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1

Trefftz function for solving a quasi-static inverse problem of thermal stresses

Grysa K., Maciąg A., Maciejewska B.

Computer Assisted Mechanics and Engineering Sciences

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2009

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Vol. 16, No. 3/4

251-266

EN

The problem of thermal stresses in a hollow cylinder is considered. The problem is two-dimensional and the cross-section of the hollow cylinder is approximated as a long and thin rectangle as the ratio of the inner and outer radiuses is close to one. On the outer boundary of the hollow cylinder the heat source moves with a constant velocity. In the case of the rectangle the heat source moves on the upper side and the conditions of eąuality of temperatures and heat fluxes are assumed on the left and right boundaries. The stresses are to be found basing on the temperature measured inside the considered region, which means that an inverse problem is considered. Both for the temperature field and the displacements and stresses the finite element method is used. Thermal displacement potentials are introduced to find displacements and stresses. In order to construct the base functions in each element the Trefftz functions are used. For the temperature field the time-space finite elements are used and for the thermal displacement potentials the spatial elements are applied. Thanks to the use of the Trefftz functions a low-order approximation has given a solution very close to the exact one.

2

Zagadnienie Stefana dla żebra pracującego przy wrzeniu

Orzechowski T.

Inżynieria i Aparatura Chemiczna

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2006

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Nr 6s

179-180

EN

The Stefan problem dealing with the determination of a boundary shape has been presented. A numerical analysis with the use of heat polynomials has been conducted. On the example of a triangular fin a methodology and its effectiveness for boiling heat transfer were shown.

3

Application of the modified method of finite elements to identification of temperature of a body heated with a moving heat source

Maciejewska B.

Journal of Theoretical and Applied Mechanics

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2004

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Vol. 42 nr 4

771-787

EN

A transient 2-dimensional problem of heat flow with a moving heat source is considerent. It is assumed that the heat source is moving along one of the sides of a rectangle with a constant velocity. The unknown is the temperature distribution in a flat rectangular area. The paper presents an approximate solution which is based on the finite element method with a modified basis function. The space-time basis functions are combinations of heat polynomials which strictly satisfy the heat equation. Cartesian coordinates were used to solve the problem.

PL

W pracy rozważane jest dwuwymiarowe niestacjonarne zagadnienie przepływu ciepła z ruchomym źródłem ciepła na brzegu obszaru. Zaklada się, że źródło ciepła porusza się wzdłuż brzegu prostokąta ze stałą prędkością. Poszukiwany jest rozkład temperatury w obszarze o kształcie prostokąta. Przybliżone rozwiązanie problemu zaprezentowane w pracy opiera się na metodzie elementów skończonych ze zmodyfikowanymi funkcjami bazowymi. Skonstruowane czasoprzestrzenne funkcje bazowe są kombinacją wielomianów cieplnych, tzn. wielomianów ściśle spełniających równanie przewodnictwa ciepła. Zagadnienie rozwiązane zostało we współrzędnych kartezjańskich.

4

On determining the temperature dependent heat transfer coefficient

Orzechowski T.

Archives of Thermodynamics

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2003

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Vol. 24, no 2

69-88

EN

The paper deals with analysis of a thermal field measured by means of a thermovision camera. A two-dimensional ill-posed problem of heat transfer was solved using a fin as an example. The quantity that needs to be found is the heat flux leaving the invisible inner surface of the fin. The method of heat functions was used for the calculations. The results of the numerical analysis of the problem are some local values of the transfer coefficients. The convergence of the calculation procedures was chacked by applying the heat balance to the considered area. Then, the optimal degree of the heat polynomials for such a problem was determined and the range of the method convergence was analysed. During the experiments, the heat transfer from the surface of a fin submerged in boiling water was observed. Values of heat transfer coefficients were determined and compared with the calculation results. A reasonable degree of congruence was found to exist between the calculation and experimental results.