Heat conduction and thermal conductivity of 3D cracked media

Sang, Nguyen Xuan; Vu, Minh‐Ngoc; Tang, Anh Minh; To, Viet Thanh

doi:10.1016/j.ijheatmasstransfer.2015.05.113

Cited by 22 publications

(7 citation statements)

References 42 publications

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“…This is an effective structure-preserving technique which leads to canonical constructions of stable finite elements, thus improving significantly the technology of the finite element method. Whilst the method has been applied to heat conduction in cracked media [18], the method inherits the challenges of the classical finite elements approach when dealing with strong heterogeneities and discontinuities, which can be overcome by operating on discrete topological spaces as in DEC.…”

Section: Introductionmentioning

confidence: 99%

TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator

2015

ACM Trans. Math. Softw.

1,299

828

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TetGen is a C++ program for generating good quality tetrahedral meshes aimed to support numerical methods and scientific computing. The problem of quality tetrahedral mesh generation is challenged by many theoretical and practical issues. TetGen uses Delaunay-based algorithms which have theoretical guarantee of correctness. It can robustly handle arbitrary complex 3D geometries and is fast in practice. The source code of TetGen is freely available.This article presents the essential algorithms and techniques used to develop TetGen. The intended audience are researchers or developers in mesh generation or other related areas. It describes the key software components of TetGen, including an efficient tetrahedral mesh data structure, a set of enhanced local mesh operations (combination of flips and edge removal), and filtered exact geometric predicates. The essential algorithms include incremental Delaunay algorithms for inserting vertices, constrained Delaunay algorithms for inserting constraints (edges and triangles), a new edge recovery algorithm for recovering constraints, and a new constrained Delaunay refinement algorithm for adaptive quality tetrahedral mesh generation. Experimental examples as well as comparisons with other softwares are presented. ACM Reference Format:Hang Si. 2015. TetGen, a Delaunay-based quality tetrahedral mesh generator.

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Section: Introductionmentioning

confidence: 99%

TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator

2015

ACM Trans. Math. Softw.

1,299

828

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“…More precisely, there is no temperature jump across a penny-shape conducting crack. For the case of non-conducting penny-shape crack ( = 0), equation 10is simplified (see also Sevostianov, 2006;Vu et al, 2015) as:…”

Section: Notationsmentioning

confidence: 99%

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods

Sang

et al. 2017

Journal of Applied Geophysics

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International audienceThe present work aims to modeling the thermal conductivity of fractured materials using homogenization-based analytical and pattern-based numerical methods. These materials are considered as a network of cracks distributed inside a solid matrix. Heat flow through such media is perturbed by the crack system. The problem of heat flow across a single crack is firstly investigated. The classical Eshelby's solution, extended to the thermal conduction problem of an ellipsoidal inclusion embedding in an infinite homogeneous matrix, gives an analytical solution of temperature discontinuity across a non-conducting penny-shaped crack. This solution is then validated by the numerical simulation based on the finite elements method. The numerical simulation allows analyzing the effect of crack conductivity. The problem of a single crack is then extended to a medium containing multiple cracks. Analytical estimations for effective thermal conductivity, that take into account the interaction between cracks and their spatial distribution, are developed for the case of non-conducting cracks. Pattern-based numerical method is then employed for both cases non-conducting and conducting cracks. In the case of non-conducting cracks, numerical and analytical methods, both account for the spatial distribution of the cracks, fit perfectly. In the case of conducting cracks, the numerical analyzing of crack conductivity effect shows that highly conducting cracks weakly affect heat flow and the effective thermal conductivity of fractured media

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“…As a result of the formation of a complex stress state in the material, micro and macro cracks are formed in the material during its cooling after reaction sintering [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 ]. These cracks provide desirable properties, such as a low macroscopic thermal expansion coefficient [ 22 ], low thermal conductivity [ 23 , 24 , 25 ], and, thus, high resistance to thermal shock [ 1 , 11 , 26 , 27 ]. Tialite also has high resistance to microcrack propagation [ 28 ].…”

Section: Introductionmentioning

confidence: 99%

Remarkable Structural Modifications of Tialite Solid Solutions Obtained by Different Methods

et al. 2022

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The structural changes occurring in tialite due to the formation of magnesium-titanate–aluminum-titanate solid solutions were determined. For this purpose, a DFT simulation of the structural changes was performed. The simulation proposed a number of possible atomic substitutions occurring in the elementary cells of the tialite, along with calculations of the lattice parameter changes in this material. Next, the actual changes occurring in the structure of the tialite due to the formation of solid solutions, obtained in different ways, were investigated. After comparing the obtained results, it was possible to confirm the mechanism of the formation of tialite solid solutions, through which one magnesium atom and one titanium atom substituted two aluminum atoms simultaneously. The results of this experimental work were confirmed by theoretical calculations (the differences in the values of the lattice parameters, measured in the experiment and calculated in the simulation, were less than 0.5%), through which changes in the lattice parameters with Mg and Ti substitution were observed.

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Heat conduction and thermal conductivity of 3D cracked media

Cited by 22 publications

References 42 publications

TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator

TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator

Modeling of heat flow and effective thermal conductivity of fractured media: Analytical and numerical methods

Remarkable Structural Modifications of Tialite Solid Solutions Obtained by Different Methods

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