This work presents the combined use of the integral transform method, for the direct problem solution, and of Bayesian inference, for the inverse problem analysis, in the simultaneous estimation of spatially variable thermal conductivity and thermal capacity for one-dimensional heat conduction within heterogeneous media. The direct problem solution is analytically obtained via integral transforms and the related eigenvalue problem is solved by the generalized integral transform technique (GITT), offering a fast, precise, and robust solution for the transient temperature field. The inverse problem analysis employs a Markov chain Monte Carlo (MCMC) method, through the implementation of the Metropolis-Hastings sampling algorithm. Instead of seeking the functions estimation in the form of local values for the thermal conductivity and capacity, an alternative approach is employed based on the eigenfunction expansion of the thermophysical properties themselves. Then, the unknown parameters become the corresponding series coefficients for the properties eigenfunction expansions. Simulated temperatures obtained via integral transforms are used in the inverse analysis, for a prescribed concentration distribution of the dispersed phase in a heterogeneous media such as particle filled composites. Available correlations for the thermal conductivity and theory of mixtures relations for the thermal capacity are employed to produce the simulated results with high precision in the direct problem solution, while eigenfunction expansions with reduced number of terms are employed in the inverse analysis itself, in order to avoid the inverse crime. Gaussian distributions were used as priors for the parameter estimation procedure. In addition, simulated results with different randomly generated errors were employed in order to test the inverse analysis robustness.
Skip Nav Destination
e-mail: cotta@mecanica.coppe.ufrj.br
Article navigation
November 2011
This article was originally published in
Journal of Heat Transfer
Research Papers
Combining Integral Transforms and Bayesian Inference in the Simultaneous Identification of Variable Thermal Conductivity and Thermal Capacity in Heterogeneous Media
Carolina P. Naveira-Cotta,
Carolina P. Naveira-Cotta
LTTC—Laboratory of Transmission and Technology of Heat, Mechanical Engineering Department – Escola Politécnica & COPPE,
Universidade Federal do Rio de Janeiro
, UFRJ, Cx. Postal 68503—Cidade Universitária, 21945-970 Rio de Janeiro, RJ, Brasil
Search for other works by this author on:
Helcio R. B. Orlande,
Helcio R. B. Orlande
LTTC—Laboratory of Transmission and Technology of Heat, Mechanical Engineering Department – Escola Politécnica & COPPE,
Universidade Federal do Rio de Janeiro
, UFRJ, Cx. Postal 68503—Cidade Universitária, 21945-970 Rio de Janeiro, RJ, Brasil
Search for other works by this author on:
Renato M. Cotta
Renato M. Cotta
LTTC—Laboratory of Transmission and Technology of Heat, Mechanical Engineering Department – Escola Politécnica & COPPE,
e-mail: cotta@mecanica.coppe.ufrj.br
Universidade Federal do Rio de Janeiro
, UFRJ, Cx. Postal 68503—Cidade Universitária, 21945-970 Rio de Janeiro, RJ, Brasil
Search for other works by this author on:
Carolina P. Naveira-Cotta
LTTC—Laboratory of Transmission and Technology of Heat, Mechanical Engineering Department – Escola Politécnica & COPPE,
Universidade Federal do Rio de Janeiro
, UFRJ, Cx. Postal 68503—Cidade Universitária, 21945-970 Rio de Janeiro, RJ, Brasil
Helcio R. B. Orlande
LTTC—Laboratory of Transmission and Technology of Heat, Mechanical Engineering Department – Escola Politécnica & COPPE,
Universidade Federal do Rio de Janeiro
, UFRJ, Cx. Postal 68503—Cidade Universitária, 21945-970 Rio de Janeiro, RJ, Brasil
Renato M. Cotta
LTTC—Laboratory of Transmission and Technology of Heat, Mechanical Engineering Department – Escola Politécnica & COPPE,
Universidade Federal do Rio de Janeiro
, UFRJ, Cx. Postal 68503—Cidade Universitária, 21945-970 Rio de Janeiro, RJ, Brasil
e-mail: cotta@mecanica.coppe.ufrj.br
J. Heat Transfer. Nov 2011, 133(11): 111301 (10 pages)
Published Online: August 31, 2011
Article history
Received:
December 21, 2009
Revised:
April 11, 2011
Online:
August 31, 2011
Published:
August 31, 2011
Citation
Naveira-Cotta, C. P., Orlande, H. R. B., and Cotta, R. M. (August 31, 2011). "Combining Integral Transforms and Bayesian Inference in the Simultaneous Identification of Variable Thermal Conductivity and Thermal Capacity in Heterogeneous Media." ASME. J. Heat Transfer. November 2011; 133(11): 111301. https://doi.org/10.1115/1.4004010
Download citation file:
Get Email Alerts
Cited By
Entropic Analysis of the Maximum Output Power of Thermoradiative Cells
J. Heat Mass Transfer
Molecular Dynamics Simulations in Nanoscale Heat Transfer: A Mini Review
J. Heat Mass Transfer
Related Articles
A Novel Methodology for Combined Parameter and Function Estimation Problems
J. Heat Transfer (December,2010)
Some Algebraically Explicit Analytical Solutions of Unsteady Nonlinear Heat Conduction
J. Heat Transfer (December,2001)
Boundary Control of Temperature Distribution in a Spherical Shell With Spatially Varying Parameters
J. Heat Transfer (January,2012)
Identification of Contact Failures in Multilayered Composites With the Markov Chain Monte Carlo Method
J. Heat Transfer (October,2014)
Related Proceedings Papers
Related Chapters
Simultaneous Thermal Conductivity and Specific Heat Measurements of Thin Samples by Transient Joule Self-Heating
Inaugural US-EU-China Thermophysics Conference-Renewable Energy 2009 (UECTC 2009 Proceedings)
Steady Heat Conduction with Variable Heat Conductivity
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow
Orthotropic Media
Thermal Spreading and Contact Resistance: Fundamentals and Applications