Please wait a minute...

Frontiers of Materials Science

Front Mater Sci    2012, Vol. 6 Issue (1) : 79-86     DOI: 10.1007/s11706-012-0156-6
RESEARCH ARTICLE |
Numerical calculations of effective thermal conductivity of porous ceramics by image-based finite element method
Yan-Hao DONG, Chang-An WANG(), Liang-Fa HU, Jun ZHOU
State Key Lab of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China
Download: PDF(466 KB)   HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

The effective thermal conductivity of heterogeneous or composite materials is an essential physical parameter of materials selection and design for specific functions in science and engineering. The effective thermal conductivity is heavily relied on the fraction and spatial distribution of each phase. In this work, image-based finite element method (FEM) was used to calculate the effective thermal conductivity of porous ceramics with different pore structures. Compared with former theoretical models such as effective media theory (EMT) equation and parallel model, image-based FEM can be applied to a large variety of material systems with a relatively steady deviation. The deviation of image-based FEM computation mainly comes from the difference between the two dimensional (2D) image and the three dimensional (3D) structure of the real system, and an experiment was carried out to confirm this assumption. Factors influencing 2D and 3D effective thermal conductivities were studied by FEM to illustrate the accuracy and application conditions of image-based FEM.

Keywords thermal conductivity      image-based FEM      porous ceramic      two-phase material     
Corresponding Authors: WANG Chang-An,Email:wangca@tsinghua.edu.cn   
Issue Date: 05 March 2012
 Cite this article:   
Yan-Hao DONG,Chang-An WANG,Liang-Fa HU, et al. Numerical calculations of effective thermal conductivity of porous ceramics by image-based finite element method[J]. Front Mater Sci, 2012, 6(1): 79-86.
 URL:  
http://journal.hep.com.cn/foms/EN/10.1007/s11706-012-0156-6
http://journal.hep.com.cn/foms/EN/Y2012/V6/I1/79
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
Yan-Hao DONG
Chang-An WANG
Liang-Fa HU
Jun ZHOU
Fig.1  Sample images used in image-based FEM computations: original; after binary.
Fig.2  Effective thermal conductivity measurement used in image-based FEM.
Fig.3  SEM image of porous ceramics with uniformly distributed pores.
Fig.4  FEM results, experimental thermal conductivity and comparison with EMT equation of porous ceramics with uniformly distributed pores.
GroupPorosity/%Thermal conductivity/(W·m-1·K-1)
Experimental resultsFEM resultsEMT results
147.20.5260.3350.689
259.70.2710.1630.328
364.70.2160.1050.212
472.70.1220.0750.101
Tab.1  Experimental thermal conductivity, FEM and EMT results of porous ceramics with uniformly distributed pores
Fig.5  SEM image of porous ceramics with unidirectionally aligned pore channels.
Fig.6  FEM results, experimental thermal conductivity and comparison with parallel model of porous ceramics with unidirectionally aligned pore channels.
GroupPorosity/%Thermal conductivity/(W·m-1·K-1)
Experimental resultsFEM resultsParallel model
174.20.2300.2120.484
275.00.3450.2860.469
377.30.4700.4140.429
Tab.2  Experimental thermal conductivity, FEM and parallel mode results of porous ceramics with unidirectionally aligned pore channels
Fig.7  SEM image of a cross section perpendicular to the pore channel of porous ceramics with unidirectionally aligned pore channels.
Fig.8  High-magnification SEM image of the channel wall.
Fig.9  FEM results of 2D and 3D effective thermal conductivity of randomly distributed two-phase system.
Fig.10  Ratio of effective thermal conductivity of experimental results () and image-based FEM results () of porous ceramics with uniformly distributed pores with different porosity.
1 Progelhof R C, Throne J L, Ruetsch R R. Methods for predicting the thermal conductivity of composite systems: A review. Polymer Engineering and Science , 1976, 16(9): 615-625
2 Loeb A L. Thermal conductivity: VIII, a theory of thermal conductivity of porous materials. Journal of the American Ceramic Society , 1954, 37(2): 96-99
3 Tsotsas E, Martin H. Thermal conductivity of packed beds: A review. Chemical Engineering and Processing , 1987, 22(1): 19-37
4 Cernuschi F, Ahmaniemi S, Vuoristo P, . Modelling of thermal conductivity of porous materials: application to thick thermal barrier coatings. Journal of the European Ceramic Society , 2004, 24(9): 2657-2667
5 Rayleigh L. On the influence of obstacles arranged in rectangular order upon the properties of a medium. Philosophical Magazine , 1892, 34: 481-507
6 Maxwell J C. A Treatise on Electricity and Magnetism, Vol. 1. 3rd ed. Oxford University Press , 1904, 361-373
7 Landauer R. The electrical resistance of binary metallic mixtures. Journal of Applied Physics , 1952, 23(7): 779-784
8 Kirkpatrick S. Percolation and conduction. Reviews of Modern Physics , 1973, 45(4): 574-588
9 Kulkarni A, Wang Z, Nakamura T, . Comprehensive microstructural characterization and predictive property modeling of plasma-sprayed zirconia coatings. Acta Materialia , 2003, 51(9): 2457-2475
10 Bakker K. Using the finite element method to compute the influence of complex porosity and inclusion structures on the thermal and electrical conductivity. International Journal of Heat and Mass Transfer , 1997, 40(15): 3503-3511
11 Grandjean S, Absi J, Smith D S. Numerical calculations of the thermal conductivity of porous ceramics based on micrographs. Journal of the European Ceramic Society , 2006, 26(13): 2669-2676
12 Tan Y, Longtin J P, Sampath S. Modeling thermal conductivity of thermal spray coatings: Comparing predictions to experiments. Journal of Thermal Spray Technology , 2006, 15(4): 545-552
13 Studart A R, Gonzenbach U T, Tervoort E, . Processing routes to macroporous ceramics: A review. Journal of the American Ceramic Society , 2006, 89(6): 1771-1789
14 Sopyan I, Mel M, Ramesh S, . Porous hydroxyapatite for artificial bone applications. Science and Technology of Advanced Materials , 2007, 8(1-2): 116-123
15 Latella B A, Henkel L, Mehrtens E G. Permeability and high temperature strength of porous mullite-alumina ceramics for hot gas filtration. Journal of Materials Science , 2006, 41(2): 423-430
16 Carson J K, Lovatt S J, Tanner D J, . Thermal conductivity bounds for isotropic, porous materials. International Journal of Heat and Mass Transfer , 2005, 48(11): 2150-2158
17 Hu L F, Wang C-A, Huang Y. Porous yttria-stabilized zirconia ceramics with ultra-low thermal conductivity. Journal of Materials Science , 2010, 45(12): 3242-3246
18 Chen R F, Huang Y, Wang C-A, . Ceramics with ultra-low density fabricated by gelcasting: An unconventional view. Journal of the American Ceramic Society , 2007, 90(11): 3424-3429
19 Chen R F, Wang C-A, Huang Y, . Ceramics with special porous structures fabricated by freeze-gelcasting: using tert-butyl alcohol as template. Journal of the American Ceramic Society , 2007, 90(11): 3478-3484
Related articles from Frontiers Journals
[1] YU Zhi-ming, FANG Mei, XIAO Zhu. Effects of enhanced nucleation on the growth and thermal performance of diamond films deposited on BeO by hot filament CVD technique[J]. Front. Mater. Sci., 2008, 2(4): 369-374.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed