Inverse analysis with integral transformed temperature fields: Identification of thermophysical properties in heterogeneous media

The objective of this work is to introduce the use of integral transformed temperature measured data for the solution of inverse heat transfer problems, instead of the common local transient temperature measurements. The proposed approach is capable of significantly compressing the measured data through the integral transformation, without losing the information contained in the measurements and required for the solution of the inverse problem. The data compression is of special interest for modern measurement techniques, such as the infrared thermography, that allows for fine spatial resolutions and large frequencies, possibly resulting on a very large amount of measured data. In order to critically address the use of integral transformed measurements, we examine in this paper the simultaneous estimation of spatially variable thermal conductivity and thermal diffusivity in 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). The inverse problem is handled with Bayesian inference by employing a Markov Chain Monte Carlo (MCMC) method. The unknown functions appearing in the formulation are expanded in terms of eigenfunctions as well, so that the unknown parameters become the corresponding series coefficients. Such projection of the functions in an infinite dimensional space onto a parametric space of finite dimension also permits that several quantities appearing in the solution of the direct problem be analytically computed. Simulated measurements are used in the inverse analysis; they are assumed to be additive, uncorrelated, normally distributed, with zero means and known covariances. Both Gaussian and non-informative uniform distributions are used as priors for demonstrating the robustness of the estimation procedure.Indisponível

Inverse analysis of forced convection in micro-channels with slip flow via integral transforms and Bayesian inference

The present work addresses the direct and inverse problems for convective heat transfer with incompressible laminar gas flow in micro-channels, within the range of validity of the slip-flow regime. The direct problem analysis combines the classical integral transform method and the generalized integral transform technique (GITT), by analytically solving the two-dimensional steady-state convection problem and finding a hybrid numerical-analytical solution for the required eigenvalue problem. The inverse problem analysis makes use of the accuracy and robustness of the direct problem solution and focus on the simultaneous identification of the momentum and thermal accommodation coefficients, related to gas flow and heat transfer within micro-channels, besides the usually unknown boundary condition parameters, here represented by the external Biot number. The inverse analysis is based on the availability solely of temperature measurements at the channel external wall, along its length, as obtained for instance via infrared camera thermography. A Bayesian inference approach is adopted in the solution of the identification problem based on the Monte Carlo Markov Chain method (MCMC) and the Metropolis-Hastings sampling algorithm. A typical example of slip flow in parallel-plates micro-channel is selected to illustrate both the direct and inverse problems solution approaches.Indisponível

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

This work illustrates the use of Bayesian inference in the estimation of spatially variable thermal conductivity for one-dimensional heat conduction in heterogeneous media, such as particle-filled composites and other two-phase dispersed systems, by employing a Markov chain Monte Carlo (MCMC) method, through the implementation of the Metropolis-Hastings algorithm. The direct problem solution is obtained analytically 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, which are desirable features for the implementation of the inverse analysis. Instead of seeking the function estimation in the form of a sequence of local values for the thermal conductivity, an alternative approach is proposed here, which is based on the eigenfunction expansion of the thermal conductivity itself. Then, the unknown parameters become the corresponding series coefficients. Simulated temperatures obtained via integral transforms are used in the inverse analysis. From the prescription of the concentration distribution of the dispersed phase, available correlations for the thermal conductivity 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 so-called inverse crime. Both Gaussian and noninformative uniform distributions were used as priors for comparison purposes. In addition, alternative correlations for the thermal conductivity that yield different predictions are also employed as Gaussian priors for the algorithm in order to test the inverse analysis robustness.Indisponível

