Magnetocaloric Fluids - Magnetocaloric Energy Conversion: From Theory to Applications - page 186

Then the total derivative of the enthalpy can be expressed as

H

dH

M
o T

þ l 0 T o ð ; Þ ¼ ð 5 : 53 Þ

dh s H c H dT M

The speci c heat c H in this case represents the speci c heat in a constant

magnetic eld for the magnetic fl uid. This means that is takes into account both, the

speci c heat of the base or carrier

liquid. The magnetocaloric material in a static magnetic

c heat of the magnetic material and the speci

eld exhibits a phase
change in the form of latent heat. In such a case, it is more convenient to keep the
energy equation in a form with the enthalpy (i.e. Eq. 5.49 ).
The enthalpy of the magnetic fl uid (at a constant magnetic eld) may be de ned

as follows:

m solid h solid þ m liquid h iiquid

h ¼ ¼ / m h solid þ 1 / m ð Þ h liquid ð 5 : 54 Þ

m

If the liquid phase does not undergo a phase change, then Eq. ( 5.54 ) may be
written as

m solid h solid þ m liquid c p liquid # liquid

m

h ¼ ¼ / m h solid þ ð 1 / m Þ c p liquid # liquid

ð 5 : 55 Þ

In this case, a special continuous-properties model can be applied, given by
Egolf and Mantz [ 96 ]. The contributions of the magnetic eld change can be added

to such a model.
In the subsequent text we apply equations that consider the magnetic material to
possess ordinary speci

c heat properties. For this particular case, the speci c heat

c H of the magnetic fl uid can be calculated using the simple relation (see also Xuan

and Roetzel [ 97 ]):

m solid c H solid þ m liquid c p liquid

c H ¼ ¼ / m c H solid þ ð 1 / m Þ c p liquid ð 5 : 56 Þ

m

With the help of Eqs. ( 5.49 5.53 ) the energy equation can be now written as

-

H

DH

h i

c H DT

M
o Dt þ l 0 M DH Dt þ l 0 T o

¼ viscous : r~

Dt ¼ r _

M q þ v ð 5 : 57 Þ

T