热参数扰动下一维相变传热定解问题的稳定性研究

Study on the Stability of One-dimension Heat Conduction Definite Solution Problem with Phase Transformation under the Thermal Parameter Perturbation

研究热参数扰动对一维相变传热方程解的稳定性的影响,应用存在解析解的一维相变传热定解问题,运用数值试验研究了热参数存在误差时,中间值γ、相变面位置及各相温度的变化规律.寒区工程热稳定性的维护取决于对其温度场的准确计算和预测,温度场计算是一个相变导热问题,计算所用的热参数由试验测定,所产生的试验误差难以避免,热参数的误差或扰动是否会引起相变导热问题中相变界面及温度场产生误差是一个微分方程稳定性问题,然而,相变导热问题由于其强非线性,目前尚无解析方法对其稳定性进行判断与分析.分析计算表明,中间值γ的扰动受已冻区比热容c1影响最大;相变面位置的扰动受已冻区导热系数k1影响最大;各相温度场分布主要受该相热参数的影响,而对其它相的热参数不敏感.研究结果可以为寒区工程温度场计算时热参数的测试方法、测试精度等提供科学依据.

The influence of thermal parameter perturbation on the stability of one-dimensional heat transfer equation with phase change is examined, and the analytical solutions of one-dimensional heat transfer solution problem with phase change are applied. Numerical experiments are carried out to study the disciplines of γ and phase change surface position when thermal parameters exist errors. The maintenance of thermal stability of constructions depends on the accurate calculation and prediction of its temperature field in cold regions. The calculation of temperature field is a heat conduction problem with phase change. The thermal parameters used in the calculation are determined by the experiment, and the experiment error is difficult to avoid. Whether the parameter error or disturbance will cause phase change surface error and temperature field error is a problem about dif- ferential equation stability. However, the heat conduction problem with phase change has no analyti- cal method to judge and analyse its stability due to its strong nonlinearity. The calculation results show that the disturbance ofγ is most affected by Cl ,the heat capacity of the frozen zone. The disturbance of the phase change surface is most affected by k1,the thermal conductivity of the frozen zone. The temperature distribution is greatly affected by the thermal parameters of its own zone and not sensitive to the thermal parameters of the other phases. The research results can provide a scientific basis for the experiment method and experiment accuracy of thermal parameters in the calculation of temperature field of constructions in cold regions.