Abstract
In the present study, the porosity formed during the solidification process is estimated by an inverse problem technique based on particle swarm optimization. The effective heat capacity method is adopted to model the heat transfer problem. The transient-diffusive heat transfer equation is solved numerically by the finite volume method with an explicit scheme, employing the central difference interpolation function. The solution of the direct problem is compared to reference solutions. The model is applied to trinitrotoluene (TNT) solidification process. The results show that the proposed procedure was able to estimate the porosity for different Stefan numbers. The analysis of the heat flux in the mold is indicated to predict the porosity formation during the casting process.
Highlights
The solidification phenomenon is present in nature and in industrial processes
The proposed numerical results match the ones by Porosity estimation during TNT solidification
The Finite Volume Method was employed to solve this model by using the explicit scheme and the central differences interpolation function
Summary
The Stefan problem is the classical mathematical model for the solidification process. It is based on the heat equation in a solid region where the phase change interface is regarded as a moving boundary (Stefan, 1891). The method of effective heat capacity has been proposed to avoid the difficulties of the Stefan approach in complex geometries. In this method, the solid and liquid regions are solved in a single domain and an effective heat capacity takes into account the phase change phenomenon, considering the existence of a mushy region, where liquid and solid are present
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