Numerical identification of the thermal conductivity tensor and the heat capacity per unit volume of an anisotropic material

Atchonouglo, Kossi; Dupre, J. C.; Germaneau, Arnaud; Vallée, Claude

doi:10.1051/meca/2019026

Cited by 7 publications

(6 citation statements)

References 19 publications

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“…6). A relative error of 0.8% is reached for a noise of 0.1 • C and 2.2% for a noise of 0.4 • C. Previous study [27] using a similar approach for an homogeneous material, gives an uncertainty of about 5% for the two components of the conductivity tensor and 4% for the heat capacity per unit volume for comparable conditions (M = 31 and dt = 4 s). Nevertheless a spatial median filter (3 × 3 pixels) coupled with an average temporal filter (on 3 images) have to be used to obtain simular results, it is not the case in this procedure.…”

Section: Influence Of the Noise Amplitudementioning

confidence: 79%

“…The objective of this work concerns the development of an identification method allowing a simultaneous estimation of the thermal conductivity tensors and heat capacity per unit volume of a orthotropic bimaterial using an experimental device constituted by an IR camera and heat electric sources. This work follows previous works [27] considering homogeneous orthotropic material. This latter was sensitive to the noisy image, and a low-pass filter was necessary.…”

Section: Introductionmentioning

confidence: 75%

“…These relative error decrease to 0.03% for σ = 0.1 • C. One of the main results is the procedure that is almost insensitive to temperature noise. This method is less sensitive to noise than the previous works [27]. The continuation of this work, in simulation, consists in studying other types of more or less conductive materials in order to see the influence on the accuracy of the parameters.…”

Section: Discussionmentioning

confidence: 99%

“…The chosen material is the polyamide. This procedure allows us to compare this new approach with the previous ones [27] developed for homogeneous material.…”

Section: Identification Of the Parameters Of A Structure Made Of One ...mentioning

confidence: 99%

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Estimation of thermophysic properties of a bimaterial by temperature field measurement and finite element model updating

Koumekpo

Atchonouglo

Ayeleh

et al. 2023

Mechanics & Industry

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The aim of this study is to identify simultaneously the thermal conductivity tensor and the heat capacity per unit volume of a bimaterial, whose heat conduction obeys Fourier’s law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution of the heat conduction equation solved numerically with the help of finite element method formulation. To identify the parameters, an inverse method is developed by using the finite element model updating (FEMU) based on the Levenberg-Marquardt algorithm. This inverse finite element method approach allowed us to estimate the thermophysical parameters sought. We validated the numerical procedure by using noiseless temperature fields at different time and space steps and two types of material: an homogeneous and a bimaterial one. To be close to real conditions, the influence of the noise on the temperature fields is also studied and shows the efficiency of the inverse method. The results of this procedure show that the identified parameters are very less sensitive to the number of infra-red images varying from 40 to 80 and the number of elements ranging from 20 to 50 for a specimen size equals to 36.6 × 36.6 mm2.

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Section: Influence Of the Noise Amplitudementioning

confidence: 79%

Section: Introductionmentioning

confidence: 75%

Section: Discussionmentioning

confidence: 99%

“…The chosen material is the polyamide. This procedure allows us to compare this new approach with the previous ones [27] developed for homogeneous material.…”

Section: Identification Of the Parameters Of A Structure Made Of One ...mentioning

confidence: 99%

See 2 more Smart Citations

Estimation of thermophysic properties of a bimaterial by temperature field measurement and finite element model updating

Koumekpo

Atchonouglo

Ayeleh

et al. 2023

Mechanics & Industry

Self Cite

View full text Add to dashboard Cite

show abstract

“…The conjugate gradient method (CGM) with adjoint problem has been used by Cao et al (2019) to determine the thermal conductivity of inhomogeneous orthotropic materials from internal temperature measurements for two-dimensional (2D) problems. CGM has also been used in the simultaneous determination of the space-dependent thermal conductivity and capacity coefficient by Atchonouglo et al (2019), and by Mohebbi and Sellier (2016) for estimating the thermal conductivity, the heat transfer coefficient and the heat flux, in a 3D irregular solid both separately and simultaneously. All above cases deal with space-dependent conductivities.…”

Section: Introductionmentioning

confidence: 99%

Thermal conductivity reconstruction method with application in a face milling operation

Boos

Bazán

Luchesi

2023

HFF

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Purpose This paper aims to reconstruct the spatially varying orthotropic conductivity based on a two-dimensional inverse heat conduction problem described by a partial differential equation (PDE) model with mixed boundary conditions. The proposed discretization uses a highly accurate technique and allows simple implementations. Also, the authors solve the related inverse problem in such a way that smoothness is enforced on the iterations, showing promising results in synthetic examples and real problems with moving heat source. Design/methodology/approach The discretization procedure applied to the model for the direct problem uses a pseudospectral collocation strategy in the spatial variables and Crank–Nicolson method for the time-dependent variable. Then, the related inverse problem of recovering the conductivity from temperature measurements is solved by a modified version of Levenberg–Marquardt method (LMM) which uses singular scaling matrices. Problems where data availability is limited are also considered, motivated by a face milling operation problem. Numerical examples are presented to indicate the accuracy and efficiency of the proposed method. Findings The paper presents a discretization for the PDEs model aiming on simple implementations and numerical performance. The modified version of LMM introduced using singular scaling matrices shows the capabilities on recovering quantities with precision at a low number of iterations. Numerical results showed good fit between exact and approximate solutions for synthetic noisy data and quite acceptable inverse solutions when experimental data are inverted. Originality/value The paper is significant because of the pseudospectral approach, known for its high precision and easy implementation, and usage of singular regularization matrices on LMM iterations, unlike classic implementations of the method, impacting positively on the reconstruction process.

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Heat conduction in an orthotropic material–numerical analysis using python

Kumar

Roy

Kumar

2022

Int J Interact Des Manuf

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Numerical identification of the thermal conductivity tensor and the heat capacity per unit volume of an anisotropic material

Cited by 7 publications

References 19 publications

Estimation of thermophysic properties of a bimaterial by temperature field measurement and finite element model updating

Estimation of thermophysic properties of a bimaterial by temperature field measurement and finite element model updating

Thermal conductivity reconstruction method with application in a face milling operation

Heat conduction in an orthotropic material–numerical analysis using python

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