Multi-phase Inverse Stefan Problems Solved by Approximation Method

Grzymkowski, R.; Słota, Damian

doi:10.1007/3-540-48086-2_75

Cited by 13 publications

(12 citation statements)

References 7 publications

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“…On the basis of the presented method a computer program was developed in the Mathematica 6.0 environment [19]. The program computes: eigenvalues of the step responses, coefficients of the field functions, spatial-temporal distributions of the temperature (20), (21a,b) and visualises the results.…”

Section: Computational Examplesmentioning

confidence: 99%

Application of Duhamel's theorem in the thermal field analysis of a DC cable with two layers of insulation

Gołębiowski¹,

Zaręba²

2009

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. In the paper we presented an asymptotic method of determination of the transient thermal field in a three-zone cable (i.e. in a core and in two layers of insulation). A basis of our method was decomposition of the system. We considered separately the region of the core, which we modelled by a concentrated element of the first order. In turn, we treated the two-zone region of insulation as the system of distributed parameters. In the analysis we applied Duhamel's theorem and the method of separation of variables. Eigenvalues of the boundary-initial problem and coefficients of eigenfunctions we determined numerically. In the result we obtained spatial-temporal heat-up curves of the investigated cable. Our results we presented in a graphic form.

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Section: Computational Examplesmentioning

confidence: 99%

Application of Duhamel's theorem in the thermal field analysis of a DC cable with two layers of insulation

Gołębiowski¹,

Zaręba²

2009

Bulletin of the Polish Academy of Sciences: Technical Sciences

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“…Two-dimensional two-phase inverse Stefan problem was also considered by Grzymkowski and Słota in papers [32][33][34][35] and by Słota in papers [36][37][38]. In works [32,34] the solution was sought in the form of linear combination of functions satisfying the heat conduction equation and for calculating the coefficients of this combination the least square method was used on the way of minimizing the maximal defect in the initial-boundary data.…”

Section: Introductionmentioning

confidence: 99%

“…In works [32,34] the solution was sought in the form of linear combination of functions satisfying the heat conduction equation and for calculating the coefficients of this combination the least square method was used on the way of minimizing the maximal defect in the initial-boundary data. The next method, investigated by Grzymkowski and Słota in papers [33,35], consisted in minimizing the functional, value of which represented the norm of difference between given positions of the moving interface and its positions reconstructed from the selected function describing the convective heat transfer coefficient.…”

Section: Introductionmentioning

confidence: 99%

Using the swarm intelligence algorithms in solution of the two-dimensional inverse Stefan problem

Hetmaniok

Słota

Zielonka

2015

Computers & Mathematics with Applications

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a b s t r a c tIn the paper a procedure for solving the two-dimensional inverse Stefan problem is presented. In considered problem the heat transfer coefficient is identified with the aid of known measurements of temperature in selected points of the region as the additional information. Direct Stefan problem is solved by using the alternating phase truncation method. Goal of the paper is to compare two swarm intelligence algorithms -the Ant Colony Optimization algorithm and the Artificial Bee Colony algorithm -applied for minimizing a functional expressing the error of approximate solution.

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“…In paper [6], for solutions of one-phase two-dimensional problems, authors used a complete family of solutions to the heat equation to minimize the maximal defect in the initial-boundary data. Similar method was used in [7,8] for two-and multi-phase problems. The solution in this method is found in a linear combination form of the functions satisfying the equation of heat conduction.…”

Section: Introductionmentioning

confidence: 99%