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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 57, 2010 - Issue 3
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Original Articles

Integral Transforms and Bayesian Inference in the Identification of Variable Thermal Conductivity in Two-Phase Dispersed Systems

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Pages 173-202 | Received 09 Sep 2009, Accepted 15 Jan 2010, Published online: 04 May 2010

REFERENCES

  • C. Zweben , Advances in Composite Materials for Thermal Management in Electronic Packaging , J. Minerals, Metals Materials Soc. , vol. 50 , pp. 47 – 51 , 1998 .
  • D. M. Bigg , Thermal Conductivity of Heterophase Polymer Compositions , Adv. Polymer Sci. , vol. 119 , pp. 1 – 30 , 1995 .
  • Y. Yang , Thermal Conductivity , in J. E. Mark (ed.), Physical Properties of Polymers Handbook , Part III, Chap. 10 , pp. 155 – 163 , 2007 .
  • R. C. Progelhof , J. L. Throne , and R. R. Ruetsch , Methods for Predicting the Thermal Conductivity of Composite Systems: A Review , Polymer Eng. Sci. , vol. 16 , pp. 615 – 625 , 1976 .
  • I. H. Tavman , Thermal and Mechanical Properties of Aluminum Powder-Filled High-Density Polyethylene Composites , J. Appl. Polymer Sci. , vol. 62 , pp. 2161 – 2167 , 1996 .
  • I. H. Tavman and H. Akinci , Transverse Thermal Conductivity of Fiber Reinforced Polymer Composites , Int. Commun. Heat Mass Transfer , vol. 27 , pp. 253 – 261 , 2000 .
  • N. M. Sofian , M. Rusu , R. Neagu , and E. Neagu , Metal Powder-Filled Polyethylene Composites. V. Thermal Properties , J. Thermoplastic Composite Mater. , vol. 14 , pp. 20 – 33 , 2001 .
  • Ye. P. Mamunya , V. V. Davydenko , P. Pissis , and E. V. Lebedev , Electrical and Thermal Conductivity of Polymers Filled with Metal Powders , Eur. Polymer J. , vol. 38 , pp. 1887 – 1897 , 2002 .
  • D. Kumlutas , I. H. Tavman , and M. T. Çoban , Thermal Conductivity of Particle Filled Polyethylene Composite Materials, Composite Sci. Technol. , vol. 63, pp. 113–117, 2003.
  • F. Danes , B. Garnier , and T. Dupuis , Predicting, Measuring and Tailoring the Transverse Thermal Conductivity of Composites from Polymer Matrix and Metal Filler , Int. J. Thermophys. , vol. 24 , pp. 771 – 784 , 2003 .
  • A. Boudenne , L. Ibos , M. Fois , E. Gehin , and J. C. Majeste , Thermophysical Properties of Polypropylene/Aluminum Composites , J. Polymer Sci., B, Polymer Phys. , vol. 48 , pp. 722 – 732 , 2004 .
  • B. Weidenfeller , M. Hofer , and F. R. Schilling , Thermal Conductivity, Thermal Diffusivity, and Specific Heat Capacity of Particle Filled Polypropylene , Composites A , vol. 35 , pp. 423 – 429 , 2004 .
  • A. Boudenne , L. Ibos , M. Fois , J. C. Majeste , and E. Gehin , Electrical and Thermal Behavior of Polypropylene Filled with Copper Particles , Composites A , vol. 36 , pp. 1545 – 1554 , 2005 .
  • D. Kumlutas and I. H. Tavman , A Numerical and Experimental Study on Thermal Conductivity of Particle Filled Polymer Composites , J. Thermoplastic Composite Mater. , vol. 19 , pp. 441 – 455 , 2006 .
  • H. Serkan Tekce , D. Kumlutas , and I. H. Tavman , Effect of Particle Shape on Thermal Conductivity of Copper Reinforced Polymer Composites , J. Reinforced Plastics Composites , vol. 26 , pp. 113 – 121 , 2007 .
  • D. Lesnic , L. Elliot , D. B. Ingham , B. Clennell , and R. J. Knioe , The Identification of the Piecewise Homogeneous Thermal Conductivity of Conductors Subjected to a Heat Flow Test , Int. J. Heat Mass Transfer , vol. 42 , pp. 143 – 152 , 1999 .
  • E. Divo , A. Kassab , and F. Rodriguez , Characterization of Space Dependent Thermal Conductivity with a BEM-Based Genetic Algorithm , Numer. Heat Transfer A , vol. 37 , pp. 845 – 875 , 2000 .
  • F. A. Rodrigues , H. R. B. Orlande , and G. S. Dulikravich , Simultaneous Estimation of Spatially Dependent Diffusion Coefficient and Source Term in a Nonlinear 1D Diffusion Problem , Math. Comput. Simulation , vol. 66 , pp. 409 – 424 , 2004 .
  • M. R. Golbahar Haghighi , M. Eghtesad , P. Malekzadeh , and D. S. Necsulescu , Two-Dimensional Inverse Heat Transfer Analysis of Functionally Graded Materials in Estimating Time-Dependent Surface Heat Flux , Numer. Heat Transfer A , vol. 54 , pp. 744 – 762 , 2008 .
  • S. H. Lin , Transient Conduction in Heterogeneous Media , Int. Commun. Heat Mass Transfer , vol. 10 , pp. 165 – 174 , 1992 .
