Finite element computation of the effective thermal conductivity of two-dimensional multi-scale heterogeneous media

Purpose The simulation of heat conduction inside a heterogeneous material with multiple spatial scales would require extremely fine and ill-conditioned meshes and, therefore, the success of such a numerical implementation would be very unlikely. This is the main reason why this paper aims to calcula...

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Bibliographic Details
Published in:Engineering computations Vol. 35; no. 5; pp. 2107 - 2123
Main Authors: Mattos, Lucas Prado, Cruz, Manuel Ernani, Bravo-Castillero, Julián
Format: Journal Article
Language:English
Published: Bradford Emerald Publishing Limited 05.09.2018
Emerald Group Publishing Limited
Subjects:
Algorithms
Boundary conditions
Composite materials
Computer simulation
Conditioning
Conduction heating
Conductive heat transfer
Conductivity
Finite element analysis
Finite element method
Heat conductivity
Homogenization
Mathematical analysis
Methodology
Methods
Multiscale analysis
Partial differential equations
Thermal conductivity
Finite elements
Effective thermal conductivity
Reiterated homogenization
Multi-scale heterogeneous media
ISSN:0264-4401, 1758-7077
Online Access:Get full text
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Summary:Purpose The simulation of heat conduction inside a heterogeneous material with multiple spatial scales would require extremely fine and ill-conditioned meshes and, therefore, the success of such a numerical implementation would be very unlikely. This is the main reason why this paper aims to calculate an effective thermal conductivity for a multi-scale heterogeneous medium. Design/methodology/approach The methodology integrates the theory of reiterated homogenization with the finite element method, leading to a renewed calculation algorithm. Findings The effective thermal conductivity gain of the considered three-scale array relative to the two-scale array has been evaluated for several different values of the global volume fraction. For gains strictly above unity, the results indicate that there is an optimal local volume fraction for a maximum heat conduction gain. Research limitations/implications The present approach is formally applicable within the asymptotic limits required by the theory of reiterated homogenization. Practical implications It is expected that the present analytical-numerical methodology will be a useful tool to aid interpretation of the gain in effective thermal conductivity experimentally observed with some classes of heterogeneous multi-scale media. Originality/value The novel aspect of this paper is the application of the integrated algorithm to calculate numerical bulk effective thermal conductivity values for multi-scale heterogeneous media.
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ISSN:0264-4401
1758-7077
DOI:10.1108/EC-11-2017-0444