Research Article
Physical-Statistical Model of Thermal
Conductivity of Nanofluids
B. Usowicz,
1
J. B. Usowicz,
2
and L. B. Usowicz
3
1
Institute of Agrophysics, Polish Academy of Sciences, Doswiadczalna 4, 20-280 Lublin, Poland
2
Torun Centre for Astronomy, Nicolaus Copernicus University, Gagarina 11, 87-100 Torun, Poland
3
Lukasz Usowicz Firm, 20-282 Lublin, Poland
Correspondence should be addressed to B. Usowicz; b.usowicz@ipan.lublin.pl
Received 4 February 2014; Revised 5 May 2014; Accepted 6 May 2014; Published 11 June 2014
Academic Editor: Christian Brosseau
Copyright © 2014 B. Usowicz et al. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A physical-statistical model for predicting the effective thermal conductivity of nanofluids is proposed. e volumetric unit of
nanofluids in the model consists of solid, liquid, and gas particles and is treated as a system made up of regular geometric
figures, spheres, filling the volumetric unit by layers. e model assumes that connections between layers of the spheres and
between neighbouring spheres in the layer are represented by serial and parallel connections of thermal resistors, respectively.
is model is expressed in terms of thermal resistance of nanoparticles and fluids and the multinomial distribution of particles in
the nanofluids. e results for predicted and measured effective thermal conductivity of several nanofluids (Al
2
O
3
/ethylene glycol-
based and Al
2
O
3
/water-based; CuO/ethylene glycol-based and CuO/water-based; and TiO
2
/ethylene glycol-based) are presented.
e physical-statistical model shows a reasonably good agreement with the experimental results and gives more accurate predictions
for the effective thermal conductivity of nanofluids compared to existing classical models.
1. Introduction
Fluids with nanoparticles suspended in them are known
as nanofluids. e thermal properties of nanofluids, that
is, thermal conductivity and specific heat, are very impor-
tant parameters for estimating the heat transfer coeffi-
cient [1–4], because nanofluids are proposed for various
uses in important fields such as electronics, space tech-
nology, medicine, and HVAC (heating, ventilation, and
air conditioning). Hence, there is a need for fundamental
understanding of the heat transfer behaviour of nanofluids
in order to exploit their potential benefits and applica-
tions [5, 6]. Earlier studies show that the enhancement
of thermal conductivity of the base fluid is essential in
order to improve the thermal efficiency of different systems
[2, 7].
In this paper, we present a physical-statistical model and
its performance in predicting the thermal conductivity of
various fluids with nanoparticles suspended in them. We
hope that this model should find wider practical application
in the study of nanofluids.
2. Physical-Statistical Model of
Thermal Conductivity
e study employs the physical-statistical model of soil
thermal conductivity proposed by Usowicz et al. [8, 9]. e
model is expressed in terms of thermal resistance (Ohm’s law
and Fourier’s law), two laws of Kirchhoff, and the multinomial
distribution [10]. e volumetric unit of soil in the model
consists of solid, liquid, and gas particles and is treated as a
system made up of regular geometric figures, spheres, filling
the volumetric unit by layers (Figure 1).
e model assumes that connections between layers of
the spheres and between neighbouring spheres in the layer
are represented by serial and parallel connections of ther-
mal resistors, respectively. A comparison of resultant resis-
tance, considering all possible configurations of sphere with
Hindawi Publishing Corporation
Journal of Nanomaterials
Volume 2014, Article ID 756765, 6 pages
http://dx.doi.org/10.1155/2014/756765