Magnetocaloric Fluids - Magnetocaloric Energy Conversion: From Theory to Applications - page 188

Table 5.4 Examples of models for effective thermal conductivity of suspensions
Author

Model Comment

/ V

0
@

1
A

Very dilute suspensions of spheres, does not account for
interaction between particles

Maxwell
[ 105 ]

k

liquid

3

solid

1

k

/ V

k ¼ k liquid 1 þ (5.63)

k k

liquid
k

liquid

solid þ

2

solid

1

k

!

Extended Maxwell ' s model to higher solid fractions Rayleigh

[ 189 ]

10
3
V

ð 2 þ a Þ=ð 1 aÞ 2 / V 0 : 525 3 ð 3 a Þ=ð 4 þ 3 a /

½ ½

k ¼ k liquid

10
3
V

½

ð 2 þ a Þ=ð 1 aÞ þ / V 0 : 525 3

½

ð 3 a Þ=ð 4 þ 3 a /

k solid
k liquid

ð 5 : 64 Þ

a ¼

Jeffrey
[ 190 ]

/ V b 2

Spherical particles 0 a1

k ¼ k liquid 1 þ 3 / V b þ 3 c

b
4 þ

3 b
16

2
2 a þ 3

a þ

c ¼ 1 þ

(5.65)

a 1

a þ 2

k solid
k liquid

b ¼ a ¼