The document discusses magnetic refrigeration and exergy analysis of magnetic refrigeration cycles. It explains the magnetocaloric effect and how magnetic fields can be used to achieve cooling via adiabatic demagnetization. Key equations presented include those relating the magnetocaloric effect to changes in magnetic field and temperature. The document also summarizes the reversible Brayton refrigeration cycle used in magnetic refrigeration and equations for the exergy efficiency and exergy destroyed. Major breakthroughs in 1997 that accelerated progress in the field are noted. In closing, the summary states that magnetic refrigeration provides an effective and efficient cooling method and has improved significantly since initial work in the 1920s-1930s.

1. Exergy analysis of Magnetic Refrigeration
Manojkumar Ashok Maurya

2. Magnetic refrigeration
• Magnetic refrigeration is cooling technology based on the Magnetocaloric effect.
• MCE is a phenomenon in which a reversible change in temperature of a suitable
material is caused by exposing the material to a changing magnetic field.
• For a ferromagnetic material near its magnetic ordering temperature (the Curie
temperature [TC]), when a magnetic field is applied, the unpaired 4f or 3d spins are
aligned with the magnetic field, which decreases the entropy in the isothermal
process or causes the sample to warm up in the adiabatic process.
• When the magnetic field is turned off the spins randomize increasing the entropy,
or the material cools.
• The phenomenon was first observed by Emil Warburg, a German physicist in the
year 1881.
• Major advances first appeared in the late 1920s when cooling via adiabatic
demagnetization was independently proposed by two scientists: Debye (1926) and
Giauque (1927).

3. Continued….
• The process was demonstrated a few years later when Giauque and
MacDougall in 1933 used it to reach a temperature of 0.25 K.
• In 1997, Prof. Karl A. Gscheidner, Jr. by the lowa State University at Ames
Laboratory demonstrated the first near room temperature proof of
concept magnetic refrigerator.

4. Working principle

5. Details of Thermodynamic Cycle
• Process is similar to gas
compression and expansion
cycle as used in regular
refrigeration cycle
• Steps of thermodynamic Cycle :->
 Adiabatic Magnetization
 Isomagnetic Enthalpy Transfer
Adiabatic demagnetization
Isomagnetic Entropic Transfer

6. Exergy
• The importance of developing thermal systems that
effectively uses energy resources such as oil, natural gas, and
coal is apparent.
• Effective use is determined by both first law and second laws
of thermodynamics
• Energy cannot be destroyed – states the first law
• However, the idea that something can be destroyed is useful
in the design and analysis of thermal systems
• This idea of destruction is not applicable for energy but exergy

7. Continue…
• Exergy can be defined as the part of the energy which has the potential to
be fully converted into mechanical work, which is the most valuable form
of energy
• According to first law of thermodynamics,
𝜙𝑑𝑞 = 𝜙𝑑𝑤
• However, on experimental basis, the second law adds some constraints on
the first law and introduces the concept of entropy
• By stating that the entropy of the universe is always increasing in the
actual processes, the concept of irreversibility and the idea of a
“spontaneous direction” in a process are therefore introduced
• Anergy derives from entropy and it represents the non-valuable part of
energy, i.e. the part that cannot be converted into work
• Exergy = Energy – Anergy

8. Idea behind Exergy
• The goal of exergy analysis is the effective energy resource use, fir it enables the
location, cause, and true magnitude of waste and loss to be determined
• Example: the expansion of a gas across a valve without a heat transfer occurs
without a loss, such an expansion is a site for thermodynamic inefficiency and can
be quantified by exergy analysis
• The concept of exergy has been derived from the 2nd law of thermodynamics and
is applicable to process or cycle
• The exergy concept help in analyzing the processes since they show the departure
of actual process from idealized process, thus suggesting the improvement in
thermodynamic cycle
• By analyzing the exergy destroyed by each component in a process, we can see
where we should be focusing our efforts to improve system efficiency.
• It can also be used to compare components or systems to help make informed
design decisions

10. Thermodynamic approach
• Magnetic refrigeration relies upon the reversible temperature change some materials
exhibit when exposed to a changing magnetic field the magnetocaloric effect (MCE.)
• By varying the magnetic field, work is performed and the internal energy of the system
changes.
• From the FLT we get
dU = dQ + dW1  (1)
TdS = dQ – dWl  (2)
• From the above equation we have,
dU = Tds + dW (3)
• A differential variation in internal energy can be accomplished by a magnetic work
interaction given by the product of the applied magnetic field, H, and the variation in
magnetization, m
𝛿𝑤 = 𝐻𝑑𝑚  (4)
• In the absence of P – V work, enthalpy E is given as E = U – HM (5)
• From the above equations we have,
dE = TdS – MdH (6)

