Transactions on Engineering Technologies by Sio-Iong Ao & Len Gelman & Haeng Kon Kim

Author:Sio-Iong Ao & Len Gelman & Haeng Kon Kim
Language: eng
Format: epub
ISBN: 9789811307461
Publisher: Springer Singapore

2 Solidification Model

Engineering calculations were performed on the example of the solidification process of an alloy. The model of solidification process is built on the basis of the equation of heat conduction with the source member [5]:

(1)

wherein: T—temperature t—time, —thermal conductivity, c—specific heat, —density, L—latent heat of solidification, —the solid phase fraction.

2.1 Discretization of the Area and of the Time

Equation (1) is converted in the model using enthalpy formulation (basic capacitive formulation). As a result, it gives one equation that describes the liquid phase and the solid area of solidification. The apparent heat capacity formulation keeps the temperature as the unknown in the equation [2].

As a result of this transformation and the implementation of the discretization of the area by the finite element and the discretization of the time with the finite difference (Euler Backward modified scheme [10]), the linear system of equations was achieved. It has a suitable form to be solved by the one of the algorithms equations above:

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