Heat Conduction with Phase Change

Problems of heat transfer accompanied by a phase change (Stefan problems) are encountered in many areas of applied science such as the process of casting, recrystallization of metals, welding, evaporation of droplets, oxygen diffusion problems, and the formation of ice. The complexity of these problems is due to the nonlinear boundary conditions at the solid/melt moving interface. Solution of the Stefan problems requires simultaneous determination of the shape and the motion of this moving front along with the temperature fields in the solidified shell and the mold. Exact solutions for the Stefan problems are known only in a few special cases. Neumann’s solution to the one-dimensional problem of solidification in a semi-infinite region is one of the most well-known exact solutions. Approximate analytical solutions can be obtained by a variety of techniques, such as the use of the heat balance and coupled integral equation methods. Many complicated problems can also be investigated with numerical methods, notably the finite difference and finite element techniques in combination with perturbation methods. 

Growth of the shell with sinusoidal variation in the mold temperature


The aim of this research is to enhance our knowledge about the effects of thermal properties on the growth instability observed in many casting processes using perturbation methods. A particular interest is to investigate the interaction of process parameters against each other, and extend earlier investigations to determine physical parameters which are most favored for growth instability. 




Faruk Yigit, Professor