11. Continued…
• Gibbs free energy equation is given by
G = E – TS, in the differential form and from above eqauations we have,
dG = - SdT – MdH (7)
• From the above equation we can write Maxwell equation as:
𝜕𝑆 𝑑𝐻 𝑇 = 𝜕𝑀 𝑑𝑇 𝐻 or 𝑑𝑆 𝑇 = 𝜕𝑀 𝑑𝑇 𝐻 𝑑𝐻 (8)
• we consider the entropy to be a function of T and H at constant pressure and
volume. Then, after calculating the full differential and multiplying by T we get,
𝑇𝑑𝑆 = 𝑇 𝜕𝑠 𝜕𝑇 𝐻 𝑑𝑇 + 𝑇 𝜕𝑆 𝜕𝐻 𝑇 𝑑𝐻 (9)
• Heat capacity at constant magnetic field is
𝐶 𝐻 = 𝑇 𝜕𝑆 𝜕𝑇 𝐻 (10)

12. Continued…
• For adiabatic process, dS = 0 and combining the equation 8, 9, 10
𝑑𝑇𝑆 = − 𝑇 𝐶 𝐻 𝜕𝑀 𝜕𝑇 𝐻 𝑑𝐻 (11)
• The MCE for a change in magnetic field from 0 to H is related as
𝑀𝐶𝐸 = 0
𝐻 𝑇
𝐶 𝐻
𝜕𝑀
𝜕𝑇 𝐻
𝑑𝐻 (12)
• Thus, MCE is a strong non-linear function of temperature
• In addition, it is a function of the magnitude of the field change and the initial
field strength.

13. ReversibleBrayton cycle
D  A : Adiabatic magnetization
A  B : Isofield cooling process
B  C : Adiabatic demagnetization
C  D : Isofield heating process

14. Continued…..
• The heat exchanged is given by:
Heat absorbed = 𝑄0 = − 𝐶
𝐷
𝑇 𝑑𝑆 = 𝑎𝑟𝑒𝑎(𝐷𝐶14) (13)
Heat rejected = 𝑄1 = 𝐵
𝐴
𝑇 𝑑𝑆 = 𝑎𝑟𝑒𝑎(𝐴𝐵14) (14)
• These integrals can be obtained by evaluating in a geometric way the two
area as:
𝑄0 = 𝑎𝑟𝑒𝑎 𝐷𝐶14 =
𝑇 𝐶+𝑇 𝐷
2
𝑆 𝐷 − 𝑆 𝐶 (15)
𝑄1 = 𝑎𝑟𝑒𝑎 𝐴𝐵14 =
𝑇 𝐴+𝑇 𝐵
2
𝑆𝐴 − 𝑆 𝐵 (16)
• Let 𝑇1𝑚 = (𝑇𝐴 + 𝑇𝐵)/2 ; 𝑇0𝑚 = (𝑇𝐶 + 𝑇 𝐷)/2 ; (𝑆𝐴 − 𝑆 𝐵) = (𝑆 𝐷 − 𝑆 𝐶) = ∆𝑆
therefore,
𝑄0 = 𝑇0𝑚 𝛥𝑆 and 𝑄1 = 𝑇1𝑚 𝛥𝑆

15. • Exergy exchanged is defined as :
B = (1 – Ta/T) Q (17)
• Consequently it follows :
𝐵0 = 1 −
𝑇𝑎
𝑇0𝑚
𝑄0 = 1 −
𝑇𝑎
𝑇0𝑚
𝑇0𝑚∆𝑆 (18)
𝐵1 = 1 −
𝑇𝑎
𝑇1𝑚
𝑄1 = 1 −
𝑇𝑎
𝑇1𝑚
𝑇1𝑚∆𝑆 (19)
𝑊 = 𝑄1 − 𝑄0 = 𝑇1𝑚 − 𝑇𝑜𝑚 ∆𝑆 (20)
𝐶𝑂𝑃 =
𝑄0
𝑊
=
𝑇𝑜𝑚
𝑇1𝑚 − 𝑇 𝑜𝑚
(21)
η 𝑒𝑥𝑒𝑟𝑔𝑦 = 𝜓 =
𝐵0
𝐵0 + 𝐵1
=
𝑇 𝑜𝑚 − 𝑇 𝑎
𝑇 𝑜𝑚+ 𝑇1𝑚−2𝑇𝑎
(22)
• Exergy destroyed is given by Gouy – Stodola equation:
𝐼 = 𝑇𝑎∆𝑆 𝑢𝑛𝑖𝑣 = 𝑇𝑎 𝑆𝑔𝑒𝑛 (23)

