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Conductivity gain predictions for multiscale fibrous composites with interfacial thermal barrier resistance
  • Ernesto Iglesias-Rodríguez,
  • Julián Bravo-Castillero,
  • Manuel Cruz
Ernesto Iglesias-Rodríguez
Universidad Nacional Autónoma de México Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas

Corresponding Author:ernesto.iglesias@iimas.unam.mx

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Julián Bravo-Castillero
Universidad Nacional Autónoma de México Instituto de Investigaciones en Matemáticas Aplicadas y Sistemas
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Manuel Cruz
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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 ($\hat{k}_{RH}$) 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 ($\hat{k}_{RH}/\hat{k}_{CH}$) where $\hat{k}_{CH}$ 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.
02 Jun 2022Submitted to Mathematical Methods in the Applied Sciences
02 Jun 2022Submission Checks Completed
02 Jun 2022Assigned to Editor
11 Jun 2022Reviewer(s) Assigned
25 Jul 2022Review(s) Completed, Editorial Evaluation Pending
26 Jul 2022Editorial Decision: Revise Major
27 Sep 20221st Revision Received
28 Sep 2022Assigned to Editor
28 Sep 2022Submission Checks Completed
30 Sep 2022Reviewer(s) Assigned
30 Sep 2022Review(s) Completed, Editorial Evaluation Pending
01 Oct 2022Editorial Decision: Accept
31 Oct 20222nd Revision Received
07 Nov 2022Submission Checks Completed
07 Nov 2022Assigned to Editor
07 Nov 2022Review(s) Completed, Editorial Evaluation Pending
07 Nov 2022Reviewer(s) Assigned
08 Nov 2022Editorial Decision: Accept