Estimativa da Variação Temporal de Condutância Térmica de Contato em Placas Termicamente Finas via Método MCMC
DOI:
https://doi.org/10.14295/vetor.v32i2.14304Palavras-chave:
Condutância térmica de contato, Método de Monte Carlo via Cadeias de Markov, Classic LumpedResumo
Este trabalho trata da solução de um problema inverso de condução de calor visando estimar a variação temporal de condutância térmica de contato, num problema unidimensional em um material de duas camadas termicamente finas, aquecidas por meio de um fluxo de calor aplicado na superfície superior e exposto a convecção térmica na superfície inferior. Para a formulação do problema direto, considerando placas termicamente finas, foi utilizado o método Classic Lumped. Esta formulação reduz o problema original em duas equações diferenciais ordinárias acopladas, desta forma, possibilita diminuir o custo computacional necessário para solucionar o problema direto associado, que foi resolvido utilizando a função NDSolve, intrínseca do software Mathematica. Para a solução do problema inverso foi utilizado o método Monte Carlo via Cadeias de Markov, dentro de uma abordagem Bayesiana, aplicando o algoritmo de Metropolis-Hastings. O método foi analisado a partir de medidas simuladas de temperatura e se mostrou capaz para estimar uma função temporal da condutância térmica de contato. Esta metodologia permite levar em conta as incertezas associadas aos parâmetros presentes nos modelos, bem como, àquelas associadas com a estimativa da condutância térmica variando com o tempo, o que não é observado nos métodos voltados para estimativa temporal da condutância térmica de contato encontrados atualmente na literatura.
Downloads
Referências
C. V. Madhusudana, Thermal Contact Conductance. Cham: Springer International Publishing, 2014.
M. J. Colaço, e C. J. S. Alves, “A fast non-intrusive method for estimating spatial thermal contact conductance by means of the reciprocity functional approach and the method of fundamental solutions,” International Journal of Heat and Mass Transfer, vol. 60, pp. 653–663, May 2013. Disponível em: https://doi.org/10.1016/j.ijheatmasstransfer.2013.01.026
L. A. Abreu, H. R. B. Orlande, C. Cotta, J. N. N. Quaresma, R. M. Cotta, J. P. Kaipio, e V. Kolehmainen, “Identification of Contact Failures in Multi-Layered Composites,” em 31st Computers and Information in Engineering Conference, Parts A and B, Washington, DC, USA, Jan. 2011, pp. 479–487. Disponível em: https://doi.org/10.1115/DETC2011-47511
M. Grosso, J. E. C. Lopez, V. M. A. Silva, S. D. Soares, J. M. A. Rebello, e G. R. Pereira, “Pulsed thermography inspection of adhesive composite joints: computational simulation model and experimental validation,” Composites Part B: Engineering, vol. 106, pp. 1–9, 2016. Disponível em: https://doi.org/10.1016/j.compositesb.2016.09.011
J. Guo, X. N. Chen, Z. G. Qu, e Q. L. Ren, “Reverse identification method for simultaneous estimation of thermal conductivity and thermal contact conductance of multilayered composites,” International Journal of Heat and Mass Transfer, vol. 173, p. 121244, Jul. 2021. Disponível em: https://doi.org/10.1016/j.ijheatmasstransfer.2021.121244
D. Gay, Composite materials: design and applications, Third edition. Boca Raton: CRC Press, Taylor & Francis, 2015.
L. A. Abreu, H. R. B. Orlande, J. Kaipio, V. Kolehmainen, R. M. Cotta, e J. N. N. Quaresma, “Identification of Contact Failures in Multilayered Composites with the Markov Chain Monte Carlo Method,” J. Heat Transfer, vol. 136, no. 10, pp. 101302–101302, 2014. Disponível em: https://doi.org/10.1115/1.4027364