Eigenfunction expansions for transient diffusion in heterogeneous media

The Generalized Integral Transform Technique (GITT) is employed in the analytical solution of transient linear heat or mass diffusion problems in heterogeneous media. The GITT is utilized to handle the associated eigenvalue problem with arbitrarily space variable coefficients, defining an eigenfunction expansion in terms of a simpler Sturm-Liouville problem of known solution. In addition, the representation of the variable coefficients as eigenfunction expansions themselves has been proposed, considerably simplifying and accelerating the integral transformation process, while permitting the analytical evaluation of the coefficients matrices that form the transformed algebraic system. The proposed methodology is challenged in solving three different classes of diffusion problems in heterogeneous media, as illustrated for the cases of thermophysical properties with large scale variations found in heat transfer analysis of functionally graded materials (FGM), of abrupt variations in multiple layer transitions and of randomly variable physical properties in dispersed systems. The convergence behavior of the proposed expansions is then critically inspected and numerical results are presented to demonstrate the applicability of the general approach and to offer a set of reference results for potentials, eigenvalues, and related quantities.Indisponível

Thermographie infrarouge et méthodes d'inférence statistique pour la détermination locale et transitoire de termes-sources et diffusivité thermique

Ce travail a pour objectif de développer des techniques théoriques et expérimentales pour la détermination des propriétés thermophysiques et terme source. Deux formes de comportement temporel pour le terme source ont été étudiées : un constant et un qui varie dans le temps. La variation dans le temps a été considérée comme une pulse carrée ou une variation sinusoïdale. Deux formes d échauffement ont été utilisées : une résistance électrique et un laser diode. Pour l acquisition des données une caméra de thermographie par infrarouge a été utilisée. La stratégie nodale a été utilisée pour contourner le problème des grosses quantités de données générées par la caméra. Le problème direct a été résolu par différences finies, et deux approches pour la solution du problème inverse ont été utilisées, en fonction du comportement temporel du terme source. Les deux approches sont basées sur des méthodes d inférence statistiques dans une approche Bayésienne, avec la méthode de Monte Carlo via les Chaînes de Markov pour le terme source constant, et le filtre de Kalman pour le problème dont le terme source varie dans le temps. Des manipulations contrôlées ont été faites dans un échantillon avec des propriétés thermophysiques déterminées par des méthodes classiques dans la littérature.This work deals with the development of new theoretical and experimental techniques for the efficient estimation of thermophysical properties and source-term in micro and macro-scale. Two kinds of source term were studied: a constant and a time varying source term. The time wise variation of the source term had a sinusoidal and a pulse form. Two devices were used for the sample heating: An electrical resistance and a laser diode. For the data acquisition, an infrared camera was used, providing a full cartography of properties of the medium and also non-contact temperature measurements. The direct problem was solved by the finite differences method, and two approaches were used for the solution of the inverse problem, depending on the time varying behavior of the source term. Both approaches deal with the parameters estimation within the Bayesian framework, using the Markov Chain Monte Carlo (MCMC) method via the Metropolis Hastings (MH) algorithm for the constant source term, and the Kalman filter for the time-varying source term. The nodal strategy is presented as a method to deal with the large number of experimental data problems. Experiments were carried out in a sample with well-known thermophysical properties, determined by classical methods.TOULOUSE-INP (315552154) / SudocSudocFranceF

Experimental Identification of Thermophysical Properties in Heterogeneous Materials with Integral Transformation of Temperature Measurements from Infrared Thermography

This work deals with the experimental estimation of spatially variable thermal conductivity and diffusivity in heterogeneous media, with temperature measurements obtained via infrared thermography being used in the inverse analysis. The direct problem solution for a one-dimensional heat conduction experiment is analytically obtained via integral transforms, and the related eigenvalue problem is solved by the generalized integral transform technique. The inverse problem is handled by Bayesian inference through a Markov chain Monte Carlo algorithm. The functional representation and estimation is based on the eigenfunction expansion of the thermal conductivity and diffusivity themselves, and the unknown parameters become the corresponding expansion coefficients. The inverse analysis is performed on the transformed experimental temperature field instead of employing the actual local temperature measurements, thus promoting a significant data reduction through the integral transformation of the experimental measurements. A demonstration experiment is built involving partially heated thin plates made of bakelite and polystyrene, including a variable thickness plate to simulate spatially variable thermophysical properties.Indisponível

