Solution of a stationary inverse heat conduction problem by means of Trefftz non-continuous method

Ciałkowski, Michał; Frąckowiak, Andrzej; Grysa, Krzysztof

doi:10.1016/j.ijheatmasstransfer.2006.11.030

Cited by 32 publications

(18 citation statements)

References 5 publications

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“…In (Ciałkowski et al, 2007) the FEM with Trefftz base functions (FEMT) has been compared with the classic FEM approach. The FEM solution of the inverse problem for the square considered was analysed.…”

Section: Kalman Filter Methodsmentioning

confidence: 99%

Inverse Heat Conduction Problems

Grysa¹

2011

Heat Conduction - Basic Research

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Section: Kalman Filter Methodsmentioning

confidence: 99%

Inverse Heat Conduction Problems

Grysa¹

2011

Heat Conduction - Basic Research

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“…This functions strictly satisfy the governing differential equation. Additional information on the Trefftz method can be found in [6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Determination of the heat transfer coefficient from IRT measurement data using the Trefftz method

Maciejewska

Strąk

Piasecka

2016

EPJ Web of Conferences

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Abstract. The paper presents the method of heat transfer coefficient determination for boiling research during FC-72 flow in the minichannels, each 1.7 mm deep, 24 mm wide and 360 mm long. The heating element was the thin foil, enhanced on the side which comes into contact with fluid in the minichannels. Local values of the heat transfer coefficient were calculated from the Robin boundary condition. The foil temperature distribution and the derivative of the foil temperature were obtained by solving the two-dimensional inverse heat conduction problem, due to measurements obtained by IRT. Calculations was carried out by the method based on the approximation of the solution of the problem using a linear combination of Trefftz functions. The basic property of this functions is they satisfy the governing equation. Unknown coefficients of linear combination of Trefftz functions are calculated from the minimization of the functional that expresses the mean square error of the approximate solution on the boundary. The results presented as IR thermographs, two-phase flow structure images and the heat transfer coefficient as a function of the distance from the channel inlet, were analyzed.

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“…The first paper devoted to the Trefftz functions in which the time is considered as a continuous variable, discussed a one-dimensional (one spatial variable) heat conduction equation (Rosenbloom and Widder 1956). This aspect of the Trefftz functions method was developed for the heat conduction problems in the papers (Ciałkowski et al 1999(Ciałkowski et al , 2007Yano et al 1983) for the wave equation and thermoelasticity problems in the papers (Grysa and Maciag 2011;Maciag 2004Maciag , 2005Maciag , 2007Maciag and Wauer 2005a, b) and for the equation of a plate vibration in the paper . So far, also monographs concerning the Trefftz method have been published (Ciałkowski and Frackowiak 2000;Grysa 2010; Kołodziej and Zieliński 2009;Li et al 2008;Maciag 2009;Qing-Hua 2000).…”

Section: Introductionmentioning

confidence: 99%

Solution of the direct and inverse problems for beam

Maciąg

Pawińska

2014

Comp. Appl. Math.

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The article presents an approximate method of solving direct and inverse problems described by Bernoulli-Euler inhomogeneous equation of vibrations of a beam. A semianalytical solution is approximated by a linear combination of the Trefftz functions (T-functions, solving functions), which satisfies identically the homogenous equation describing the vibrations of a beam. In the paper, the properties of the solving functions have been investigated, theorems concerning their linear independence have been formulated and proved. A method of obtaining the particular solution of the inhomogeneous equation has been shown. To get this solution, recurrent formulas enabling us to determine the inverse operator for monomials have been derived. The paper discusses two kinds of inverse problems. The first one is a boundary inverse problem, in which the boundary conditions are to be determined, based on known displacements within the area. In the second one, the load on the beam needs to be found (identification of the source). The solving functions can be used as a finite element method base functions. This approach is tested for solving inverse problems. The paper includes examples which illustrate the usefulness of the method.

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Solution of a stationary inverse heat conduction problem by means of Trefftz non-continuous method

Cited by 32 publications

References 5 publications

Inverse Heat Conduction Problems

Inverse Heat Conduction Problems

Determination of the heat transfer coefficient from IRT measurement data using the Trefftz method

Solution of the direct and inverse problems for beam

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