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Inverse problems in the thermal theory of foundry processes

Mochnacki B., Majchrzak E., Szopa R., Suchy J. S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2006

Vol. 5, nr 1

154-169

In the paper the applications of inverse problems in the thermal theory of foundry processes are discussed. Both the macro models of solidification (in particular the fixed domain approach) and macro/micro ones are considered. The information necessary in order to determine the unknown parameters of the process results from the knowledge of cooling (heating) curves at the selected set of points from casting and/or mould subdomains. The identified values can correspond to the thermophysical parameters of casting and mould, parameters appearing in boundary conditions and initial temperatures. In the paper the newest results obtained in this scope by the authors are presented. The examples of numerical solutions are also shown.

Application of generalized finite difference method in numerical modelling of moving boundary problems

Mochnacki B., Lara S.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2003

Vol. 2, nr 1

129--143

The application of generalized finite difference method for numerical modelling of thermal processes proceeding in the solidifying casting domain is presented. The solidification of pure metals and eutectic alloys is considered. In such case the solidification process takes place at the constant temperature (the Stefan problem). From the numerical point of view the solution of this task is very complex; in particular, in the case of 2D or 3D domains; and in literature one can find the procedures enabling to avoid the difficulties with the direct modelling of the problem discussed. The part of them consist in the substitution of the solidification point T* by the certain interval [T* - ΔT, T* + ΔT]. In this way the subdomain of artificial mushy zone is introduced and the fixed domain approach [1] can be used. On the stage of numerical algorithm construction and numerical simulation the generalized finite difference method is used. In the final part of the paper the examples of computations are shown.