Mechanical Engineering, University of Tabriz
In this work, Boltzmann transform has been used to analyze the problem of freezing of pure Aluminum in semi-infinite domain. The uniqueness of solution (solidification front location) has been proved using the characteristics of the functions appeared in solution. The effect of density change on temperature distribution and errors resulting from ignoring this change have been investigated. The solidification problem in finite media was solved using the boundary element method (BEM), with quadratic shape functions. The applicability of the fundamental solution, as weighting function in BEM, in finite domain has been investigated. The accuracy of the method is illustrated through one-dimensional numerical examples. Some careful experiments were carried out, using the facilities of the School of Metallurgy and Materials at the University of Birmingham, UK, to obtain the data. Comparison of theoretical, numerical and experimental results revealed that good agreement exists between them. However, minor differences were observed due to imposing of the simplifying boundary conditions. The effects of density change may be ignored in small volumes, but they must be taken into account in real applications.