Conference on Applied Inverse Problems, July 20-24, 2009, Vienna, Austria
Poster Presentation
Mohammad Rahim Hematiyan: An artificial heat source method for inverse analysis of solidification problems

Mon, 20 July, 2009, 17:15-18:15, Foyer

In this work, a method for evaluation of unknown heat flux on a part of boundary of two dimensional castings to produce a desired motion of solidification front is presented. With control of solidification front in casting, suitable mechanical properties can be obtained.
The unknown heat flux is calculated using an inverse method. In each time step, latent heat effect is applied by introducing an artificial heat source over transition region. By this technique the inverse solidification problem is converted into several inverse heat conduction problems, which can be solved more efficiently. Sensitivity analysis is carried out using finite element method. In the inverse analysis, a main regularization and a secondary regularization are accomplished to obtain more smooth solutions. The main regularization in each time step is carried out by considering some imaginary future time steps. Secondary regularization is applied after main calculations, for better reduction of oscillations in time domain. To show the accuracy and efficiency of the present method, three examples are presented. In these examples solidification of materials with constant and temperature dependent properties are analyzed. In the first example a unidirectional solidification inverse problem is solved. In the second example, the unknown heat flux on the boundary to produce a desired motion of solidification front in a square section is found. In this example, effects of time step size on the results of the inverse analysis are also studied. In the third example, material properties are considered to be temperature dependent. In this example, a more complicated motion for solidification front has been considered. The results obtained from the three examples are satisfactory.

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