Abstract
Analytical solutions of problems in an unsteady-state linear heat conduction which involves two phases separated by a moving-plane interface have been obtained approximately under the assumption that the physical properties of the mould and the solidified phase are identical and independent of temperature. The temperature distribution in the mould and the solidified phase is given by Eq. (12), and the freezing-front motion by Eq. (17) or (20).
If N is infinite, Eqs. (22), (18) and (21) will be derived from these three equations, respectively and can be compared with the exact solutions given by Neumann et al.(1)∼(4) under the condition of Xl=0.
As regards the temperature distribution, it can be seen in Fig. 1 that the calculated results from the approximate solution Eq. (22) are in good agreement with those from the exact solution Eq. (23) given by Neumann(1).
In case of N→∞ and Xl=0, the solidification constant ν in this work can be derived from Eq. (26), while in Neumann’s solution ν is defined by Eq. (25) and can be calculated from Eq. (24).
In Fig. 2, the values of υ are compared with each other and their accordance is satisfactory.
Under the condition where N is not infinite, ν can be defined by Eq. (28) and the values of ν calculated from Eqs. (17) and (20) are illustrated in Figs. 7 and 8. The values of ν are invariable in regard to Xl.
The solidification constant q which is defined conventionally by Eq. (27) varies with Xl and the calculated values of q are in good agreement with the observed values.
On the other hand, the calculated values of c′ in Eq. (27) are not consistent with the observed values. It is presumed that this arises from the difference between the initial distribution of temperature in the experimental mould and that described theoretically by Eq. (30).
