy change by the effect of the change in applied magnetic field (∆𝑠)
3. Curie temperature (𝑇6)
Note that the Curie temperature is the temperature that the highest magnetocaloric effect occurs and it is
depends on the magnetocaloric material.
An example of the T-s diagram of the thermodynamic cycle for 1T magnetic field change could be seen in
Fig. (5). Also the adiabatic temperature change (∆𝑇) and the Isothermal entropy change (∆𝑠) could be seen
in the diagram.
Figure 5: Brayton Cycle for first order phase transition material. First order tansition is delimited by dashed lines. [4]
As traditional vapor compression/expansion cycles, the coefficient of the performans (COP) of the cycle
could be determined with respect to heat rejected from the cooled space and the work input to the system.
However, as the first law of thermodynamics, shaft work in the COP equation of traditional cycles should
be replaced with the magnetic work. The final form of the COP equation could be seen in Eq. (5)

6. 4. Magnetic Refrigeration Systems
There are various different magnetic refrigeration system according to the different needs. Although that
differences between systems could be directly thermodynamic based (e.g. usage of Cascade cycle for the
applications with high cooling loads) it also could be based on physical components (e.g. usage of different
heat exchanger types for heat transfer under the constant magnetic field). In that part, only one example
of the magnetic refrigeration systems and its components will be discussed. Examples of other magnetic
refrigeration systems could be seen at [adfwefc]
Following example is a refrigerator application at the near room temperature and its schematic drawing
could be seen at Fig. (6).
Figure 6: Flow process diagram of a magnetic refrigeration system [6]
Consists of two beds containing spherical powder of Gadolinium with water being used as the heat transfer
fluid. The fluid first passes through the hot heat exchanger, which uses air to transfer heat to the
atmosphere. The fluid then passes through the copper plates attached to the no magnetized cooler-
magneto caloric beds and loses heat. A fan blows air over this cold fluid into the freezer. The heat transfer
fluid then gets heated up as it passes through the copper plates adjoined by the magnetized warmer
magneto caloric beds, where it continues to cycle around the loop. However, the magneto caloric beds
simultaneously move up and down, into and out of the magnetic field. The cold air from the freezer is blown
into the refrigerator by the freezer fan.

7. Figure 7: Flow process diagram of a magnetic refrigeration system [6]
The components to be able to construct the magnetic refrigeration system which is given in the Fig. (7) are
as follows:
1. Magnets: Magnets are the main functioning element of the magnetic refrigeration. Magnets
provide the magnetic field to the material so that they can lose or gain the heat to the surrounding
and from the space to be cooled respectively.
2. Hot Heat Exchanger: The hot heat exchanger absorbs the heat from the material used and gives
off to the surrounding. It makes the transfer of heat much effective.
3. Cold Heat Exchanger: The cold heat exchanger absorbs the heat from the space to be cooled and
gives it to the magnetic material. It helps to make the absorption of heat effective.
4. Drive: Drive provides the right rotation to the heat to rightly handle it. Due to this heat flows in the
right desired direction.
5. Magnetocaloric Wheel: It forms the structure of the whole device. It joins both the two magnets
to work properly.

8. 5. Magnetocaloric Materials
Magnetocaloric materials are materials which show the magnetocaloric bahavior under a magnetic field.
Although in transition metals and lanthanide-series elements shows the magnetocaloric behavior, only a
limited number of magnetic materials possess a large enough magnetocaloric effect to be used in practical
refrigeration systems. The search for the "best" materials is focused on rare earth metals, either in pure
form or combined with other metals into alloys and compounds.
The magnetocaloric effect is an intrinsic property of a magnetic solid. This thermal response of a solid to
the application or removal of magnetic fields is maximized when the solid is near its magnetic ordering
temperature.
The magnitudes of the magnetic entropy and the adiabatic temperature changes are strongly dependent
upon the magnetic order process: the magnitude is generally small in antiferromagnets, ferrimagnets and
spin glass systems; it can be substantial for normal ferromagnets which undergo a second order magnetic
transition; and it is generally the largest for a ferromagnet which undergoes a first order magnetic
transition.
Also, crystalline electric fields and pressure can have a substantial influence on magnetic entropy and
adiabatic temperature changes. Currently, alloys of gadolinium producing 3 to 4 K per tesla of change in a
magnetic field can be used for magnetic refrigeration or power generation purposes.
The magnetocaloric materials can be categorized as regards the order of the phase transition:
1. 1st Order Phase Transition
2. 2nd Order Phase Transition
1st Order Phase Transition is also called as 1st order magneto-structural transition and it should take place
at constant temperature. Thus, the change in magnetization with temperature, can be infinitely large,
resulting quite large MCE values. This is called as giant magnetocaloric effect (GMCE) by Pecharsky and
Gschneidner in 1997. Example material: Gd5Si2Ge2 (Gadolinium-silicon-germanium alloy).
The second order phase transition is also referred as continuous phase transition. Gadolinium (Gd) or
transition metal based amorphous alloys are examples of magnetic refrigerant materials which undergo
this kind of transition.
One of the most important examples of the magnetocaloric effect is in the chemical element gadolinium
and some of its alloys. Gadolinium's temperature is observed to increase when it enters certain magnetic
fields. When it leaves the magnetic field, the temperature returns to normal. The effect is considerably
stronger for the gadolinium alloy Gd5 (Si2Ge2). Since Brown first applied ferromagnetic material gadolinium
(Gd) in the room temperature magnetic refrigerator in 1976, the research range for magnetic refrigeration
working materials has been greatly expanded. Praseodymium alloyed with nickel (Pr Ni 5) has such a strong
magnetocaloric effect that it has allowed scientists to approach within one thousandth of a degree of
absolute zero. [7] This compound is used as a cryogenic refrigerant in an adiabatic demagnetization
refrigerator to reach the millidegree Kelvin temperature range in 1975. [8]

