Research Article
Effect of Micro- to Nanosize Inclusions upon the
Thermal Conductivity of Powdered Composites with
High and Low Interface Resistance
Muhammad Zain-ul-abdein,
1
Waqas S. Awan,
1
Hassan Ijaz,
1
Aqeel A. Taimoor,
2
Ayyaz Muhammad,
2,3
and Sami ullah Rather
2
1
Mechanical Engineering Department, University of Jeddah, Jeddah, Saudi Arabia
2
Department of Chemical and Materials Engineering, King Abdulaziz University, Jeddah, Saudi Arabia
3
Institute of Chemical Engineering and Technology, University of Punjab, Lahore, Pakistan
Correspondence should be addressed to Muhammad Zain-ul-abdein; mzainulabdein@gmail.com
Received 17 June 2015; Accepted 28 September 2015
Academic Editor: Christian Brosseau
Copyright © 2015 Muhammad Zain-ul-abdein et al. Tis 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.
Materials for thermal management application require better control over the thermophysical properties, which has largely been
achieved by fabricating powdered composite. Tere are, however, several factors like fller volume fraction, shape morphology,
inclusion size, and interfacial thermal resistance that limit the efective properties of the medium. Tis paper presents a methodology
to estimate the efective thermal conductivity of powdered composites where the fller material is more conductive than the matrix.
Only a few theoretical models, such as Hasselman and Johnson (HJ) model, include the efect of interfacial resistance in their
formulation. Nevertheless, HJ model does not specify the nature of the interfacial thermal resistance. Although Sevostianov and
Kachanov (SK) method takes care of interface thickness, they, on the other hand, have not taken into account the interfacial
resistance due to atomic imperfections. In the present work, HJ model has been modifed using SK method and the results were
compared with experimental ones from the literature. It has been found that the efect of interfacial resistance is signifcant in highly
resistive medium at microscale compared to nanoscale, such as Cu/diamond system, while, in a highly conductive medium, like
bakelite/graphite system, the efect of shape factor is more signifcant than interfacial thermal resistance.
1. Introduction
Termal conductivity is one of the fundamental properties
of key importance in the energy applications where vari-
able (fast/slow) heat dissipation/storage is ofen required.
Although metals and alloys provide a large range of con-
ductivities to be used in several electronic and mechanical
appliances, the quest for the search of new composite materi-
als with modifable properties has still been unquenched. In
addition to fabricating the two-phase composites with difer-
ent inclusions, like metal matrix composite (MMC), polymer
matrix composite (PMC), and so forth, the researchers
have shown growing inclination towards manipulating the
inclusion size. It is, therefore, of interest to be able to observe
the efective conductive properties of a given composite from
micro- to nanoregimes.
In the current framework, Clausius (1879) [1] and
Maxwell (1884) [2] introduced one of the earliest mod-
els based upon self-consistent scheme (SCS). Both models
attempted to predict the efective properties of a two-phase
medium where the inclusions, in dilute concentration, were
treated as isolated particles immersed into a given matrix.
Bruggeman (1935) [3], later on, implemented an incremental
scheme called diferential scheme (DS) or efective medium
scheme (EMS). Te basic idea was to introduce the second
phase particle into a homogenous matrix in small increments
and estimate the overall properties of the resulting medium.
Nevertheless, the very frst upper and lower bounds based
Hindawi Publishing Corporation
Journal of Nanomaterials
Volume 2015, Article ID 843914, 8 pages
http://dx.doi.org/10.1155/2015/843914