在纵向自由薄膜凝固期内温度分布的数值分析

NUMERICAL ANALYSIS OF TEMPERATURE DISTRIBUTION IN VERTICAL FREE THIN FILMS DURING SOLIDIFICATION

考虑到薄膜表面的热通量主要是来自辐射，因而采用一个依赖时间的拟二维拟线性扩散方程的Ｓｔｅｆａｎ问题（混合初边值问题）作为该问题的数学模型．用一种具有Ｃｒａｎｋ－Ｎｉｃｈｏｌｓｏｎ格式的无条件稳定的有限差分法来求解抛物型偏微分方程的定解问题．用追赶法求解离散化的三对角方程组，然后用预估校正法求解拟线性扩散方程，从而避免了求解非线性差分方程组．琥珀亚硝酸酯在纵向自由薄膜凝固期内的温度分布数值计算结果和凝固前沿动力学特性与实验结果彼此吻合．

Since the film thickness is very small compared with its two large free surfaces, the heat flux from the film surfaces is considered as mainly via radiation. Hence the Stefan problem (the mixed initial and boundary problem) of a time dependent quasi two dimensional quasilinear diffusion equation is adopted as the mathematical model of that problem. An unconditionally stable finite difference method with the Crank Nicholson scheme has been used to solve the parabolic partial differential equation. The chase method for solving the discretized tridiagonal system of equations is used. Then the predictor corrector approach for solving the quasilinear diffusion equation is adopted in order to avoid solveing the system of nonlinear difference equations. The numerically computed temperature distribution and a solidification front dynamics in the succinonitrile vertical free thin film during solidification agree rather well with the experiments.