Bayesian estimation of the hydraulic and solute transport properties of a small-scale unsaturated soil column

In this study the hydraulic and solute transport properties of an unsaturated soil were estimated simultaneously from a relatively simple small-scale laboratory column infiltration/outflow experiment. As governing equations we used the Richards equation for variably saturated flow and a physical non-equilibrium dual-porosity type formulation for solute transport. A Bayesian parameter estimation approach was used in which the unknown parameters were estimated with the Markov Chain Monte Carlo (MCMC) method through implementation of the Metropolis-Hastings algorithm. Sensitivity coefficients were examined in order to determine the most meaningful measurements for identifying the unknown hydraulic and transport parameters. Results obtained using the measured pressure head and solute concentration data collected during the unsaturated soil column experiment revealed the robustness of the proposed approach.Indisponível

Theoretical–experimental analysis of heat transfer in nonhomogeneous solids via improved lumped formulation, integral transforms and infrared thermography

Theoretical and experimental methodologies for the identification of spatially variable thermophysical properties and for simulating multidimensional heat transfer in heterogeneous materials are illustrated by using plate samples with aluminum oxide nanoparticles dispersed in a polymeric matrix. First, the heterogeneous nanocomposite plate is thermally characterized by means of a fairly simple experimental setup which can be modeled by a one-dimensional heat conduction formulation with space variable properties. Non-intrusive temperature measurements are obtained via infrared thermography, while the direct problem is handled by an error-controlled integral transform solution with an improved lumped-differential formulation, and the inverse analysis is undertaken via Bayesian inference, making use of the Markov Chain Monte Carlo method. Then, in order to illustrate the application of the methodologies here presented, an experimental multidimensional demonstration is provided consisting of a small electrical resistance attached to the plate, simulating a heat generating electronic device installed on the nanocomposite substrate, which in such situation works as a heat spreader modeled by an improved lumped-differential two-dimensional heat conduction formulation. The integral transform solution of the lumped-differential two-dimensional problem is then critically compared against the infrared thermography experimental results.Indisponível

Space-variable thermophysical properties identification in nanocomposites via integral transforms, Bayesian inference and infrared thermography

Simultaneous estimation of space-variable thermal conductivity and heat capacity in heterogeneous samples of nanocomposites is dealt with by employing a combination of the generalized integral transform technique (GITT), for the direct problem solution, Bayesian inference as implemented with the Markov chain Monte Carlo (MCMC) method, for the inverse analysis and infrared thermography, for the temperature measurements. Another aspect of the proposed approach is the integral transformation of the thermographic experimental data along the space variable, which allows for a significant data compression since the inverse analysis is undertaken within the transformed field. Results are presented for the covalidation of the experiment with a homogeneous polyester plate, as well as for a plate made of polyester–alumina nanoparticles composite with abrupt variation of the filler concentration.Indisponível

An Analysis of Heat Conduction Models for Nanofluids

The mechanism of heat transfer intensification recently brought about by nanofluids is analyzed in this article, in the light of the non-Fourier dual-phase-lagging heat conduction model. The physical problem involves an annular geometry filled with a nanofluid, such as typically used for measurements of the thermal conductivity with Blackwell's line heat source probe. The mathematical formulation for this problem is analytically solved with the classical integral transform technique, thus providing benchmark results for the temperature predicted with the dual-phase-lagging model. Different test cases are examined in this work, involving nanofluids and probe sizes of practical interest. The effects of the relaxation times on the temperature at the surface of the probe are also examined. The results obtained with the dual-phase-lagging model are critically compared to those obtained with the classical parabolic model, showing that the increase in the thermal conductivity of nanofluids measured with the line heat source probe cannot be attributed to hyperbolic effects.Indisponível