Three-dimensional boundary inverse heat conduction problem for regular coordinate systems

Alifanov, O. M.; Ненарокомов, А. В.

doi:10.1080/174159799088027701

Cited by 30 publications

(25 citation statements)

References 4 publications

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“…Small changes in the input data can produce large deviations in the solution [1,2,17]. The iterative regularization method [1,11] is used to stabilize the solution of the studied inverse problem. The idea of the method is based on the use the discrepancy principle as a stopping criterion for the iterative process:…”

Section: Algorithmmentioning

confidence: 99%

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Numerical solution of 3D unsteady nonlinear inverse problem of estimating surface heat flux for cylindrical geometry

Loulou

Artioukhine²

2006

Inverse Problems in Science and Engineering

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A numerical algorithm is proposed for solving a three-dimensional unsteady nonlinear inverse heat conduction problem of estimating the boundary conditions at the heated surface of a solid. In this study, the geometrical form of the solid is a finite hollow half-cylinder. As additional information, needed to solve the inverse problem under study, we use both temperature measurements at the internal surface (case of the use of thermo-couples or an infrared camera) inside the half-cylinder (case of the use of thermo-couples) and those at the heated surface (case of the use of an infrared camera). The iterative regularization method is used to build the numerical algorithm. The method is based on the residual functional minimization by using the unconstrained conjugate gradient method with the regularizing discrepancy principle as a stopping criterion of the iterative processes. The unknown function of three variables is sought for as a grid function.

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Section: Algorithmmentioning

confidence: 99%

“…This is one of the main reasons why just a few works are published in this promising direction of inverse problems up to date. The last developed studies were performed by Alifanov and Nenarokomov [11], Huang and Wang [12], Huang and Chen [13], Nortershauser and Millan [14], and Dowding and Beck [9].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of 3D unsteady nonlinear inverse problem of estimating surface heat flux for cylindrical geometry

Loulou

Artioukhine²

2006

Inverse Problems in Science and Engineering

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“…Such formulation of the problem locates it in the class of inverse problems. Threedimensional ill-posed boundary inverse problems are solved by an iterative regularization method in [19]. A general method for solving multidimensional inverse heat conduction is presented in [18].…”

Section: Introductionmentioning

confidence: 99%

Solution of an inverse axisymmetric heat conduction problem in complicated geometry

Duda

2015

International Journal of Heat and Mass Transfer

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“…A multidimensional approach to the IHCP is adopted by Jarny et al [33] and Alifanov and Nenarokomov [34,35]. Regarding the UIHCP, a CGM with an adjoint variable has been also adopted to estimate the heat source distribution by means of the iterative regularization methodology [36].…”

Section: Introductionmentioning

confidence: 99%

Comparative application of CGM and Wiener filtering techniques for the estimation of heat flux distribution

Bozzoli

Rainieri

2011

Inverse Problems in Science and Engineering

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The conjugate gradient method (CGM), formulated with the adjoint problem, is adopted in this study as the functional minimization tool for the solution of the 2-D steady-state linear inverse heat conduction problem with the aim of estimating the heat flux density distribution on a given surface using the temperature distribution as input data. The robustness of the solution strategy, based on an iterative regularization scheme, is compared with another consolidated estimation methodology adopted in the literature to handle the same problem: the Wiener filtering technique. The comparison is performed by adopting a noisy test signal aimed at simulating infrared temperature maps. Using a comparative approach, the problem's particular difficulties related to the high number of unknowns and to the deficiency of the estimation techniques at the domain's geometrical boundaries are discussed. NomenclatureSignal amplitude, A ( C) Spatial domain, D Error, Equation (33), E Heat flux density, g (W m À2 ) Performance function, J ( C 2 ) J/M, J* ( C 2 ) Total number of sensors, M Direction of the descent, q (W m À2 ) Heat rate generation per unit volume, q g (W m À3 ) Thickness, s (m) Temperature, T ( C) Spatial coordinates, x, y, X, Y (m) Search step size, Dirac delta function,

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Three-dimensional boundary inverse heat conduction problem for regular coordinate systems

Cited by 30 publications

References 4 publications

Numerical solution of 3D unsteady nonlinear inverse problem of estimating surface heat flux for cylindrical geometry

Numerical solution of 3D unsteady nonlinear inverse problem of estimating surface heat flux for cylindrical geometry

Solution of an inverse axisymmetric heat conduction problem in complicated geometry

Comparative application of CGM and Wiener filtering techniques for the estimation of heat flux distribution

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