Wyniki 1-1 spośród 1 dla zapytania: authorDesc:"Jarosław MATLAK"

Reconstruction of the heat transfer coefficient in the inverse Stefan problem DOI:10.15199/24.2018.1.2


  Introduction. In this paper we intend to reconstruct the heat transfer coefficient on the boundary of the mould, within which the pure metal solidifies. Mathematically, the solidification of pure metals is modeled with the aid of the Stefan problem [1, 2]. This problem consists in determining the distribution of temperature in the liquid phase and in the solid phase and in determining the location of the moving boundary separating these phases. In the applied model we take into account also the shrinkage of material and the air-gap created between the material and the mould. With regard to the different densities of the liquid and solid phases the shrinkage of metal occurs during the solidification. Then, the air gap appears between the cast and the mould influencing the creation of the interfacial thermal resistance between the mould and the cast. This thermal resistance determines the mould heat flux, and in this way it influences the billet quality causing the cracks and oscillation marks. The direct one-dimensional problem of pure metal solidification including the shrinkage of metal is considered in paper [3]. For solving this problem the perturbation method for the small Stefan numbers is used. Next, in papers [4, 5] the Stefan problem is applied for determining the thermal resistance of the gap between the ingot and the crystallizer in the continuous casting process. For the given constant width of the gap the problem is reduced to determination of the thermal conductivity coefficient of the gap. This coefficient is calculated basing on the known measurements of temperature in the crystallizer wall. For finding the solution the following methods are used: the front tracking method combined with the method of automatic mesh generation for the finite element method and the method of adjustment computations. The thermal resistance of the gap between the crystallizer (or mould) and the ingot is also determined in papers [...]

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