Temperature distribution in a moving material subjected to surface energy transfer

A numerical study of the thermal characteristics in a continuously moving system, such as the crystal growing process, has been carried out. In several manufacturing processes, the material is continuously fed and the temperature distribution in the material is to be determined as a function of the physical variables in the problem. The study considers the one-dimensional, two-dimensional and axisymmetric cases of a heated material which moves at a given velocity. The transient as well as the steady-state problems are considered and the temperature distribution is obtained as a function of the Peclet number, which determines the relative importance of the motion, of the Biot number and of various other governing parameters in the problem. The transient problem is a moving boundary circumstance and a numerical scheme is developed to study the time-dependent length of the material and the temperature distribution. The steady-state temperature distribution is also obtained. Results are obtained over a wide range of governing parameters and are discussed in terms of the basic mechanisms. Several very interesting features are observed and the importance of the work in practical systems is outlined.