Etude des problèmes de conduction thermique avec changement de phase solide/liquide

Abstract

Solid-liquid phase change phenomena are generally present in natural processes and in a large number of industrial applications. The purpose of this study is to solve a problem of solidification of a pure material. The first chapter is devoted to a bibliographical synthesis. In the second chapter, we applied an inverse method of thermal conduction associated with a solid/liquid phase change process in a one-dimensional spherical geometry. The results obtained are compared to an exact solution constructed. The solution is sensitive to noise introduced into the data. To restore the well-posed character. On the one hand, filtered the data and on the other hand, introduced a technique of regularization of the solution. The results obtained show the algorithm developed is effective. In the second chapter, we modeled a problem of solidification of a pure material in geometry (1-d) by the enthalpic method. A study of two-dimensional natural convection is conducted in the last chapter in order to apply it to an optimization problem. The comparison of the numerical results obtained is in good agreement with those found in the literature