A Two-Dimensional Heat Transfer Model for Thermal Barrier Coating Average Thermal Conductivity Computation

REFERENCES

• A. Kulkarni , Z. Wang , T. Nakamura , S. Sampath , A. Goland , H. Herman , J. Allen , J. Ilavsky , G. Long , J. Frahm , and R.W. Steinbrech , Comprehensive Microstructural Characterization and Predictive Property Modeling of Plasma-Sprayed Zirconia Coatings , Acta Mater. , vol. 51 , pp. 2457 – 2475 , 2003 .
   Web of Science ®Google Scholar
• P. Roy , G. Bertrand , and C. Coddet , Influence of Spraying Variables and of a New Zirconia Hollow Powder on the Microstructure of Plasma Sprayed Thermal Barrier Coating , in B. R. Marple and C. Moreau (eds.), Thermal Spray 2003: Advancing the Science & Applying the Technology , pp. 1617 – 1622 , ASM , Materials Park , OH , 2003 .
   Google Scholar
• W. J. Parker , R. J. Jenkins , C. P. Butler , and G. L. Abbott , Flash Method of Determining Thermal Diffusivity, Heat Capacity, and Thermal Conductivity , J. Appl. Phys. , vol. 32 , no. 9 , pp. 1679 – 1684 , 1961 . [CROSSREF]
   Web of Science ®Google Scholar
• H. Wang and R. B. Dinwiddie , Reliability of Laser Flash Thermal Diffusivity Measurements of the Thermal Barrier Coatings , J. Thermal Spray Technol. , vol. 9 , no. 2 , pp. 210 – 214 , 2000 . [CSA] [CROSSREF]
   Google Scholar
• P. G. Klemens , Thermal Conductivity of Inhomogeneous Media , High Temp. High Press. , vol. 23 , no. 3 , pp. 241 – 248 , 1991 .
   Google Scholar
• K. W. Schlichting , N. P. Padture , and P. G. Klemens , Thermal Conductivity of Dense and Porous Yttria-Stabilized Zirconia , J. of Mater. Sci. , vol. 36 , pp. 3003 – 3010 , 2001 . [CROSSREF]
   Web of Science ®Google Scholar
• J. Wu , N. P. Padture , P. G. Klemens , M. Gell , E. Garcia , P. Miranzo , and M. I. Osendi , Thermal Conductivity of Ceramics in the ZrO2-GdO1.5 System , J. Mater. Res. , vol. 17 , no. 12 , pp. 3193 – 3200 , 2002 . [CSA]
   Google Scholar
• S. Raghavan , H. Wang , R. B. Dinwiddie , W. D. Porter , and M. J. Mayo , The Effect of Grain Size, Porosity and Yttria Content on the Thermal Conductivity of Nanocrystalline Zirconia, Scripta Mater. , vol. 39, no. 8, pp. 1119–1125, 1998. [CROSSREF]
   Google Scholar
• R. Dutton , R. Wheeler , K. S. Ravichandran , and K. An , Effect of Heat Treatment on the Thermal Conductivity of Plasma-Sprayed Thermal Barrier Coatings , J. Thermal Spray Technol. , vol. 9 , no. 2 , pp. 204 – 209 , 2000 . [CSA] [CROSSREF]
   Google Scholar
• D. P. H. Hasselman , Effect of Cracks on Thermal Conductivity , J. Comp. Mater. , vol. 12 , no. 10 , pp. 403 – 407 , 1978 .
   Google Scholar
• K. Bakker , Using the Finite Element Method to Compute the Influence of Complex Porosity and Inclusion Structures on the Thermal and Electrical Conductivity , Int. J. Heat Mass Transfer , vol. 40 , no. 15 , pp. 3503 – 3511 , 1997 . [CROSSREF]
   Web of Science ®Google Scholar
• K. J. Hollis , Pore Phase Mapping and Finite-Element Modeling of Plasma Sprayed Tungsten Coatings , in C. C. Berndt and S. Sampath (eds.), Thermal Spray Science & Technology , pp. 403 – 408 , ASM , Materials Park , OH , 1995 .
   Google Scholar
• J. M. Dorvaux , O. Lavigne , R. Mévrel , M. Poulain , Y. Renollet , and C. Rio , Modelling the Thermal Conductivity of Thermal Barrier Coatings , Proc. 85th AGARD SMP Meeting on Thermal Barrier Coatings , Aalborg , Denmark , 1997 .
   Google Scholar
• G. Antou , R. Bolot , G. Montavon , C. Coddet , F. Hlawka , and A. Cornet , Prediction of Thermal Spray Coating Thermal Conductivity by 2D Heat Transfer Modelling , Int. Thermal Spray Conf. , Osaka , May 2004 .
   Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , pp. 44 – 45 , Hemisphere , New York , 1980 .
