Developments in Ceramic Materials Research

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190 M. A. Sheik analysis using FEM involves applying a temperature gradient Δ T Δx across the composite section in a 1D heat flow simulation. Using Fourier Law, k x , is given as: k x = q x Δ x ΔT where qx is the overall heat flux in the x -direction calculated by integrating the nodal flux values across rear face. In the current analysis, q x is obtained using the nodal flux values (in x -direction) given by the FE solution on one of the faces where the temperature boundary condition is applied as in Figure 16. However, due to a high degree of mesh non- uniformity and a significant difference in the thermal properties of the matrix and fibre, the nodal flux values vary quite considerably across that surface, and the summation employed to calculate the overall flux as: Figure 16. Boundary conditions for steady-state FE analysis. Figure 17. Boundary conditions for transient analysis. (11)
q x = Modeling of Thermal Transport in Ceramics Matrix Composites 191 N ∑ i= 1 q A i i N ∑ i= 1 A i In the case of transient thermal analysis, a heat flux is applied to one face (Figure 17) of the composite section for a short time and the temperature history is recorded on the opposite face to simulate the experimental conditions. The temperature profile is obtained by averaging temperature across the complete rear face. This is obtained from an expression similar to Equation 12, as here q i is replaced by the nodal temperatures Ti as: T av = N ∑ i= 1 T A i i N ∑ i= 1 A i T av , the average temperature, is calculated for each time step through the transient analysis and a temperature history is recorded. Assuming 1D uniaxial heat flow, the half rise time related to this average temperature value is then used in Equation 8 to calculate thermal diffusivity α and thermal conductivity k is found from Equation 10. The remaining scalar properties, density ρ and specific heat C p for the composite are determined using the rule of mixtures in Equation 14 shown in Table 4. It is important to emphasize that two different volume fractions are involved here. One is 75% Carbon fibre with in the Carbon matrix, forming the fibre tow. The other is the 65% fibre tow in the composite with remaining being SiC matrix surrounding it. Using rule of mixtures, specific heat C p and density ρ as calculated as: Cp ρ = ρ V C C f = Cp f f V f + + ( ) ( ) ⎭ ⎬⎫ 1− V f ρm 1− V Cp f m Table 4. C p and ρ for CMC from constituent materials’ property values Material Property Carbon Fibre Carbon Matrix SiC Matrix Composite Density ρ (kg m -3 ) Specific Heat p C (x 10 -6 J kg -1 K -1 ) 1928 1800 2310.000 1832 (fibre tow) 3200 921 717.48 1063.278 870.12 (fibre tow) 1422 (12) (13) (14)
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DEVELOPMENTS IN CERAMIC MATERIALS R
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Copyright © 2007 by Nova Science P
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PREFACE Ceramics are refractory, in
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Preface ix crystals is discussed. A
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Preface xi spectra and the directio
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2 Leslie G. Cecil comprehensive dat
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4 Leslie G. Cecil Ringle et al. (19
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6 Leslie G. Cecil The main architec
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8 Leslie G. Cecil can study “the
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10 Leslie G. Cecil Middleton et al.
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12 Leslie G. Cecil The laser ablate
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14 Leslie G. Cecil There are two ge
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16 Leslie G. Cecil distinct recipes
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18 Leslie G. Cecil second group (Fi
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20 Leslie G. Cecil The Vitzil-Orang
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22 Leslie G. Cecil Table 3. Mahalan
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24 Leslie G. Cecil Ixlú and Ch’i
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26 Leslie G. Cecil structures (D. R
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28 Leslie G. Cecil paste and Macanc
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30 Leslie G. Cecil Bieber, A. M. Jr
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32 Leslie G. Cecil Kepecs, S. M., a
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34 Leslie G. Cecil Schele, L., Grub
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36 Z. C. Li, Z. J. Pei and C. Tread
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54 T. T. Basiev, V. A. Demidenko, K
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62 I, % 100 80 60 40 20 0 T. T. Bas
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68 Fluorescence, a.u. 1 T. T. Basie
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70 Fluorescence, a.u. 1 0.1 0.01 0.
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78 k, cm -1 20 18 16 14 12 10 8 6 4
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82 Photon counts 300 250 200 150 10
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84 Fluorescence, a.u. I transfer ,
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86 ln(I transfer (t)) -4.2 -4.4 -4.
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88 Fluorescence, a.u. I transfer ,
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In: Developments in Ceramic Materia
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Synthesis, Spectroscopic and Magnet
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a c Synthesis, Spectroscopic and Ma
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Transmission Transmission Transmiss
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Sm (J/Kmol) Sm (J/Kmol) 15 10 5 Syn
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Intensity (a.u.) Intensity (a.u.) 8
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Page 179 and 180: D50 0.8 0.7 0.6 0.5 0.4 0.3 The Use
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240 R. Ramesh, H. Kara, Ron Stevens
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242 Development of Display Technolo
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244 Li Chen technology moved to the
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246 Li Chen The continuing evolutio
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248 Li Chen the back contact cathod
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250 Li Chen Figure 3. Vertical side
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252 Li Chen Figure 6. Molybdenum mi
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254 Li Chen Figure 8(a). I-V curve
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256 Li Chen Figure 9. Life time tes
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258 Figure 11(a). Plasma generated
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260 Li Chen [13] C.A. Spindt, K.R.
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262 S. Ardizzone, C. L. Bianchi, G.
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A absorption spectra, 66, 67, 77, 7
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correlation function, 156 corrosion
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group membership, 13, 20, 21, 22, 2
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microstructure(s), x, xi, 73, 74, 2
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efraction index, 61 refractive inde
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time, vii, ix, 1, 3, 7, 8, 11, 26,
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Developments in Ceramic Materials Research

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