16. Major breakthrough in the field of M.R.
• Progress has been accelerated by two breakthroughs that were announced in 1997.
• First was the announcement on February 20, 1997 that scientists at Astronautics Corporation of America
(Madison, Wisconsin) and Ames laboratory, Iowa state university (Ames, Iowa) had successfully
demonstrated magnetic refrigeration to a viable and competitive technology with gas cycle refrigeration.
• Second was the june 10, 1997 report of the discovery of a reversible giant magnetocaloric effect by the
Ames laboratory, Iowa state university group.
• A proof-of-principle device based on this AMR cycle has been operated for more than 1500 hours over an
18-month period (8 hours a day, 5 days a week), and during that time the Astronautics Corporation of
America/Ames Laboratory team has reported some impressive results.
• They achieved a cooling power of 600 watts, a maximum COP (coefficient of performance - the heat
removed at the cold end divided by the work required to operate the refrigerator) of 16, a Carnot
efficiency of 60% and a temperature span (the difference in the hot and cold heat exchanger
temperatures) of 38K for a magnetic-field change of 0 to 5T near room temperature using Gd metal
spheres.
• Between 1998 and 2006, following the Ames Laboratory and Astronautics Corporation of America
footsteps, 19 more magnetic refrigerators have been built and tested by scientists and engineers in
Canada (1), China (7), Europe (4), Japan (5) and the USA (3), signalling the dawn of a new era of
environmentally friendly, energy efficient and affordable magnetic cooling, refrigeration and air
conditioning.

17. Summary
• Equations (8) and (11) explains the fundamentals of cooling by adiabatic magnetization. By
studying those equations we come to know that effective cooling by adiabatic
demagnetization requires materials with the largest value of |(∂M⁄∂T)| and T/𝐶 𝐻 at
temperatures close to absolute zero.
• Equation (12) states that MCE is a non-linear function of temperature and its value depend
on the initial and final of the magnetic field.
• Equation (22) and (23) gives the exergy efficiency and the exergy destroyed of the Brayton
magnetic cycle. Exergy destruction can be reduced if the ambient temperature can be
reduced if the rate of entropy generation is less. Exergy analysis of the system allows to
obtain how far the real system deviate from the ideal system and thus appropriate
modifications can be done to improve the system efficiency.
• we can conclude that magnetic refrigeration is an effective and efficient method to achieve
cooling, it is also a clean source when compared to conventional gas system. It has come a
long way since the pioneering work of Giauque (1927) and Deby (1926). A lot of researches
are done on the suitable refrigerants that could be used in the process to perform efficiently.
We can hope to see this technology taking over the conventional system in coming years.

18. References
[1] K.A. Gschneidner, Jr. and V.K. Pecharsky, Chapter 25, Magnetic Refrigeration, Intermetallic Compunds – Principles
and Practice – Volume 3: Progress (2002) 519 – 539.
[2] William F. Giauque ,Some consequences of low temperature research in chemical thermodynamics,Nobel Lecture,
December 12, 1949.
[3] Ibrahim Dincer, Marc A. Rosen, Exergy: Energy, Environment and Sustainable Development, 1st edition, Elsevier
Science 2007, pp. 11 – 14, 23 -32.
[4] Adrian Bejan, George Tsatsaronis, Michael Moran, Thermal Design & Optmization, A Wiley – Interscience
Publication, pp. 113 – 137.
[5] Andrej Kitanovski, Peter W. Egolf, Thermodynamics of magnetic refrigeration, International journal of Refrigeration
29 (2006) 3 – 21.
[6] Umberto Lucia, Entropy and exergy in irreversible renewable energy systems, Renewable and Sustainable Energy
Reviews 20 (2013) 559-564.
[7] Umberto Lucia, General approach to obtain the magnetic refrigeration ideal coefficient of performance COP, Physica
A 387 (2008) 3477-3479.
[8] Umberto Lucia, Second law analysis of the ideal Ericsson magnetic refrigeration,
Renewable and Sustainable Energy Reviews 15 (2011) 2872-2875.
[9] Feng-xia Hu, Ling Chen, Li-fu Bao, Jing Wang, Ji-rong Sun, and Bao-gen Shen, La(Fe,Si)13-based materials prepared
by coarse rare earth product during purification, Oct. 25, 2011, DDMC, Delft, Netherlands.
[10]http://risoecampus.dtu.dk/Research/sustainable_energy/new_energy_technologies
/projects/magnetic_cooling/physics.aspx?sc_lang=da
[11] http://en.wikipedia.org/wiki/Magnetic_refrigeration