   Google Scholar
• N. Padture and P. G. Klemens , Low Thermal Conductivity in Garmets , J. Am. Ceram. Soc. , vol. 80 , no. 4 , pp. 1018 – 1020 , 1997 . [CSA]
   Google Scholar
• P. G. Klemens and M. Gell , Thermal Conductivity of Thermal Barrier Coatings , Mater. Sci. and Eng. A , vol. 245 , pp. 143 – 149 , 1998 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• P. G. Klemens , Phonon Scattering by Oxygen Vacancies in Ceramics , Physica B , vol. 263–264 , pp. 102 – 104 , 1999 .
   Google Scholar
• S. Raghavan , H. Wang , W. D. Porter , R. B. Dinwiddie , and M. J. Mayo , Thermal Properties of Zirconia Co-doped with Trivalent and Pentavalent Oxides , Acta Mater. , vol. 49 , pp. 169 – 179 , 2001 . [CROSSREF]
   Web of Science ®Google Scholar
• M. Roufosse and P. G. Klemens , Lattice Thermal Conductivity of Minerals at High Temperatures , J. Geophys. Res. , vol. 79 , no. 5 , pp. 703 – 705 , 1974 .
   Google Scholar
• R. Mévrel , J. C. Laizet , A. Azzopardi , B. Leclercq , M. Poulain , O. Lavigne , and D. Demange , Thermal Diffusivity and Conductivity of Zr1−x Y x O2−x/2 (x = 0., 0.084 and 0.179) Single Crystals , J. Eur. Ceram. Soc. , vol. 24 , pp. 3081 – 3089 , 2004 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• J. O. Hirschfelder , C. F. Curtiss , and R. B. Bird , Molecular Theory of Gases and Liquids , 4th ed. , p. 549 , Wiley , New York , 1967 .
   Google Scholar
• R. McPherson , A Model for the Thermal Conductivity of Plasma-Sprayed Ceramic Coatings , Thin Solid Films , vol. 112 , pp. 89 – 95 , 1984 . [CSA] [CROSSREF]
   Web of Science ®Google Scholar
• A. Mogro-Campero , C. A. Johnson , P. J. Bednarczyk , R. B. Dinwiddie , and H. Wang , Effect of Gas Pressure on Thermal Conductivity of Zirconia Thermal Barrier Coatings , Surface Coatings Technol. , vol. 94–95 , pp. 102 – 105 , 105 .
   Google Scholar
• I. O. Golosnoy , S. A. Tsipas , and T. W. Clyne , An Analytical Model for Simulation of Heat Flow in Plasma Sprayed Thermal Barrier Coatings , J. Thermal Spray Technol. , in press . [CSA]
   Google Scholar
• G. E. Forsythe and W. R. Wasow , Finite-Difference Methods for Partial Differential Equations , Wiley , New York , 1960 .
   Google Scholar
• A. R. Mitchell and D. F. Griffiths , The Finite Difference Method in Partial Differential Equations , Wiley , New York , 1980 .
   Google Scholar
• J. P. Nougier , Méthodes de calcul numérique, vol. 1, Systèmes d'équations , Hermès , Paris , 2001.
   Google Scholar
• G. Engeln-Müllges and F. Uhlig , Numerical Algorithms with Fortran , Berlin , Springer-Verlag , 1996 .
   Google Scholar
• S. Karaa and J. Zhang , A Note on Convergence of Line Iterative Methods for a Nine-Point Matrix , Appl. Math. Lett. , vol. 15 , pp. 495 – 503 , 2002 . [CROSSREF]
   Google Scholar
• I. Faragó and P. Tarvainen , Qualitative Analysis of Matrix Splitting Methods , Comput. and Math. with Appl. , vol. 42 , pp. 1055 – 1067 , 2001 . [CROSSREF]
   Google Scholar
• V. Thomée , From Finite Differences to Finite Elements: A Short History of Numerical Analysis of Partial Differential Equations , J. Computat. Appl. Math. , vol. 128 , pp. 1 – 54 , 2001 . [CROSSREF]
   Google Scholar
• D. A. Anderson , J. C. Tannehill , and R. H. Pletcher , Computational Fluid Mechanics and Heat Transfer , pp. 132 – 135 , Hemisphere , New York , 1984 .
   Google Scholar
• P. J. Roache , Computational Fluid Dynamic , rev. ed. , pp. 117 – 123 , Hermosa , Albuquerque , NM , 1982 .
   Google Scholar
• T. Y. Wang and C. C. P. Chen , Thermal-ADI—A Linear-Time Chip-Level Dynamic Thermal-Simulation Algorithm Based on Alternating-Direction-Implicit (ADI) Method , IEEE Trans. on Very Large Scale Integration (VLSI) Syst. , vol. 11 , no. 4 , pp. 691 – 700 , 2003 . [CROSSREF]
   Google Scholar