The Thermodynamics of Magnetocaloric Energy Conversion - Magnetocaloric Energy Conversion: From Theory to Applications - page 16

where T R denotes the temperature at which the refrigeration is performed. The work
performed during the cycle is equal to:

I

l 0 MdH ¼ l 0 Z MdH þ l 0 Z

b d

w ¼ MdH ð 1 : 42 Þ

a c

The magnetic Ericsson cycle requires a regenerative process. Without it,

Eq. ( 1.42 ) can also be written in other terms:

I Z Z Z Z

d c b d

w ¼ dq ¼ T R ds þ T H ds þ T ds þ T ds

ð 1 : 43 Þ

a a c

b

¼ T R D s a d þ T H D s c b þ ð h d h c Þþ ð h b h a Þ

Now the COP can be de ned as:

q R
w

T R D s a d

COP ¼

jj ¼

ð 1 : 44 Þ

j T R D s a d þ T H D s c b þ ð h d h c Þþ ð h b h a Þ j

If we assume that the regeneration is performed without irreversible heat transfer
losses,

then the two enthalpy differences would have to be equal

(h d − h a ). Furthermore, in the ideal Ericsson regenerative cycle, the

entropy difference during refrigeration and heat

h c ) = (h b −

rejection would be equal

Δ s c − b. Then the COP of the ideal regenerative Ericsson cycle has the

same value as that of the Carnot cycle:

s a − d = −Δ

T R D

q R
w

s a d T R

T H

COP ¼

jj ¼ j ¼

ð 1 : 45 Þ

j T R D s a d T H D s a d T R

Magnetic Carnot Thermodynamic Cycle
The magnetic Carnot refrigeration cycle (Fig. 1.7 ) is only useful for a comparison
with the other refrigeration cycles. In practice its low cooling capacity limits any
applicability in real devices. This well-known cycle operates between two isen-
tropic processes of magnetization and demagnetization and two isothermal pro-
cesses of magnetization and demagnetization. The last process is related to
refrigeration, where the cooling capacity is de

ned as: