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在求解伴随凝固和熔融的热传导问题时,本文试用一种奇异摄动方法,选择显热与潜热之比—Ste数为摄动参数,将温度、移动的固液界面位置以及时间按摄动参数的幂级数展开,求得了初态在熔点,表面因对流冷却而凝固的热传导问题的一阶近似解;给出了凝固总时间与Ste数以及Bi数之间的良好近似公式.所得结果与基用于焓模型求得的数值解和实验结果相符得很好.
In solving the problem of heat conduction with solidification and melting, a singular perturbation method is adopted in this paper. The ratio of sensible heat to latent heat is selected as perturbation parameter. The temperature and moving position and time of solid-liquid interface are determined according to perturbation parameters The first order approximate solution of the heat conduction problem of the initial state at the melting point and the surface solidification due to the convection cooling is obtained. The approximate approximate formula between the total solidification time and the number of Ste and the number of Bi is given. The numerical solution based on the enthalpy model is in good agreement with the experimental results.