9. 6. Future of the Magnetocaloric Materials and Magnetic Refrigeration
Recent research on materials that exhibit a giant entropy change showed that Gd5(SixGe1 − x)4, La(FexSi1
− x)13Hx and MnFeP1 – xAsx alloys, for example, are some of the most promising substitutes for Gadolinium
and its alloys (GdDy, GdTy, etc...). These materials are called giant magnetocaloric effect materials (GMCE).
Gadolinium and its alloys are the best material available today for magnetic refrigeration near room
temperature since they undergo second-order phase transitions which have no magnetic or thermal
hysteresis involved.
Some magnetic materials that are promise to be used in the future, the following list of promising categories
of magnetocaloric materials for application in magnetic refrigerators:
1. binary and ternary intermetallic compounds
2. gadolinium-silicon-germanium compounds
3. manganites
4. lanthanum-iron based compounds
5. manganese-antimony arsenide
6. iron-manganese-arsenic phosphides
7. amorphous fine met-type alloys (very recent)
In general, at the present stage of the development of magnetic refrigerators with permanent magnets,
hardly any freezing applications are feasible. These results, because large temperature spans occur between
the heat source and the heat sink.
An option to realize magnetic freezing applications could be the use of superconducting magnets. However,
this may only be economic in the case of rather large refrigeration units. Such are used for freezing, e.g. in
cooling plants in the food industry or in large marine freezing applications.
Some of the future applications of the magnetic refrigeration systems are:
1. Magnetic household refrigeration appliances
2. Magnetic cooling and air conditioning in buildings and houses
3. Central cooling system
4. Refrigeration in medicine
5. Cooling in food industry and storage
6. Cooling in transportation
7. Cooling of electronics

10. References
[1] Bohigas, X., Molins, E., Roig, A., Tejada, J., Zhang, X.X. (2000). Room-temperature magnetic refrigerator
using permanent magnets. IEEE Transactions on Magnetics, 36 (3), 538- 544.
[2] Gschneidner, K., Pecharsky, V. (1998). The Giant Magnetocaloric Effect in Gd5 (SixGe1-x4) Materials for
Magnetic Refrigeration” Advances in Cryogenic Engineering, Plenum Press, New York, pp. 1729.
[3] https://www.ifw-dresden.de/institutes/imw/research/functional-magnetic-films/caloric-films/
[4] Morgan Almanza, Afef Kedous-Lebouc, Jean-Paul Yonnet, Ulrich Legait, Julien Roudaut. Magnetic
refrigeration: recent developments and alternative configurations. European Physical Journal: Applied
Physics, EDP Sciences, 2015, 71 (1), pp.10903. ff10.1051/epjap/2015150065ff. ffhal-01315678f
[5] N. A. Mezaal, K. V. Osintsev, T. B. Zhirgalova, Review of magnetic refrigeration system as alternative to
conventional refrigeration system, 2017 IOP Conf. Ser.: Earth Environ. Sci. 87 032024
[6] Agrawal, A. (2009) A Seminar Report On Magnetic Refrigeration, Rajasthan Technıcal Unıversıty, Kota.
[7] Leitão, José Vieira. “High Refrigerant Capacity of PrNi5−XCox Magnetic Compounds Exploiting Its Spin
Reorientation and Magnetic Transition over a Wide Temperature Zone.” JOURNAL OF PHYSICS D: APPLIED
PHYSICS (2009): n. pag. Print.
[8]https://patents.google.com/patent/US4028905
[9]https://ntrs.nasa.gov/search.jsp?R=19820012245&hterms&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3D
All%26N%3D0%26No%3D50%26Ntt%3Drefrigeration
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