A linear inverse model for the temperature-dependent thermal conductivity determination in one-dimensional problems

Yang, Ching-yu

doi:10.1016/s0307-904x(97)00101-7

Cited by 48 publications

(19 citation statements)

References 17 publications

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“…In the case when thermal conductivity depends on temperature, Kirchhoff substitution is useful, (Ciałkowski & Grysa, 2010a). Also in the case of material properties determination some additional information concerning temperature and/or heat flux in the domain has to be known, usually the temperature measurements taken at the interior points, compare (Yang, 1998;Onyango et al, 2008;Hożejowski et al, 2009). …”

Section: Materials Properties Determination Inverse Problemsmentioning

confidence: 99%

Inverse Heat Conduction Problems

Grysa¹

2011

Heat Conduction - Basic Research

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Section: Materials Properties Determination Inverse Problemsmentioning

confidence: 99%

Inverse Heat Conduction Problems

Grysa¹

2011

Heat Conduction - Basic Research

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“…Many researches [15][16][17][18][19][20][21][22][23][24][25][26] in various domains have used the reverse matrix method to solve the inverse problems. The method is used to determine the thermal conditions by Yang [15,16], Lin et al [17], and Hsu et al [18], to estimate the thermophysics properties by Yang [19], Lin et al [20], and Chang et al [21], to solve the dynamics by Yang [22], Shaw [23], and Kau and Yang [24], and to deal with the manufacturing problems by Hong and Lo [25] and Lee et al [26].…”

Section: Introductionmentioning

confidence: 99%

“…The method is used to determine the thermal conditions by Yang [15,16], Lin et al [17], and Hsu et al [18], to estimate the thermophysics properties by Yang [19], Lin et al [20], and Chang et al [21], to solve the dynamics by Yang [22], Shaw [23], and Kau and Yang [24], and to deal with the manufacturing problems by Hong and Lo [25] and Lee et al [26]. However, there are two problems in the reverse matrix approach.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the effect of the measurement with the abrupt noise and the number of approximated terms in conductional boundary estimation problem

Shiau¹,

Yang²

2009

Applied Mathematical Modelling

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a b s t r a c tA direct error vector analysis of inverse heat conduction problem is presented to detect the measured noise. Based on the reverse matrix approach that the inverse problem is solved directly in a linear domain, and the error vector is formulated from the difference between the measured temperature and the estimated temperature. There is no prior knowledge on the exact solution while the error vector is constructed. The error vector is used to investigate the consistence of the measured data in the domain and lead to detect the noise data. Furthermore, the proper number of the undetermined variable is able to suggest based on the mean value of the error vector and the value of the condition number of the reverse matrix. In the first example, a test problem with the measurement noise is presented. The estimated result is influent by the noise globally. The result shows that the value of error vector is changed significantly at the coordinate of the measurement noise appeared. In other words, the error vector analysis is able to identify the noise data. In the second example, the proper number of series expansion terms is investigated. From the result, it shows that the number of expansion terms with the small mean value and condition number can better approximate to the unknown condition. It means that the proposed method is able to suggest a proper number of expansion terms when the function of the recovered boundary is unknown.

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“…It is more difficult than that of the determination of the thermophysical properties of the temporal-dependent type and the spatial-dependent type. In order to calculate this inverse problem, there have appeared certain progress of the methodologies in this issue, including the Laplace transformation method [1], the conjugate gradient method [2][3][4], the least-square method [5], the linear inverse method [6][7][8], the Davidon-Fletcher-Powell method [9], the Kirchhoff and other transformation methods [10][11][12], and the boundary element method [13], as well as the finite difference method [14,15].…”

Section: Introductionmentioning

confidence: 99%

Identification of temperature‐dependent thermophysical properties in a partial differential equation subject to extra final measurement data

Liu

2007

Numerical Methods Partial

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We consider an inverse problem for estimating the two coefficient functions c and k in a parabolic type partial differential equation c(u)u t = ∂[k(u)u x ]/∂x with the aid of the measurements of u at two different times. The first-and second-order one-step group preserving schemes are developed. Solving the resultant algebraic equations with a closed-form, we can estimate the unknown temperature-dependent thermal conductivity and heat capacity. The new methods possess threefold advantages: they do not require any a priori information on the functional forms of thermal conductivity and heat capacity; no initial guesses are required; and no iterations are required. Numerical examples are examined to show that the new approaches have high accuracy and efficiency, even there are rare measured data. When the measured temperatures are polluted by uniform or normal random noise, the estimated results are also good.

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A linear inverse model for the temperature-dependent thermal conductivity determination in one-dimensional problems

Cited by 48 publications

References 17 publications

Inverse Heat Conduction Problems

Inverse Heat Conduction Problems

Investigation of the effect of the measurement with the abrupt noise and the number of approximated terms in conductional boundary estimation problem

Identification of temperature‐dependent thermophysical properties in a partial differential equation subject to extra final measurement data

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