A Backward Reciprocity Function Approach to the Estimation of Spatial and Transient Thermal Contact Conductance in Double-Layered Materials Using Non-Intrusive Measurements

Abstract

This paper presents a computationally fast methodology for the estimation of spatial and transient unknown thermal contact conductance between sandwiched materials, using non-intrusive measurements. The methodology is formulated in such a way that the spatial and temporal variations of the unknown function are obtained simply by solving a linear system, whose solution vector is composed of integrals containing measured temperatures and known heat fluxes applied at an external boundary. Good estimates are obtained, even for functions containing discontinuities in both time and space. Simulated measurements with and without errors are considered, showing very good results.

Detection of contact failures with the Markov chain Monte Carlo method by using integral transformed measurements

“…where Θ P ( ) is the solution of the direct (forward) problem, given by equation (2.a-k) with vector P given by equation (11).…”

“…The detection of internal failures in materials is a subject of extensive research due to its importance in several fields, for example, in structural health monitoring [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. With the recent advancement and practical applications (e.g., in the aeronautic, space and petroleum industries) of composites consisting of layers of different materials, nondestructive and noninvasive methods for the detection of adhesion failures between the composite layers have been developed [2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Heat transfer techniques can be found among these methods, by using qualitative [1,2,7,13,14] as well quantitative analyses based on the solutions of inverse problems [3][4][5][6][7][8][9][10][11][12].…”

Identification of the Thermal Conductance of a Hidden Barrier from Outer Thermal Data

“…Deviations of H from the reference known value H due to interface anomalies are evaluated by solving an Inverse Heat Conduction Problem (IHCP). An effective approach to this problem, based on the Reciprocity Function technique, is described in [4]. Here we improve the results in [4] by means of Thin Plate Approximation (TPA) (see for example [5]) and Fourier Filtering.…”

“…An effective approach to this problem, based on the Reciprocity Function technique, is described in [4]. Here we improve the results in [4] by means of Thin Plate Approximation (TPA) (see for example [5]) and Fourier Filtering. The idea of using a perturbative approach such as TPA is supported by the general assumption (see [2] Section 9.2.1) that thermography works mainly in detection of subsurface anomalies i.e., has the chance to be effective in thermally thin domains (Biot number ≤0.1 see [6] Section 5.2).…”

Estimativa da Variação Temporal de Condutância Térmica de Contato em Placas Termicamente Finas via Método MCMC

“…Muitos trabalhos, especialmente nesta última década, se dedicaram na proposta de metodologias experimentais de condutância térmica de contato [11][12][13][14], em aplicações e na sua identificação envolvendo a solução de problemas inversos, que tipicamente são resolvidos por meio de abordagens analíticas e Bayesianas. Os primeiros, tem sua solução obtida por meio de métodos que não envolvem uma análise sob incerteza das estimativas e dos demais parâmetros presentes nos modelos utilizados, como métodos envolvendo gradiente conjugado ou funcionais de reciprocidade [2,[15][16][17][18][19][20][21][22][23][24]. Entre as abordagens envolvendo técnicas Bayesianas [3,7,25], que permitem análise sob incerteza, foram consideradas estimativas e análises apenas em funções com variação espacial da condutância térmica de contato.…”