No abstract

The model described in this paper treats the numerical solution of a heat transfer problem in a one-dimensional way determining the axial temperature characteristics. The physical quantities are considered as values depending on temperature and the real wall temperature profile of the heating-cooling system is included. The sample shape corresponds t o the numerous cases of long and thin cylinders. The calculation were carried out by a medium desk computer. Cfeneral remarksThe temperature field and its alteration per unit time are of importance for solidification and crystal growth from the melt. Some characteristic parameters of this field, e.g. the velocity (w,) of the phase boundary solid-liquid or the temperature gradient (G) at the phase boundary solid-liquid have a significant effect e.g. on the effective segregation coefficient (k) (BURTON et al.) on the stability at the phase boundary solid-liquid (SEKERKA) or on morphologic parameters such as the thickness of lamellae or the rod spacing during the eutectic solidification or eutectoid transformation analogously considered (JACKSON, HUNT ; HELLAWELL). A great number of these crystallization processes is carried out by unidirectional solidification or Bridgman-Stockbarger-Technique. By that the velocity of the phase boundary solidliquid (further on called interface velocity) can differ with the mechanical relative velocity between sample and heating-cooling system. I n such a case a special measurement is necessary. Temperature gradient (a) can only be found out by another special measurement involving considerable effort in most the cases. Eventual disturbances of the temperature field caused by measuring system recommend checking by an appropriate calculation. By CHANG, WILCOX, by SEN, WILCOX, and RIQUET, DURAXD, interface shapes, effects of crucibles and interface velocities are treated while neglecting temperature dependencies of physical quantities and assuming an ideal temperature step between the heating and cooling region. By EL-MAHALLAWY and FARAG the problem of heat transfer is numerically solved. But a high computing effort is needed.The model described in this paper is based on a simple calculation of the axial temperature characteristics of a unidirectionally solidified sample as outlined in the abstract above.