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Heat conduction and thermal conductivity of 3D cracked media

Vu, M.N. and Nguyen, S.T. and Vu, M.H. and Tang, A.M. and To, V.T. (2015) Heat conduction and thermal conductivity of 3D cracked media. International Journal of Heat and Mass Transfer, 89. pp. 1119-1126. ISSN 179310

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Abstract

This study deals with the heat conduction within a medium containing cracks that are assumed to be perfect insulators. Multi-region boundary element approach is employed to obtain a boundary singular integral equation governing the steady state thermal transfer within this medium. This equation presents the temperature field within the whole cracked body as a function of temperature and rate of heat flow on the domain's boundary and temperature discontinuity across the cracks. For the particular case of an infinite domain under far-field condition, the temperature field solution is only a function of the cracks temperature's discontinuity. The basic problem of a single crack in an infinite domain is investigated and a closed-form solution is derived for a crack of elliptic plane from this analysis. This solution is the key issue to estimate the effective thermal conductivity of the whole domain by coupling with the classical homogenization schemes. The arbitrary crack form is covered up by using the excluded volume definition. Estimations of effective thermal conductivities stemming from diluted, differential and self-consistent approaches are compared to numerical solution obtained by the finite volume modeling that is available in literature. This comparison shows that the self-consistent scheme is the most appropriate model to estimate the thermal conductivity of materials containing cracks. © 2015 Elsevier Ltd. All rights reserved.

Item Type: Article
Divisions: Faculties > Faculty of Vehicle and Energy Engineering
Identification Number: 10.1016/j.ijheatmasstransfer.2015.05.113
Uncontrolled Keywords: Cracks; Heat conduction; Integral equations; Temperature; Effective thermal conductivity; Insulator; MR-BEM; Self-consistent; Self-consistent approach; Self-consistent scheme; Singular integral equations; Temperature discontinuity; Thermal conductivity
Additional Information: Language of original document: English. All Open Access, Green.
URI: http://eprints.lqdtu.edu.vn/id/eprint/9914

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