M. N. Ozisik, Heat Conduction. John Wiley & Sons, 1993.
F. A. Kulacki, Handbook of thermal science and engineering. New York, NY: Springer Berlin Heidelberg, 2018.
M. Grosso, C. A. Marinho, D. A. Nesteruk, J. M. Rebello, S. D. Soares, e V. P. Vavilov, “Evaluating quality of adhesive joints in glass-fiber plastic piping by using active thermal NDT,” SPIE Defense, Security and Sense, Baltimore, Maryland, USA, May 2013. Disponível em: https://doi.org/10.1117/12.2016762
X. Zhang, P. Cong, S. Fujiwara, e M. Fujii, “A new method for numerical simulation of thermal contact resistance in cylindrical coordinates,” International Journal of Heat and Mass Transfer, vol. 47, no. 5, pp. 1091–1098, 2004. Disponível em: https://doi.org/10.1016/j.ijheatmasstransfer.2003.04.001
H. Zhang, C. Shang, e G. Tang, “Measurement and identification of temperature-dependent thermal conductivity for thermal insulation materials under large temperature difference,” International Journal of Thermal Sciences, vol. 171, p. 107261, 2022. Disponível em: https://doi.org/10.1016/j.ijthermalsci.2021.107261
T. Cui, Q. Li, Y. Xuan, e P. Zhang, “Multiscale simulation of thermal contact resistance in electronic packaging,” International Journal of Thermal Sciences, vol. 83, pp. 16–24, 2014. Disponível em: https://doi.org/10.1016/j.ijthermalsci.2014.04.006
T. Zhou, Y. Zhao, e Z. Rao, “Fundamental and estimation of thermal contact resistance between polymer matrix composites: A review,” International Journal of Heat and Mass Transfer, vol. 189, p. 122701, 2022. Disponível em: https://doi.org/10.1016/j.ijheatmasstransfer.2022.122701
G. Inglese e R. Olmi, “Identification of time-varying inaccessible thermal conductance from data at the boundary,” Applicable Analysis, vol. 101, no. 10, pp. 3576–3590, 2020. Disponível em: https://doi.org/10.1080/00036811.2020.1761017
M. J. Colaço e C. J. S. Alves, “A Backward Reciprocity Function Approach to the Estimation of Spatial and Transient Thermal Contact Conductance in Double-Layered Materials Using Non-Intrusive Measurements,” Numerical Heat Transfer, Part A: Applications, vol. 68, no. 2, pp. 117–132, 2015. Disponível em: https://doi.org/10.1080/10407782.2014.994435
R. S. Padilha, M. J. Colaço, H. R. B. Orlande, e L. A. S. Abreu, “An analytical method to estimate spatially-varying thermal contact conductances using the reciprocity functional and the integral transform methods: Theory and experimental validation,” International Journal of Heat and Mass Transfer, vol. 100, pp. 599–607, 2016. Disponível em: https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.052
L. A. S. Abreu, M. J. Colaço, H. R. B. Orlande, e C. J. S. Alves, “Thermography detection of contact failures in double layered materials using the reciprocity functional approach,” Applied Thermal Engineering, vol. 100, pp. 1173–1178, 2016. Disponível em: https://doi.org/10.1016/j.applthermaleng.2016.02.078
C. R. de Lacerda, M. J. Colaço, e L. A. S. Abreu, “An extension of the reciprocity functional approach to the estimate of two-dimensional spatially dependent thermal contact conductances using regularization via TSVD: numerical and experimental results,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 40, no. 9, 2018. Disponível em: https://doi.org/10.1007/s40430-018-1344-9
L. Zhuo, D. Lesnic, e S. Meng, “Reconstruction of the heat transfer coefficient at the interface of a bi-material,” Inverse Problems in Science and Engineering, vol. 28, no. 3, pp. 374–401, 2020. Disponível em: https://doi.org/10.1080/17415977.2019.1574781
H. R. B. Orlande e M. N. Ozisik, “Inverse problem of estimating interface conductance between periodically contacting surfaces,” Journal of Thermophysics and Heat Transfer, vol. 7, no. 2, pp. 319–325, 1993. Disponível em: https://doi.org/10.2514/3.422
L. A. S. Abreu, C. J. S. Alves, M. J. Colaço, e H. R. B. Orlande, “A Non-Intrusive Inverse Problem Technique for the Identification of Contact Failures in Double-Layered Composites,” Proceedings of 15th International Heat Transfer Conference, Kyoto, Japan, 2014. Disponível em: https://doi.org/10.1615/IHTC15.inv.009532
S. Kumar e A. Tariq, “Effects of contact-nature on transient thermal contact conductance,” International Journal of Thermal Sciences, vol. 137, pp. 299–312, 2019. Disponível em: https://doi.org/10.1016/j.ijthermalsci.2018.11.029
M. Parikh, S. Shah, H. Vaghela, e A. K. Parwani, “A comprehensive experimental and numerical estimation of thermal contact conductance,” International Journal of Thermal Sciences, vol. 172, pp. 107285, 2022. Disponível em: https://doi.org/10.1016/j.ijthermalsci.2021.107285
L. A. S. Abreu, H. R. B. Orlande, M. J. Colaço, J. Kaipio, V. Kolehmainen, C. C. Pacheco, e R. M. Cotta, “Detection of contact failures with the Markov chain Monte Carlo method by using integral transformed measurements,” International Journal of Thermal Sciencies, vol. 132, pp. 486–497, 2018. Disponível em: https://doi.org/10.1016/j.ijthermalsci.2018.06.006
