A generalized effective medium theory (EMT) is proposed to account for the fractal structure of the dispersed phase in a dispersing medium under the dilute limit. The thermal conductivity of nanofluids with fractal aggregates is studied using the proposed model. Fractal aggregates are considered as functionally graded spherical inclusions and its effective thermal conductivity is derived as a function of its fractal dimension. The results are studied for self-consistency and accuracy within the limitations of the analytical approximations used.

References

References
1.
Maxwell
,
J. C.
,
1904
,
A Treatise on Electricity and Magnetism
,
3rd ed.
,
Oxford University Press
, Oxford, UK.
2.
Eucken, A.
, 1940, “
General Rules for the Thermal Conductivity of Different Types of Substances and Aggregate States
,”
Res. Field Eng. A
,
11
(1), pp. 6–20.
3.
Hamilton
,
R. L.
, and
Crosser
,
O. K.
,
1962
, “
Thermal Conductivity of Heterogeneous Two-Component Systems
,”
Ind. Eng. Chem. Fundam.
,
1
(
3
), pp.
187
191
.
4.
Nan
,
C. W.
,
Shi
,
Z.
, and
Lin
,
Y.
,
2003
, “
A Simple Model for Thermal Conductivity of Carbon Nanotube-Based Composites
,”
Chem. Phys. Lett.
,
375
(
5–6
), pp.
666
669
.
5.
Bruggeman
,
V. D.
,
1935
, “
Berechnung Verschiedener Physikalischer Konstanten Von Heterogenen Substanzen—I: Dielektrizitätskonstanten Und Leitfähigkeiten Der Mischkörper Aus Isotropen Substanzen
,”
Ann. Phys.
,
416
(
7
), pp.
636
664
.
6.
Xuan
,
Y.
,
Li
,
Q.
, and
Hu
,
W.
,
2003
, “
Aggregation Structure and Thermal Conductivity of Nanofluids
,”
AIChE J.
,
49
(
4
), pp.
1038
1043
.
7.
Evans
,
W.
,
Prasher
,
R.
,
Fish
,
J.
,
Meakin
,
P.
,
Phelan
,
P.
, and
Keblinski
,
P.
,
2008
, “
Effect of Aggregation and Interfacial Thermal Resistance on Thermal Conductivity of Nanocomposites and Colloidal Nanofluids
,”
Int. J. Heat Mass Transfer
,
51
(
5–6
), pp.
1431
1438
.
8.
Heinson
,
W. R.
,
Sorensen
,
C. M.
, and
Chakrabarti
,
A.
,
2012
, “
A Three Parameter Description of the Structure of Diffusion Limited Cluster Fractal Aggregates
,”
J. Colloid Interface Sci.
,
375
(
1
), pp.
65
69
.
9.
Markworth
,
A. J.
,
Ramesh
,
K. S.
, and
Parks
,
W. P.
,
1995
, “
Modelling Studies Applied to Functionally Graded Materials
,”
J. Mater. Sci.
,
30
(
9
), pp.
2183
2193
.
10.
Eastman
,
J. A.
,
Choi
,
U. S.
,
Li
,
S.
,
Thompson
,
L.
, and
Lee
,
S.
, 1996, “
Enhanced Thermal Conductivity Through the Development of Nanofluids
,” Argonne National Lab., Lemont, IL, Report No.
ANL/MSD/CP-90462; CONF-961202-94
.https://www.osti.gov/biblio/459378-enhanced-thermal-conductivity-through-development-nanofluids
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