鋳片の限界冷却速度の半無限1次元モデルによる数学的解析

抄録

Cooling rate is an important index to estimate solidification structure or property of cast products.
In order to evaluate the upper limit of the cooling rate in near net shape casting processes of various kinds, heat conduction in the semi-infinite region with and without solidification was calculated analytically. On the basis of Neumann's solution for the semi-infinite region (y>0) initially at constant temperature U with the surface (y=0) maintained at zero for the subsequent time (t>0), cooling rate was calculated for the cases in which location, time or temperature was fixed respectively.
The results are as follows.
(1) In case of cooling without solidification, the maximum cooling rate at any fixed location takes place at the constant temperature 0.92U independent of the thermal characteristics. While in case time is fixed, the maximum cooling rate occurs at another constant temperature of 0.68U.
(2) In case of cooling with solidification, cooling rate is determined by location, time and the dimensionless parameter Ya, which is the ratio between sensible and latent heat, And for any kind of metal the maximum cooling rate at any fixed location or time appears just behind the solidification front. Approximate equations for the maximum cooling rate are proposed.