M. N. Ozisik e H. R. B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, 2nd ed. CRC Press, 2021.
J. Kaipio e E. Somersalo, Statistical and Computational Inverse Problems, vol. 160. New York: Springer-Verlag, 2005.
M. J. Colaço, H. R. B. Orlande, e G. S. Dulikravich, “Inverse and optimization problems in heat transfer,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 28, no. 1, pp. 1–24, 2006. Disponível em: https://doi.org/10.1590/S1678-58782006000100001
H. R. B. Orlande, “Inverse Problems in Heat Transfer: New Trends on Solution Methodologies and Applications,” Journal of Heat Transfer, vol. 134, no. 3, p. 031011, 2012. Disponível em: https://doi.org/10.1115/1.4005131
J. P. Kaipio e C. Fox, “The Bayesian Framework for Inverse Problems in Heat Transfer,” Heat Transfer Engineering, vol. 32, no. 9, pp. 718–753, 2011. Disponível em: https://doi.org/10.1080/01457632.2011.525137
R. M. Cotta e M. D. Mikhaĭlov, Heat conduction: lumped analysis, integral transforms, symbolic computation. Chichester ; New York: Wiley, 1997.
H. R. B. Orlande, G. S. Dulikravich, M. Neumayer, D. Watzenig, e M. J. Colaço, “Accelerated Bayesian Inference for the Estimation of Spatially Varying Heat Flux in a Heat Conduction Problem,” Numerical Heat Transfer, Part A: Applications, vol. 65, no. 1, pp. 1–25, 2014. Disponível em: https://doi.org/10.1080/10407782.2013.812008
H. R. B. Orlande, O. Fudym, D. Maillet, e R. M. Cotta, Eds., Thermal measurements and inverse techniques. Boca Raton, FL: CRC Press, 2011.
O. M. Alifanov, Inverse heat transfer problems. Berlin ; New York: Springer-Verlag, 1994.
J. V. Beck e K. J. Arnold, Parameter estimation in engineering and science. New York: Wiley, 1977.
J. V. Beck, B. Blackwell, e C. R. St. Clair, Inverse heat conduction: ill-posed problems. New York: Wiley, 1985.
F. Colin, H. Heikki, e C. J. Andrés, “Inverse problems,” in Bayesian Theory and Applications, P. Damien, P. Dellaportas, N. G. Polson, and D. A. Stephens, Eds. Oxford University Press, 2013, pp. 619–643.
J. Hadamard, Lectures on Cauchy’s Problem in Linear Partial Differential Equations. New Haven, CT: Yale University Press, 1923.
V. Isakov, Inverse Problems for Partial Differential Equations, 3rd ed. 2017. Cham: Springer International Publishing : Imprint: Springer, 2017.
D. Colton e R. Kress, Inverse acoustic and electromagnetic scattering theory, Fourth edition. Cham, Switzerland: Springer Nature, 2019.
D. Gamerman e H. F. Lopes, Markov chain Monte Carlo: stochastic simulation for Bayesian inference, 2nd ed. Boca Raton: Taylor & Francis, 2006.
N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, e E. Teller, “Equation of State Calculations by Fast Computing Machines,” The Journal of Chemical Physics, vol. 21, no. 6, pp. 1087–1092, 1953. Disponível em: https://doi.org/10.1063/1.1699114
W. K. Hastings, “Monte Carlo sampling methods using Markov chains and their applications,” Biometrika, vol. 57, no. 1, pp. 97–109, 1970. Disponível em: https://doi.org/10.2307/2334940
H. Massard da Fonseca, H. R. B. Orlande, O. Fudym, e F. Sepúlveda, “A statistical inversion approach for local thermal diffusivity and heat flux simultaneous estimation,” Quantitative InfraRed Thermography Journal, vol. 11, no. 2, pp. 170–189, 2014. Disponível em: https://doi.org/10.1080/17686733.2014.947860
Downloads
Publicado
Como Citar
Edição
Seção
