Identification of conductivity in inhomogeneous orthotropic media

Mahmood, Mohammed Shuker; Lesnic, D.

doi:10.1108/hff-11-2017-0469

Cited by 6 publications

(3 citation statements)

References 30 publications

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“…For example, the temperatures measured by the flash method can be used to estimate thermal conductivity tensor and heat capacity at the same time [11,12]. To solve the inverse problem, many works are rather oriented towards the use of a conjugate gradient method and stochastic algorithms [13,14]. The hybrid optimization strategy combining a Particle Swarm Optimization (PSO) algorithm and a gradient based method is used by El Rassy et al [15] for resolving such complex and non-linear inverse problem.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

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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“…However, estimation of the thermal conductivity in most engineering application remains challenging due to factors that influence the material properties of solids. In particular, the estimation of thermal properties of composite materials is an ill-posed inverse heat conduction problem (IHCP) and presents difficulties because it is intrinsically unstable and thus very sensitive to the inaccuracy of input data (Baralić et al , 2019; Cao et al , 2019; Özişik, 1993; Mahmood and Lesnic, 2019). Contrary to IHCP, transient heat conduction problems used for the determination of temperature distribution are well-posed and treated numerically by a number of integration methods such as finite difference method (FDM), the finite element method (FEM), the boundary element method (BEM) and most recently, collocation pseudospectral methods (CPM) (Bazán et al , 2017; Ismailov et al , 2018; Cao et al , 2019; Mahmood and Lesnic, 2019; Mohebbi and Sellier, 2016; Pasdunkorale and Turner, 2003; Boos et al , 2020; Telejko and Malinowski, 2004).…”

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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“…However, in the time-dependent case the scenario has received limited attention from researchers. Here, we only highlight the nonlinear identification of a temperature-dependent orthotropic material, [18], the recovery of the leading coefficients of a heterogeneous orthotropic medium, [8,9,14], and the space-dependent anisotropic case addressed in [12].…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of an orthotropic thermal conductivity from non-local heat flux measurements

Huntul

Hussein

Lesnic

et al. 2020

IJMMNO

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Raw materials are anisotropic and heterogeneous in nature, and recovering their conductivity is of utmost importance to the oil, aerospace and medical industries concerned with the identification of soils, reinforced fiber composites and organs. Due to the ill-posedness of the anisotropic inverse conductivity problem certain simplifications are required to make the model tracktable. Herein, we consider such a model reduction in which the conductivity tensor is orthotropic with the main diagonal components independent of one space variable. Then, the conductivity components can be taken outside the divergence operator and the inverse problem requires reconstructing one or two components of the orthotropic conductivity tensor of a two-dimensional rectangular conductor using initial and Dirichlet boundary conditions, as well as non-local heat flux over-specifications on two adjacent sides of the boundary. We prove the unique solvability of this inverse coefficient problem. Afterwards, numerical results indicate that accurate and stable solutions are obtained.

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Identification of conductivity in inhomogeneous orthotropic media

Abstract: This is a repository copy of Identification of conductivity in inhomogeneous orthotropic media.

Cited by 6 publications

References 30 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

Reconstruction of an orthotropic thermal conductivity from non-local heat flux measurements

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