The Thermodynamics of Magnetocaloric Energy Conversion - Magnetocaloric Energy Conversion: From Theory to Applications - page 18

Fig. 1.8 The magnetic Stirling refrigeration cycle in a T - s diagram (with gadolinium as the
refrigerant)

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

I

l 0 HdM ¼ l 0 Z

b

HdM þ l 0 Z

d

w ¼ HdM ð 1 : 50 Þ

a c

Like with the Ericsson cycle, in the Stirling cycle it is also necessary to operate
with regeneration. Without this regeneration, Eq. ( 1.50 ) 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 D s c b þ T ds þ T ds ð 1 : 51 Þ

a a c

b

In the ideal Stirling regenerative cycle, the heat during iso-magnetization pro-
cesses would be regenerated without any irreversible losses. If the entropy differ-
ences during the refrigeration and the heat rejection were to be equal s c − b,

then the COP of the ideal regenerative Stirling cycle has the same value as that of the
Carnot cycle:

Δ s a − d = − Δ

q R
w

T R D s a d T R

T H

COP ¼

jj ¼ j ¼

ð 1 : 52 Þ

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