具有振荡边界热源的两类融化问题的数值研究

摘要

Finite difference method with fixed time-step is established to calculate spherical and cylindrical melting problems with periodically oscillating heat sources . The evolution of the moving interface and the temperature field within the liquid media in the melting process are numerically simulated. Also the effects of the Stefan number, the amplitude and frequency of the periodically oscillating heat sources on the evolution of the moving interface and the temperature distribution are analyzed. Numerical experiment results show that the Stefan number strongly influences the temperature distribution and the evolution of the moving interface, while the effect of the periodically oscillating heat sources on the evolution of the moving interface diminishes the phase change domain grows. Numerical simula⁃tion of the problem provides an important theoretical reference for phase change heat transfer problems in engineer⁃ing practice.%构造定时间步长的有限差分方法求解具有周期振荡热源的球型和柱型两类融化问题，对融化过程中移动界面的运动和液态介质内温度场的变化进行数值模拟，并分析Stefan数、热源周期振荡的振幅和频率对移动界面运动和温度场分布的影响。数值实验结果表明，Stefan数对于移动界面的运动和温度场的变化会产生非常大的影响，而边界热源周期性的振荡对移动界面的运动会随着相变区域的增大而不断减弱。该问题的数值模拟为工程实践中的相变传热问题提供重要的理论参考。