Exergy analysis of Magnetic Refrigeration

Manojkumar Ashok Maurya

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).

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.

Working principle

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

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

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, • 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

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

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 getdU = 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

(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)

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: or (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, (9)

• Heat capacity at constant magnetic field is

(10)

Continued…• For adiabatic process, dS = 0 and combining the equation 8, 9, 10

(11)

• The MCE for a change in magnetic field from 0 to H is related as

(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.

ReversibleBrayton cycle

D A : Adiabatic magnetizationA B : Isofield cooling processB C : Adiabatic demagnetizationC D : Isofield heating process

Continued…..• The heat exchanged is given by: Heat absorbed = (13)

Heat rejected = (14)

• These integrals can be obtained by evaluating in a geometric way the two area as:

(15) (16)

• Let ; ; ( therefore, and

• Exergy exchanged is defined as :B = (1 – Ta/T) Q(17)

• Consequently it follows :(18)

(19)

(20)

(21)

(22)• Exergy destroyed is given by Gouy – Stodola equation:

(23)

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.

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/ 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.

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