What is the most suitable fixed grid solidification method for handling time-varying inverse Stefan problems in high temperature industrial furnaces?

Marois, M.-A.; Désilets, Martin; Lacroix, Marcel

doi:10.1016/j.ijheatmasstransfer.2012.05.011

Cited by 14 publications

(3 citation statements)

References 18 publications

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“…In paper [17], by means of solving the heat equation for 2D model in a steady-state with the use of the inverse problem, thermal conductivity of material as the polynomial depending on temperature was sought for. Paper [14] discusses heat flow in high-temperature industrial furnaces. Solving direct and inverse problems with the use of the conjugate gradient method for the changes of phase of metal solidification were analysed.…”

Section: Plusmentioning

confidence: 99%

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Non-linear unsteady inverse boundary problem for heat conduction equation

Joachimiak¹,

Ciałkowski²

2017

Archives of Thermodynamics

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Direct and inverse problems for unsteady heat conduction equation for a cylinder were solved in this paper. Changes of heat conduction coefficient and specific heat depending on the temperature were taken into consideration. To solve the non-linear problem, the Kirchhoff's substitution was applied. Solution was written as a linear combination of Chebyshev polynomials. Sensitivity of the solution to the inverse problem with respect to the error in temperature measurement and thermocouple installation error was analysed. Temperature distribution on the boundary of the cylinder, being the numerical example presented in the paper, is similar to that obtained during heating in the nitrification process.Keywords: Inverse problem; Sensitivity of the solution to the inverse problem; Application of Chebyshev polynomials

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Section: Plusmentioning

confidence: 99%

“…Coefficients a i and b i were determined with the use of the least squares approximation method [14]. They are presented in Tab.…”

Section: Inverse Problemmentioning

confidence: 99%

Non-linear unsteady inverse boundary problem for heat conduction equation

Joachimiak¹,

Ciałkowski²

2017

Archives of Thermodynamics

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“…Therefore for solving problems of that type the numerical methods of different kinds are the most often used [3][4][5][6][7][8][9][10][11][12][13][14][15]. Application of analytical or analytic-numerical methods is rather insignificant.…”

Section: Introductionmentioning

confidence: 99%

An analytical method for solving the two-phase inverse Stefan problem

Hetmaniok¹,

Słota²,

Wituła³

et al. 2015

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. In the paper we present an application of the homotopy analysis method for solving the two-phase inverse Stefan problem. In the proposed approach a series is created, having elements which satisfy some differential equation following from the investigated problem. We reveal, in the paper, that if this series is convergent then its sum determines the solution of the original equation. A sufficient condition for this convergence is formulated. Moreover, the estimation of the error of the approximate solution, obtained by taking the partial sum of the considered series, is given. Additionally, we present an example illustrating an application of the described method.

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An inverse heat transfer method for predicting the thermal characteristics of a molten material reactor

Hafid

Lacroix

2016

Applied Thermal Engineering

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What is the most suitable fixed grid solidification method for handling time-varying inverse Stefan problems in high temperature industrial furnaces?

Cited by 14 publications

References 18 publications

Non-linear unsteady inverse boundary problem for heat conduction equation

Non-linear unsteady inverse boundary problem for heat conduction equation

An analytical method for solving the two-phase inverse Stefan problem

An inverse heat transfer method for predicting the thermal characteristics of a molten material reactor

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