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\begin{document}

\title{Conductivity gain predictions for multiscale fibrous composites with
interfacial thermal barrier resistance}



\author[1]{Ernesto Iglesias-Rodríguez}%
\author[1]{Julián Bravo-Castillero}%
\author[2]{Manuel Cruz}%
\affil[1]{Universidad Nacional Autónoma de México Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas}%
\affil[2]{COPPE}%


\vspace{-1em}



  
  \date{June 18, 2024}


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\begin{abstract}
Nanocomposites are heterogeneous media with two or more microstructural
levels. For instance, a nano-level characterized by isolated
nano-inclusions and a micro-level represented by the clusters resulting
from aggregation processes. Our goal is to present a procedure to study
the influence of this aggregation process and interfacial thermal
resistance on the effective thermal conductivity. The procedure is based
on the Reiterated Homogenization Method and consists of two stages.
First, an effective intermediate thermal property is obtained by taking
into account only the influence of the individual nano-inclusions in the
matrix. Second, the final effective thermal coefficient
(\$\textbackslash{}hat\{k\}\_\{RH\}\$) is calculated considering the
clusters immersed in the intermediate effective medium derived in the
first step. The conductivity gain (\$k\_\{gain\}\$) is defined as the
quotient
(\$\textbackslash{}hat\{k\}\_\{RH\}/\textbackslash{}hat\{k\}\_\{CH\}\$)
where \$\textbackslash{}hat\{k\}\_\{CH\}\$ is the effective thermal
coefficient computed considering only one micro-structural level. The
scheme is exemplified for 2-D square arrays of circular cylinders. The
analytical formulas of the effective coefficient used in the
calculations generalize other well known formulas reported in the
literature. Finally, the effect of thermal conductivity gain is
illustrated as a function of the Biot number, the quotient of the
thermal conductivity, the fibers volume fraction and an aggregation
parameter. The present contribution could be useful for nano-reinforced
fibers applications and nanofluids. Furthermore, the present formulas
can be used to assess numerical computations. An appendix is included
showing similarities and differences between the obtained analytical
formulas of effective coefficients, for different truncation orders, and
those derived from the trifasic model.%
\end{abstract}%



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