  • E. Divo and A. Kassab , Generalized Boundary Integral Equation for Transient Heat Conduction in Heterogeneous Media , J. Thermophys. Heat Transfer , vol. 12 , p. 364 , 1998 .
  • B. Chen , L. Tong , Y. Gu , H. Zhang , and O. Ochoa , Transient Heat Transfer Analysis of Functionally Graded Materials Using Adaptive Precise Time Integration and Graded Finite Elements , Numer. Heat Transfer B , vol. 45 , pp. 181 – 200 , 2004 .
  • J. Fang , G. F. Zhao , J. Zhao , and A. Parriaux , On the Truly Meshless Solution of Heat Conduction Problems in Heterogeneous Media , Numer. Heat Transfer B , vol. 55 , pp. 1 – 13 , 2009 .
  • M. D. Mikhailov and M. N. Ozisik , Unified Analysis and Solutions of Heat and Mass Diffusion , Wiley , Newyork , 1984; Dover, Newyork , 1994 .
  • R. M. Cotta , Integral Transforms in Computational Heat and Fluid Flow , CRC Press , Boca Raton , FL , 1993 .
  • R. M. Cotta and M. D. Mikhailov , Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computation , Wiley-Interscience , New York , 1997 .
  • R. M. Cotta , The Integral Transform Method in Thermal and Fluids Sciences and Engineering , Begell House , New York , 1998 .
  • R. M. Cotta and M. D. Mikhailov , Hybrid Methods and Symbolic Computations, in W. J. Minkowycz , E. M. Sparrow , and J. Y. Murthy (eds.), Handbook of Numerical Heat Transfer, , 2nd ed., pp. 493–522, Wiley , New York , 2006.
  • M. D. Mikhailov and R. M. Cotta , Integral Transform Method for Eigenvalue Problems , Commun. Numer. Meth. Eng. , vol. 10 , pp. 827 – 835 , 1994 .
  • L. A. Sphaier and R. M. Cotta , Integral Transform Analysis of Multidimensional Eigenvalue Problems within Irregular Domains , Numer. Heat Transfer B , vol. 38 , pp. 157 – 175 , 2000 .
  • S. C. Hirata , B. Goyeau , D. Gobin , and R. M. Cotta , Stability of Natural Convection in Composite Enclosures Using Integral Transforms , Numer. Heat Transfer B , vol. 50 , pp. 409 – 424 , 2006 .
  • C. P. Naveira-Cotta , R. M. Cotta , H. R. B. Orlande , and O. Fudym , Eigenfunction Expansions for Transient Diffusion in Heterogeneous Media , Int. J. Heat Mass Transfer , vol. 52 , pp. 5029 – 5039 , 2009 .
  • S. Wolfram , The Mathematica Book , version 5.2 , Cambridge-Wolfram Media , Urbana-Champaign , IL , 2005 .
  • J. Beck and K. Arnold , Parameter Estimation in Engineering and Science , Wiley Interscience , New York , 1977 .
  • M. N. Ozisik and H. R. B. Orlande , Inverse Heat Transfer: Fundamentals and Applications , Taylor & Francis , New York , 2000 .
  • J. Kaipio and E. Somersalo , Statistical and Computational Inverse Problems , Springer-Verlag , Berlin , 2004 .
  • P. Lee , Bayesian Statistics , Oxford University Press , London , 2004 .
  • D. Gamerman and H. F. Lopes , Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, , 2nd ed. , Chapman & Hall/CRC , Boca Raton , FL , 2006 .
  • H. S. Migon and D. Gamerman , Statistical Inference: An Integrated Approach , Arnold , Oxford , London, New York , 1999 .
  • H. R. B. Orlande , M. J. Colaço , and G. S. Dulikravich , Approximation of the Likelihood Function in the Bayesian Technique for the Solution of Inverse Problems , Inverse Prob. Sci. Eng. , vol. 16 , pp. 677 – 692 , 2008 .
  • O. Fudym , H. R. B. Orlande , M. Bamford , and J. C. Batsale , Bayesian Approach for Thermal Diffusivity Mapping from Infrared Images Processing with Spatially Random Heat Pulse Heating , J. Phys. Conf. Ser. (online) , vol. 135 , pp. 12 – 42 , 2008 .
  • N. Metropolis , A. W. Rosenbluth , M. N. Rosenbluth , A. H. Teller , and E. Teller , Equations of State Calculations by Fast Computating Machines , J. Chemi. Phys. , vol. 21 , pp. 1087 – 1092 , 1953 .
  • W. K. Hastings , Monte Carlo Sampling Methods Using Markov Chains and Their Applications , Biometrika , vol. 57 , pp. 97 – 109 , 1970 .
  • A. A. Barker , Monte Carlo Calculation of the Radial Distribution Functions for a Proton-Electron Plasma , Austral. J. Phys. , vol. 18 , pp. 119 – 133 , 1965 .
  • P. H. Peskun , Optimum Monte Carlo Sampling Using Markov Chain , Biometrika , vol. 60 , pp. 607 – 612 , 1973 .
  • J. C. Maxwell , A Treatise on Electricity and Magnetism , Dover , New York , 1954 .
  • T. Lewis and L. Nielsen , Dynamic Mechanical Properties of Particulate-Filled Polymers , J. Appl. Polymer Sci. , vol. 14 , pp. 1449 – 1471 , 1970 .
  • Y. Agari and T. Uno , Estimation on Thermal Conductivities of Filled Polymers , J. Appl. Polymer Sci. , vol. 32 , pp. 5705 – 5712 , 1986 .

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