Inverse Determination of Boundary Conditions and Sources in Steady Heat Conduction With Heat Generation

Martin, Thomas J.; Dulikravich, George S.

doi:10.1115/1.2822666

Cited by 62 publications

(34 citation statements)

References 6 publications

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“…When a large number of sampling points are considered, the number of equations are usually greater than the number of unknowns and the system is overdetermined. To solve an overdetermined system of equations one can use the least-squares or singular-value decomposition methods [1]. Equation (9) is very sensitive to even small errors in the sampling quantities.…”

Section: Determination Of Heat Intensity Of Sourcesmentioning

confidence: 99%

“…The application of the BEM to inverse heat conduction problems has also come under investigation in recent years [1][2][3][4][5][6]. In most of the inverse problems the main intention have been focused on ÿnding the unknown conditions only on the boundary in the form of boundary conditions [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…In most of the inverse problems the main intention have been focused on ÿnding the unknown conditions only on the boundary in the form of boundary conditions [2][3][4][5]. In addition, Martin and Dulikravich [1] have included unknown distributed heat sources. In order to do so, they have discretized the domain of the problem and the integration processes have been carried out over the solution domain.…”

Section: Introductionmentioning

confidence: 99%

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A boundary element method of inverse non-linear heat conduction analysis with point and line heat sources

Karami

Hematiyan

2000

Commun. Numer. Meth. Engng.

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SUMMARYAn analysis of inverse non-linear heat conduction with point or line distributed heat sources is presented. The contribution due to the loading vector coming from heat sources integrals are evaluated analytically. The inverse solution may be categorized into ÿnding either the solution of the problem in the form of the intensity of the loading at a speciÿc location, or the location and orientation of the generators assuming the intensity is known. The ÿrst category is an ill-posed problem and the solution to the second category may be found by an iterative search procedure. To regularize the solution to the ÿrst category, least-squares method is employed in conjunction with an addition of a regularization term. To ÿnd the solution to the second category a new and simple algorithm, called 'A Good Neighbour' is devised. For non-linear problems where the thermal conductivities are functions of the temperature, the Kirchho transformation is employed. The eciency and accuracy of the proposed methods employed are explored through several examples.

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Section: Determination Of Heat Intensity Of Sourcesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A boundary element method of inverse non-linear heat conduction analysis with point and line heat sources

Karami

Hematiyan

2000

Commun. Numer. Meth. Engng.

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“…Similarly, determination of unknown steady thermal boundary conditions when temperature, heat flux, or heat transfer coefficient data are unavailable on certain boundaries is a common class of inverse problem [34][35][36][37]. The missing boundary conditions can be found if both temperature and heat flux are available on other, accessible boundaries or at a finite number of points within the domain.…”

Section: Determining Steady Boundary Conditions Using Boundary Elemenmentioning

confidence: 99%

“…Additional equations may be added to this equation set if temperature measurements are known at certain locations within the domain. The known nodal variables are then multiplied by their respective coefficient matrix terms and transferred to the right hand side [33][34][35][36][37]. Similarly, all unknown nodal variables are multiplied by their respective coefficient matrix terms and transferred to the left hand side.…”

Section: Determining Steady Boundary Conditions Using Boundary Elemenmentioning

confidence: 99%

Inverse Problems in Aerodynamics, Heat Transfer, Elasticity and Materials Design

Dulikravich¹,

Dennis²,

Baker³

et al. 2012

International Journal of Aeronautical and Space Sciences

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A number of existing and emerging concepts for formulating solution algorithms applicable to multidisciplinary inverse problems involving aerodynamics, heat conduction, elasticity, and material properties of arbitrary three-dimensional objects are briefly surveyed. Certain unique features of these algorithms and their advantages are sketched for use with boundary element and finite element methods.

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Filter digital form of two future temperature methods for the inverse heat conduction: A spectral comparison

Cabeza

García²,

Rodríguez

2008

Numer Methods Biomed Eng

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Sequential methods that use future times in order to solve an inverse heat conduction problem can be re-formulated as a sequential digital filter algorithm. The aim of this paper is to explore the filter effect of the function specification method and the truncated singular value decomposition method, in a sequential form. For this purpose, the power spectral densities of the corresponding filter coefficients are evaluated and it is shown that they act as band-pass filter. Three numerical tests with different frequency spectra are considered in order to solve a linear one-dimensional transient inverse problem. Furthermore, three models of crescent complexity are used in each method. It is shown that both methods provide similar results and in most cases, the optimum estimations require the same number of future times. As it is expected, similar estimations correspond to a similar band-pass filter. The effect of the number of future times, the influence of the frequency spectrum of the input and the complexity of the model used can be clearly interpreted in the spectral space. The most complex models act as a highly selective band-pass filter, but they require greater number of future times. 555 design problems, for example, the identification of the boundary shape of a domain subject to natural convection from temperature measurements on the other boundary [5]. The IHCP is a clear example of an ill-posed problem [1]. The main difficulty of this type of problem is the instability. From a mathematical point of view, the algebraic formulation of IHCP leads to an ill-conditioned problem, so that a small perturbation in the measured data (due to the unavoidable measurement errors) may cause great oscillations in the estimated function. This difficulty (from a physical point of view) is a consequence of the diffusive nature of heat flow, so that the thermal response at some distance of the boundary is damped and lagged with respect to the active input at the boundary [1]. In order to add stability at the solution of the inverse problem, many and different methods have been reported to solve IHCPs. Among the more versatile methods (applicable to solve multidimensional and non-linear IHCP) the following can be mentioned: Tikhonov regularization [6], iterative regularization [7], mollification [8] and the function specification method (FSM) [1]. The first two methods are considered as 'whole domain' because all the measured temperature data (N ) are used in order to estimate simultaneously all the components of the unknown input. In these methods, the sensitivity matrix can be of great dimensions (N × N ). In contrast, the last two methods are sequential. Therefore, only a small part of the available measurement is used in each step and only one component of the unknown input is estimated at each step. This fact can be an advantage in an online process. A considerable number of contributions have been published considering combinations, modifications and comparisons of the previous methods [9][10][11][12][13][14].Another ...

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Inverse Determination of Boundary Conditions and Sources in Steady Heat Conduction With Heat Generation

Cited by 62 publications

References 6 publications

A boundary element method of inverse non-linear heat conduction analysis with point and line heat sources

A boundary element method of inverse non-linear heat conduction analysis with point and line heat sources

Inverse Problems in Aerodynamics, Heat Transfer, Elasticity and Materials Design

Filter digital form of two future temperature methods for the inverse heat conduction: A spectral comparison

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